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New Special Instructions
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Wed, 30 Jul 2014 15:58:21 +0200
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1 <?xml version="1.0" encoding="utf-8" ?>
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5 <html>
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7 <head><title></title>
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9 <meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/mn.html)" />
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10 <meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/mn.html)" />
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12 <meta name="src" content="Einst_Zurth_de_1906_01.tex" />
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13 <meta name="date" content="2005-03-02 20:13:00" />
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14 <link rel="stylesheet" type="text/css" href="Einst_Zurth_de_1906_01.css" />
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15 </head><body >
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17 <!--l. 12--><p class="noindent"><pb/></p>
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18 <div class="center" >
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20 <!--l. 13--><p class="noindent">
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21 </p><!--l. 14--><p class="noindent"><span
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22 class="cmr-12">12. </span><span
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23 class="cmbxti-10x-x-120">Zur Theorie </span> <br/><span
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24 class="cmbxti-10x-x-120">der Lichterzeugung und Lichtabsorption;</span>
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25 <br/><span
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26 class="cmbxti-10x-x-120">von A. Einstein.</span></p></div>
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27 <div class="center" >
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29 <!--l. 18--><p class="noindent">
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30 </p><!--l. 19--><p class="noindent">--------</p></div>
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31 <!--l. 22--><p class="indent"> In einer letztes Jahr erschienenen Arbeit<sup ><span
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32 class="cmr-7">1</span></sup>) habe ich ge-<br/>zeigt, daß die Maxwellsche Theorie der Elektrizität in Ver-<br/>bindung mit der Elektronentheorie zu Ergebnissen führt, die <br/>mit den Erfahrungen über die Strahlung des schwarzen Körpers <br/>im Widerspruch sind. Auf einem dort dargelegten Wege wurde <br/>ich zu der Ansicht geführt, daß Licht von der Frequenz <span
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33 class="cmmi-10"><img
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34 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span> <br/>lediglich in Quanten von der Energie (<span
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35 class="cmmi-10">R</span><img
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36 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_010x.png" alt="/" class="left" align="middle" /> <span
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37 class="cmmi-10">N</span>)<span
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39 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-c.png" alt="b" class="cmmi-10x-x-c" align="middle" /> <img
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40 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>absorbiert und <br/>emittiert werden könne, wobei <span
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41 class="cmmi-10">R </span>die absolute Konstante der <br/>auf das Grammolekül angewendeten Gasgleichung, <span
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42 class="cmmi-10">N </span>die An-<br/>zahl der wirklichen Moleküle in einem Grammolekül, <span
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43 class="cmmi-10"><img
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44 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-c.png" alt="b" class="cmmi-10x-x-c" align="middle" /> </span>den <br/>Exponentialkoeffizienten der Wienschen (bez. der Planckschen) <br/>Strahlungsformel und <span
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45 class="cmmi-10"><img
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46 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>die Frequenz des betreffenden Lichtes <br/>bedeutet. Diese Beziehung wurde entwickelt für einen Be-<br/>reich, der dem Bereich der Gültigkeit der Wienschen Strah-<br/>lungsformel entspricht.
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47 </p><!--l. 43--><p class="indent"> Damals schien es mir, als ob die Plancksche Theorie <br/>der Strahlung<sup ><span
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48 class="cmr-7">2</span></sup>) in gewisser Beziehung ein Gegenstück bildete <br/>zu meiner Arbeit. Neue Überlegungen, welche im <span
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49 class="cmsy-10">§ </span>1 dieser <br/>Arbeit mitgeteilt sind, zeigten mir aber, daß die theoretische
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50 <br/>Grundlage, auf welcher die Strahlungstheorie von Hrn. Planck <br/>ruht, sich von der Grundlage, die sich aus der Maxwellschen <br/>Theorie und Elektronentheorie ergeben würde, unterscheidet, <br/>und zwar gerade dadurch, daß die Plancksche Theorie im-<br/>plizite von der eben erwähnten Lichtquantenhypothese Ge-<br/>brauch macht.
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51 </p><!--l. 51--><p class="indent"> In <span
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52 class="cmsy-10">§ </span>2 der vorliegenden Arbeit wird mit Hilfe der Licht-<br/>quantenhypothese eine Beziehung zwischen Voltaeffekt und licht-<br/>elektrischer Zerstreuung hergeleitet.
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53 </p><!--l. 54--><p class="noindent">----------
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54 </p><!--l. 57--><p class="indent"> 1) A. Einstein, Ann. d. Phys. <span
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55 class="cmbx-10">17. </span>p. 132. 1905.
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56 </p><!--l. 59--><p class="indent"> 2) M. Planck, Ann. d. Phys. <span
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57 class="cmbx-10">4. </span>p. 561. 1901. <pb/>
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58 </p><!--l. 64--><p class="indent">
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59
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60 </p>
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61 <div class="center" >
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63 <!--l. 65--><p class="noindent">
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64 </p><!--l. 66--><p class="noindent"><span
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65 class="cmsy-10">§ </span>1. Die Plancksche Theorie der Strahlung und die <br/>Lichtquanten.</p></div>
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66 <!--l. 69--><p class="indent"> In <span
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67 class="cmsy-10">§ </span>1 meiner oben zitierten Arbeit habe ich gezeigt, daß <br/>die Molekulartheorie der Wärme zusammen mit der Maxwell-<br/>schen Theorie der Elektrizität und Elektronentheorie zu der <br/>mit der Erfahrung im Widerspruch stehenden Formel für die
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68 <br/>Strahlung des schwarzen Körpers führt:
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69 </p>
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70 <table width="100%"
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71 class="equation"><tr><td><a
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72 id="x1-2r1"></a>
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73 <center class="math-display" >
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74 <img
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75 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_011x.png" alt=" 2 rn = R-8pn--T. N L3 " class="math-display" /></center></td><td width="5%">(1)</td></tr></table>
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76 <!--l. 77--><p class="nopar">
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77 </p><!--l. 81--><p class="indent"> Hierbei bedeutet <span
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78 class="cmmi-10"><img
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79 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-25.png" alt="r" class="cmmi-10x-x-25" align="middle" /></span><sub ><span
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80 class="cmmi-7"><img
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81 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span></sub> die Dichte der Strahlung bei der <br/>Temperatur <span
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82 class="cmmi-10">T</span>, deren Frequenz zwischen <span
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84 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>und <span
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85 class="cmmi-10"><img
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86 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>+ 1 liegt.
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87 </p><!--l. 85--><p class="indent"> Woher kommt es, daß Hr. Planck nicht zu der gleichen <br/>Formel, sondern zu dem Ausdruck
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88 </p>
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89 <table width="100%"
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90 class="equation"><tr><td><a
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91 id="x1-3r2"></a>
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92 <center class="math-display" >
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93 <img
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94 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_012x.png" alt=" a n3 rn = -b-n---- -T- e - 1 " class="math-display" /></center></td><td width="5%">(2)</td></tr></table>
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95
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96 <!--l. 91--><p class="nopar">
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97 </p><!--l. 95--><p class="noindent">gelangt ist?
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98 </p><!--l. 98--><p class="indent"> Hr. Planck hat abgeleitet<sup ><span
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99 class="cmr-7">1</span></sup>), daß die mittlere Energie <img
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100 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_013x.png" alt="E" class="bar" /><sub ><span
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101 class="cmmi-7"><img
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102 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span></sub> <br/>eines Resonators von der Eigenfrequenz <span
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104 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span>, der sich in einem <br/>mit ungeordneter Strahlung erfüllten Raume befindet, durch <br/>die Gleichung
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105 </p>
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106 <table width="100%"
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107 class="equation"><tr><td><a
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108 id="x1-4r3"></a>
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109 <center class="math-display" >
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110 <img
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111 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_014x.png" alt=" --L3- En = 8 pn2 rn " class="math-display" /></center></td><td width="5%">(3)</td></tr></table>
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112 <!--l. 107--><p class="nopar">
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113 </p><!--l. 111--><p class="noindent">gegeben ist. Damit war das Problem der Strahlung des <br/>schwarzen Körpers reduziert auf die Aufgabe, <img
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114 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_015x.png" alt="E" class="bar" /><sub ><span
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115 class="cmmi-7"><img
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116 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span></sub> als Funktion <br/>der Temperatur zu bestimmen. Die letztere Aufgabe aber ist <br/>gelöst, wenn es gelingt, die Entropie eines aus einer gro$B;en
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117 <br/>Anzahl im dynamischen Gleichgewicht sich befindender, mit-<br/>einander in Wechselwirkung stehender, gleich beschaffener <br/>Resonatoren von der Eigenfrequenz <span
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118 class="cmmi-10"><img
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119 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span>
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120 zu berechnen.
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121 </p><!--l. 121--><p class="indent"> Die Resonatoren denken wir uns als Ionen, welche um <br/>eine Gleichgewichtslage geradlinige Sinusschwingungen aus-<br/>zuführen vermögen. Bei der Berechnung dieser Entropie spielt <br/>die Tatsache, daß die Ionen elektrische Ladungen besitzen, <br/>keine Rolle; wir haben diese Ionen einfach als Massenpunkte <br/>(Atome) aufzufassen, deren Momentanzustand durch ihre <br/>momentane Abweichung <span
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122 class="cmmi-10">x </span>von der Gleichgewichtslage und <br/>----------
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123 </p><!--l. 131--><p class="indent"> 1) M. Planck, Ann. d. Phys. <span
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124 class="cmbx-10">1. </span>p. 99. 1900. <pb/>
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125 </p><!--l. 136--><p class="indent">
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126
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127 </p><!--l. 137--><p class="noindent">durch ihre Momentangeschwindigkeit <span
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128 class="cmmi-10">dx</span><img
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129 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_016x.png" alt="/" class="left" align="middle" /> <span
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130 class="cmmi-10">dt</span> = <span
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131 class="cmmi-10"><img
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132 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-18.png" alt="q" class="cmmi-10x-x-18" align="middle" /> </span>vollkommen <br/>bestimmt ist.
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133 </p><!--l. 142--><p class="indent"> Damit bei thermodynamischem Gleichgewicht die Zustands-<br/>verteilung dieser Resonatoren eine eindeutig bestimmte sei, <br/>hat man anzunehmen, daß außer den Resonatoren frei beweg-<br/>liche Moleküle in beliebig kleiner Zahl vorhanden seien, welche <br/>dadurch, daß sie mit den Ionen zusammenstoßen, Energie von <br/>Resonator zu Resonator übertragen können; die letzteren Mole-<br/>küle werden wir bei Berechnung der Entropie nicht berück-<br/>sichtigen.
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134 </p><!--l. 152--><p class="indent"> Wir könnten <img
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135 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_017x.png" alt="E" class="bar" /><sub ><span
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136 class="cmmi-7"><img
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137 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span></sub> als Funktion der Temperatur aus dem <br/>Maxwell-Boltzmannschen Verteilungsgesetz ermitteln und <br/>würden dadurch zu der ungültigen Strahlungsformel (1) ge-<br/>langen. Zu dem von Hrn. Planck eingeschlagenen Wege <br/>wird man in folgender Weise geführt.
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138 </p><!--l. 159--><p class="indent"> Es seien <span
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139 class="cmmi-10">p</span><sub ><span
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140 class="cmr-7">1</span></sub><img
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141 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_018x.png" alt="..." class="@cdots" /><span
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142 class="cmmi-10">p</span><sub ><span
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143 class="cmmi-7">n</span></sub> geeignet gewählte Zustandsvariable<sup ><span
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144 class="cmr-7">1</span></sup>), <br/>welche den Zustand eines physikalischen Systems vollkommen <br/>bestimmen (z. B. in unserem Falle die Größen <span
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145 class="cmmi-10">x</span>
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146 und <span
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147 class="cmmi-10"><img
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148 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-18.png" alt="q" class="cmmi-10x-x-18" align="middle" /> </span>sämt-<br/>licher Resonatoren). Die Entropie <span
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149 class="cmmi-10">S </span>dieses Systems bei der <br/>absoluten Temperatur <img
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150 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmr10-0.png" alt="G" class="10x-x-0" /> ist dargestellt durch die Gleichung<sup ><span
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151 class="cmr-7">2</span></sup>):
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152 </p>
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153 <table width="100%"
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154 class="equation"><tr><td><a
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155 id="x1-5r4"></a>
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156 <center class="math-display" >
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157 <img
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158 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_019x.png" alt=" integral N-- H- R- - RT H S = T + N lg e dp1...dpn, " class="math-display" /></center></td><td width="5%">(4)</td></tr></table>
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159 <!--l. 171--><p class="nopar">
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160 </p><!--l. 175--><p class="noindent">wobei <img
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161 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0110x.png" alt="H" class="bar" /> die Energie des Systems bei der Temperatur <span
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162 class="cmmi-10">T</span>, <br/><span
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163 class="cmmi-10">H </span>die Energie als Funktion der <span
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164 class="cmmi-10">p</span><sub ><span
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165 class="cmr-7">1</span></sub><img
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166 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0111x.png" alt="..." class="@cdots" /><span
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167 class="cmmi-10">p</span><sub ><span
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168 class="cmmi-7">n</span></sub> bedeutet, und das <br/>Integral über alle möglichen Wertkombinationen der
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169 <span
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170 class="cmmi-10">p</span><sub ><span
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171 class="cmr-7">1</span></sub><img
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172 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0112x.png" alt="..." class="@cdots" /><span
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173 class="cmmi-10">p</span><sub ><span
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174 class="cmmi-7">n</span></sub> <br/>zu erstrecken ist.
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175 </p><!--l. 181--><p class="indent"> Besteht das System aus sehr vielen molekularen Gebilden <br/>-- und nur in diesem Falle hat die Formel Bedeutung und <br/>Gültigkeit, so tragen nur solche Wertkombinationen der <span
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176 class="cmmi-10">p</span><sub ><span
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177 class="cmr-7">1</span></sub><img
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178 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0113x.png" alt="..." class="@cdots" /><span
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179 class="cmmi-10">p</span><sub ><span
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180 class="cmmi-7">n</span></sub> <br/>merklich zu dem Werte des in <span
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181 class="cmmi-10">S </span>auftretenden Integrales bei, <br/>deren <span
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182 class="cmmi-10">H </span>sehr wenig von <img
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183 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0114x.png" alt="H" class="bar" /> abweicht.<sup ><span
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184 class="cmr-7">3</span></sup>) Berücksichtigt man
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185 <br/>dies, so ersieht man leicht, daß bis auf Vernachlässigbares <br/>gesetzt werden kann:
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186 </p>
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187 <center class="par-math-display" >
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188 <img
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189 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0115x.png" alt=" H+D integral H S = R-lg dp1...dpn, N H " class="par-math-display" /></center>
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190 <!--l. 194--><p class="nopar">
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191 </p><!--l. 197--><p class="noindent">----------
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192 </p><!--l. 200--><p class="indent"> 1) A. Einstein, Ann. d. Phys. <span
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193 class="cmbx-10">11. </span>p. 170. 1903.
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194 </p><!--l. 202--><p class="indent"> 2) l. c. <span
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195 class="cmsy-10">§ </span>6.
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196 </p><!--l. 204--><p class="indent"> 3) Folgt aus <span
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197 class="cmsy-10">§ </span>3 und <span
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198 class="cmsy-10">§ </span>4 l. e. <pb/>
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199 </p><!--l. 209--><p class="indent">
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200
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201 </p><!--l. 210--><p class="noindent">wobei <img
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202 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmr10-1.png" alt="D" class="10x-x-1" /><span
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203 class="cmmi-10">H </span>zwar sehr klein, aber doch so groß gewählt sei, <br/>daß <span
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204 class="cmmi-10">R</span> lg (<img
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205 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmr10-1.png" alt="D" class="10x-x-1" /><span
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206 class="cmmi-10">H</span>)<img
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207 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0116x.png" alt="/" class="left" align="middle" /> <span
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208 class="cmmi-10">N </span>eine vernachlässigbare Größe ist. <span
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209 class="cmmi-10">S </span>ist dann <br/>von der Größe von <img
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210 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmr10-1.png" alt="D" class="10x-x-1" /><span
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211 class="cmmi-10">H </span>unabhängig.
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212 </p><!--l. 218--><p class="indent"> Setzt man nun die Variabeln <span
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213 class="cmmi-10">x</span><sub ><span
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214 class="cmmi-7"><img
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215 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-b.png" alt="a" class="7x-x-b" /></span></sub> und <span
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216 class="cmmi-10"><img
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217 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-18.png" alt="q" class="cmmi-10x-x-18" align="middle" /></span><sub ><span
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218 class="cmmi-7"><img
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219 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-b.png" alt="a" class="7x-x-b" /></span></sub> der Resonatoren <br/>an Stelle der <span
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220 class="cmmi-10">dp</span><sub ><span
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221 class="cmr-7">1</span></sub><img
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222 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0117x.png" alt="..." class="@cdots" /><span
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223 class="cmmi-10">dp</span><sub ><span
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224 class="cmmi-7">n</span></sub>
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225 in die Gleichung ein und berück-<br/>sichtigt man, daß für den <span
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226 class="cmmi-10"><img
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227 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-b.png" alt="a" class="10x-x-b" /></span><sup ><span
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228 class="cmmi-7">ten</span></sup> Resonator die Gleichung
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229 </p>
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230 <center class="par-math-display" >
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231 <img
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232 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0118x.png" alt="Ea+ integral d Ea dxad qa = konst.dEa E a " class="par-math-display" /></center>
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233 <!--l. 228--><p class="nopar">
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234 </p><!--l. 232--><p class="noindent">gilt (da <span
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235 class="cmmi-10">E</span><sub ><span
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236 class="cmmi-7"><img
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237 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-b.png" alt="a" class="7x-x-b" /></span></sub> eine quadratische, homogene Funktion von <span
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238 class="cmmi-10">x</span><sub ><span
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239 class="cmmi-7"><img
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240 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-b.png" alt="a" class="7x-x-b" /></span></sub> und <span
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241 class="cmmi-10"><img
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242 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-18.png" alt="q" class="cmmi-10x-x-18" align="middle" /></span><sub ><span
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243 class="cmmi-7"><img
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244 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-b.png" alt="a" class="7x-x-b" /></span></sub> <br/>ist), so erhält man für <span
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245 class="cmmi-10">S </span>den Ausdruck:
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246 </p>
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247 <table width="100%"
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248 class="equation"><tr><td><a
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249 id="x1-6r5"></a>
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250 <center class="math-display" >
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251 <img
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252 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0119x.png" alt="S = R- lg W, N " class="math-display" /></center></td><td width="5%">(5)</td></tr></table>
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253 <!--l. 239--><p class="nopar">
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254 </p><!--l. 243--><p class="noindent">wobei
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255 </p>
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256 <table width="100%"
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257 class="equation"><tr><td><a
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258 id="x1-7r6"></a>
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259 <center class="math-display" >
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260 <img
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261 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0120x.png" alt=" H+D integral H W = dE ...dE 1 n H
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262 " class="math-display" /></center></td><td width="5%">(5a)</td></tr></table>
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263 <!--l. 250--><p class="nopar">
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264 </p><!--l. 254--><p class="noindent">gesetzt ist.
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265 </p><!--l. 257--><p class="indent"> Würde man <span
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266 class="cmmi-10">S </span>nach dieser Formel berechnen, so würde <br/>man wieder zu der ungültigen Strahlungsformel (1) gelangen. <br/>Zur Planckschen Formel aber gelangt man, indem man <br/>voraussetzt, daß die Energie <span
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267 class="cmmi-10">E</span><sub ><span
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268 class="cmmi-7"><img
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269 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-b.png" alt="a" class="7x-x-b" /></span></sub> eines Resonators nicht jeden <br/>beliebigen Wert annehmen kann, sondern nur Werte, welche <br/>ganzzahlige Vielfache von <span
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270 class="cmmi-10"><img
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271 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /> </span>sind, wobei
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272 </p>
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273 <center class="par-math-display" >
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274 <img
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275 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0121x.png" alt=" R- e = N bn. " class="par-math-display" /></center>
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276 <!--l. 268--><p class="nopar">
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277 </p><!--l. 272--><p class="indent"> Setzt man nämlich <img
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278 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmr10-1.png" alt="D" class="10x-x-1" /><span
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279 class="cmmi-10">H </span>= <span
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280 class="cmmi-10"><img
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281 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /></span>, so ersieht man sofort aus <br/>Gleichung (5a), daß nun <span
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282 class="cmmi-10">W</span>
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283 bis auf einen belanglosen Faktor <br/>gerade in diejenige Größe übergeht, welche Hr. Planck ,,An-<br/>zahl der Komplexionen&#8220; genannt hat.
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284 </p><!--l. 278--><p class="indent"> Wir müssen daher folgenden Satz als der Planckschen <br/>Theorie der Strahlung zugrunde liegend ansehen:
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285 </p><!--l. 281--><p class="indent"> Die Energie eines Elementarresonators kann nur Werte <br/>annehmen, die ganzzahlige Vielfache von (<span
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286 class="cmmi-10">R</span><img
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287 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0122x.png" alt="/" class="left" align="middle" /> <span
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288 class="cmmi-10">N</span>)<span
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289 class="cmmi-10"><img
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290 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-c.png" alt="b" class="cmmi-10x-x-c" align="middle" /> <img
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291 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>sind; die <br/>Energie eines Resonators ändert sich durch Absorption und <br/>Emission sprungweise, und zwar um ein ganzzahliges Viel-<br/>fache von (<span
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292 class="cmmi-10">R</span><img
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293 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0123x.png" alt="/" class="left" align="middle" /> <span
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294 class="cmmi-10">N</span>)<span
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295 class="cmmi-10"><img
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296 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-c.png" alt="b" class="cmmi-10x-x-c" align="middle" /> <img
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297 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" />. </span><pb/>
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298 </p><!--l. 293--><p class="indent">
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299
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300 </p><!--l. 294--><p class="indent"> Diese Voraussetzung involviert aber noch eine zweite, <br/>indem sie im Widerspruch steht mit der theoretischen Grund-<br/>lage, aus der heraus Gleichung (3) entwickelt ist. Wenn die <br/>Energie eines Resonators sich nur sprungweise ändern kann, <br/>so kann nämlich zur ermittelung der mittleren Energie eines <br/>in einem Strahlungsraum befindlichen Resonators die übliche <br/>Theorie der Elektrizität nicht Anwendung finden, da diese <br/>keine <span
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301 class="cmti-10">ausgezeichneten </span>Energiewerte eines Resonators kennt. Es <br/>liegt also der Planckschen Theorie die Annahme zugrunde:
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302 </p><!--l. 306--><p class="indent"> Obwohl die Maxwellsche Theorie auf Elementarresonatoren <br/>nicht anwendbar ist, so ist doch die <span
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303 class="cmti-10">mittlere </span>Energie eines in <br/>einem Strahlungsraume befindlichen Elementarresonators gleich <br/>derjenigen, welche man mittels der Maxwellschen Theorie
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304 <br/>der Elektrizität berechnet.
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305 </p><!--l. 313--><p class="indent"> Der letztere Satz wäre ohne weiteres plausibel, wenn in <br/>allen Teilen des Spektrums, die für die Beobachtung in Be-<br/>tracht kommen, <span
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306 class="cmmi-10"><img
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307 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /> </span>= (<span
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308 class="cmmi-10">R</span><img
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309 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0124x.png" alt="/" class="left" align="middle" /> <span
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310 class="cmmi-10">N</span>)<span
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311 class="cmmi-10"><img
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312 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-c.png" alt="b" class="cmmi-10x-x-c" align="middle" /> <img
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313 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>klein wäre gegen die mittlere <br/>Energie <img
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314 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0125x.png" alt="E" class="bar" /><sub ><span
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315 class="cmmi-7"><img
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316 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span></sub> eines Resonators; dies ist aber durchaus nicht der <br/>Fall. Innerhalb des Gültigkeitsbereiches der Wienschen <br/>Strahlungsformel ist nämlich
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317 <span
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318 class="cmmi-10">e</span><sup ><span
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319 class="cmmi-7"><img
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320 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-c.png" alt="b" class="cmmi-7x-x-c" align="middle" /><img
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321 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span><img
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322 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0126x.png" alt="/" class="left" align="middle" /> <span
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323 class="cmmi-7">T</span></sup> groß gegen 1. Man be-<br/>weist nun leicht, daß nach der Planckschen Strahlungs-<br/>theorie <img
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324 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0127x.png" alt="E" class="bar" /><sub ><span
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325 class="cmmi-7"><img
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326 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span></sub><img
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327 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0128x.png" alt="/" class="left" align="middle" /> <span
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328 class="cmmi-10"><img
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329 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /> </span>innerhalb des Gültigkeitsbereiches der Wienschen
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330 <br/>Strahlungsformel den Wert <span
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331 class="cmmi-10">e</span><sup ><span
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332 class="cmsy-7">-</span><span
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333 class="cmmi-7"><img
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334 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-c.png" alt="b" class="cmmi-7x-x-c" align="middle" /><img
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335 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span><img
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336 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0129x.png" alt="/" class="left" align="middle" /> <span
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337 class="cmmi-7">T</span></sup> hat; <img
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338 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0130x.png" alt="E" class="bar" /><sub ><span
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339 class="cmmi-7"><img
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340 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi7-17.png" alt="n" class="7x-x-17" /></span></sub> ist also weit kleiner <br/>als <span
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341 class="cmmi-10"><img
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342 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /></span>. Es kommt also überhaupt nur wenigen Resonatoren ein <br/>von Null verschiedener Wert der Energie zu.
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343 </p><!--l. 335--><p class="indent"> Die vorstehenden Überlegungen widerlegen nach meiner <br/>Meinung durchaus nicht die Plancksche Theorie der Strahlung; <br/>sie scheinen mir vielmehr zu zeigen, daß Hr. Planck in seiner <br/>Strahlungstheorie ein neues hypothetisches Element -- die
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344 <br/>Lichtquantenhypothese -- in die Physik eingeführt hat.
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345 </p>
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346 <div class="center" >
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347
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348 <!--l. 342--><p class="noindent">
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349 </p><!--l. 343--><p class="noindent"><span
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350 class="cmsy-10">§ </span>2. Eine zu erwartende quantitative Beziehung zwischen <br/>lichtelektrischer Zerstreuung und Voltaeffekt.</p></div>
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351 <!--l. 347--><p class="indent"> Ordnet man die Metalle nach ihrer lichtelektrischen <br/>Empfindlichkeit in eine Reihe, so erhält man bekanntlich die <br/>Voltasche Spannungsreihe, wobei die Metalle desto licht-<br/>empfindlicher sind, je näher sie dem elektropositiven Ende <br/>der Spannungsreihe liegen. <pb/>
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352 </p><!--l. 357--><p class="indent">
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353
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354 </p><!--l. 358--><p class="indent"> Man begreift diese Tatsache bis zu einem gewissen Grade <br/>unter alleiniger Zugrundelegung der Annahme, daß die die <br/>wirksamen Doppelschichten erzeugenden, hier nicht zu unter-<br/>suchenden Kräfte nicht an der Berührungsfläche zwischen <br/>Metall und Metall, sondern an der Berührungsfläche zwischen <br/>Metall und Gas ihren Sitz haben.
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355 </p><!--l. 366--><p class="indent"> Jene Kräfte mögen an der Oberfläche eines an ein Gas <br/>angrenzenden Metallstückes
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356 <span
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357 class="cmmi-10">M </span>eine elektrische Doppelschicht <br/>erzeugen, welcher eine Potentialdifferenz <span
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358 class="cmmi-10">V</span>
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359 zwischen Metall <br/>und Gas entspreche -- positiv gerechnet, wenn das Metall das
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360 <br/>höhere Potential besitzt.
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361 </p><!--l. 373--><p class="indent"> Es seien <span
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362 class="cmmi-10">V</span> <sub ><span
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363 class="cmr-7">1</span></sub> und <span
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364 class="cmmi-10">V</span> <sub ><span
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365 class="cmr-7">2</span></sub> die Spannungsdifferenzen zweier <br/>Metalle <span
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366 class="cmmi-10">M</span><sub ><span
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367 class="cmr-7">1</span></sub> und <span
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368 class="cmmi-10">M</span><sub ><span
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369 class="cmr-7">2</span></sub> bei elektrostatischem Gleichgewichte, falls <br/>die Metalle gegeneinander isoliert sind. Bringt man die beiden <br/>Metalle zur Berührung, so wird das elektrische Gleichgewicht <br/>gestört und es findet ein vollständiger<sup ><span
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370 class="cmr-7">1</span></sup>) Spannungsausgleich <br/>zwischen den Metallen statt. Dabei werden sich über die <br/>vorerwähnten Doppelschichten an den Grenzflächen Metall-Gas <br/>einfache Schichten superponieren; diesen entspricht ein elektro-<br/>statisches Feld im Luftraume, dessen Linienintegral gleich <br/>der Voltadifferenz ist.
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371 </p><!--l. 381--><p class="indent"> Nennt man <span
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372 class="cmmi-10">V</span> <sub ><span
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373 class="cmmi-7">l</span><sub ><span
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374 class="cmr-5">1</span></sub></sub> bez. <span
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375 class="cmmi-10">V</span> <sub ><span
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376 class="cmmi-7">l</span><sub ><span
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377 class="cmr-5">2</span></sub></sub> die elektrischen Potentiale in <br/>Punkten des Gasraumes, welche den einander berührenden <br/>Metallen unmittelbar benachbart sind, und <span
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378 class="cmmi-10">V </span><span
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379 class="cmsy-10">' </span>das Potential <br/>im Innern der Metalle, so ist
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380 </p>
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381 <center class="par-math-display" >
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382 <img
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383 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0131x.png" alt="V'- Vl1 = V1, V'- Vl2 = V2, " class="par-math-display" /></center>
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384 <!--l. 392--><p class="nopar">
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385 </p><!--l. 396--><p class="noindent">also
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386 </p>
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387 <center class="par-math-display" >
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388 <img
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389 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0132x.png" alt="Vl2- Vl1 = V1- V2. " class="par-math-display" /></center>
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390 <!--l. 402--><p class="nopar">
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391 </p><!--l. 406--><p class="indent"> Die elektrostatisch meßbare Voltadifferenz ist also nume-<br/>risch gleich der Differenz der Potentiale, welche die Metalle <br/>im Gase annehmen, falls sie voneinander isoliert sind.
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392 </p><!--l. 411--><p class="indent"> Ionisiert man das Gas, so findet im Gasraum eine durch <br/>die daselbst vorhandenen elektrischen Kräfte hervorgerufene <br/>Wanderung der Ionen statt, welcher Wanderung in den Metallen <br/>ein Strom entspricht, der an der Berührungsstelle der Metalle
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393 <br/>----------
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394 </p><!--l. 418--><p class="indent"> 1) Von der Wirkung der thermoelektrischen Kräfte sehen wir ab. <pb/>
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395 </p><!--l. 424--><p class="indent">
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396
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397 </p><!--l. 425--><p class="noindent">vom Metall mit größerem <span
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398 class="cmmi-10">V </span>(schwächer elektropositiv) nach dem <br/>Metall mit kleinerem <span
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399 class="cmmi-10">V </span>(stärker elektropositiv) gerichtet ist.
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400 </p><!--l. 429--><p class="indent"> Es befinde sich nun ein Metall <span
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401 class="cmmi-10">M </span>isoliert in einem Gase. <br/>Seine der Doppelschicht entsprechende Potentialdifferenz gegen <br/>das Gas sei <span
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402 class="cmmi-10">V </span>. Um die Einheit negativer Elektrizität aus <br/>dem Metall in das Gas zu befördern, muß eine dem Potential <span
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403 class="cmmi-10">V</span>
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404 <br/>numerisch gleiche Arbeit geleistet werden. Je größer <span
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405 class="cmmi-10">V </span>, d. h. <br/>je weniger elektropositiv das Metall ist, desto mehr Energie <br/>ist also für die lichtelektrische Zerstreuung nötig, desto weniger <br/>lichtelektrisch empfindlich wird also das Metall sein.
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406 </p><!--l. 440--><p class="indent"> Soweit übersieht man die Tatsachen, ohne über die Natur <br/>der lichtelektrischen Zerstreuung Annahmen zu machen. Die <br/>Lichtquantenhypothese liefert aber außerdem eine quantitative <br/>Beziehung zwischen Voltaeffekt und lichtelektrischer Zerstreuung. <br/>Es wird nämlich einem negativen Elementarquantum (Ladung
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407 <span
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408 class="cmmi-10"><img
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409 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /></span>) <br/>mindestens die Energie <span
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410 class="cmmi-10">V <img
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411 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /> </span>zugeführt werden müssen, um es <br/>aus dem Metall in das Gas zu bewegen. Es wird also eine <br/>Lichtart nur dann negative Elektrizität aus dem Metall ent-<br/>fernen können, wenn das ,,Lichtquant&#8220; der betreffenden Licht-<br/>art mindestens den Wert <span
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412 class="cmmi-10">V <img
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413 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /> </span>besitzt. Wir erhalten also:
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414 </p>
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415 <center class="par-math-display" >
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416 <img
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417 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0133x.png" alt=" 3R- V e &lt;= 2N b n, " class="par-math-display" /></center>
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418 <!--l. 458--><p class="nopar">
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419 </p><!--l. 462--><p class="noindent">oder
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420 </p>
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421 <center class="par-math-display" >
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422 <img
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423 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0134x.png" alt=" R V &lt;= A-b n, " class="par-math-display" /></center>
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424 <!--l. 468--><p class="nopar">
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425 </p><!--l. 472--><p class="noindent">wobei <span
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426 class="cmmi-10">A </span>die Ladung eines Grammoleküls eines einwertigen <br/>Ions ist.
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427 </p><!--l. 475--><p class="indent"> Nehmen wir nun an, daß ein Teil der absorbierenden <br/>Elektronen das Metall zu verlassen befähigt ist, sobald die <br/>Energie der Lichtquanten <span
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428 class="cmmi-10">V <img
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429 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /> </span>übertrifft<sup ><span
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430 class="cmr-7">1</span></sup>) -- welche Annahme <br/>sehr plausibel ist --, so erhalten wir
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431 </p>
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432 <center class="par-math-display" >
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433 <img
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434 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0135x.png" alt="V = R-b n, A " class="par-math-display" /></center>
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435 <!--l. 484--><p class="nopar">
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436 </p><!--l. 488--><p class="noindent">wobei <span
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437 class="cmmi-10"><img
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438 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /> </span>die kleinste lichtelektrisch wirksame Frequenz be-<br/>deutet.
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439 </p><!--l. 491--><p class="indent"> Sind also <span
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440 class="cmmi-10"><img
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441 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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442 class="cmr-7">1</span></sub> und <span
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443 class="cmmi-10"><img
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444 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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445 class="cmr-7">2</span></sub> die kleinsten Lichtfrequenzen, welche <br/>auf die Metalle <span
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446 class="cmmi-10">M</span><sub ><span
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447 class="cmr-7">1</span></sub> und
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448 <span
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449 class="cmmi-10">M</span><sub ><span
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450 class="cmr-7">2</span></sub> wirken, so soll für die Voltasche <br/>----------
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451 </p><!--l. 497--><p class="indent"> 1) Von der thermischen Energie der Elektronen ist dabei abgesehen.
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452 <pb/>
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453 </p><!--l. 503--><p class="indent">
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454
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455 </p><!--l. 504--><p class="noindent">Spannungsdifferenz <span
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456 class="cmmi-10">V</span> <sub ><span
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457 class="cmr-7">12</span></sub> der beiden Metalle die Gleichung <br/>gelten:
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458 </p>
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459 <center class="par-math-display" >
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460 <img
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461 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0136x.png" alt=" R- - V12 = V1- V2 = A b(n1- n2), " class="par-math-display" /></center>
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462 <!--l. 511--><p class="nopar">
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463 </p><!--l. 515--><p class="noindent">oder, wenn <span
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464 class="cmmi-10">V</span> <sub ><span
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465 class="cmr-7">12</span></sub> in Volt gemessen wird:
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466 </p>
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467 <center class="par-math-display" >
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468 <img
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469 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Zurth_de_1906_01/fulltext/img/Einst_Zurth_de_1906_0137x.png" alt=" -15 V12 = 4,2.10 (n2- n1). " class="par-math-display" /></center>
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470 <!--l. 521--><p class="nopar">
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471 </p><!--l. 525--><p class="indent"> In dieser Formel ist folgender, im großen ganzen jeden-<br/>falls gültige Satz enthalten: Je stärker elektropositiv ein Metall <br/>ist, desto kleiner ist die unterste wirksame Lichtfrequenz für <br/>das betreffende Metall. Es wäre von hohem Interesse zu
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472 <br/>wissen, ob die Formel auch in quantitativer Beziehung als <br/>Ausdruck der Tatsachen zu betrachten ist.
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473 </p><!--l. 533--><p class="indent"> Bern, März 1906.
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474 </p>
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475 <div class="center" >
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476
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477 <!--l. 535--><p class="noindent">
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478 </p><!--l. 536--><p class="noindent">(Eingegangen 13. März 1906.)</p></div>
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479 <div class="center" >
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482 </p><!--l. 541--><p class="noindent">----------</p></div>
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484 </body></html>
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