Formeln für die Arbeit am 14.12.2004
Bragg-Bedingung
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{\displaystyle \mathrm {2} d\cdot \sin \phi \mathrm {\ =\ } \lambda {,}\ \mathrm {2} \lambda {,}\ \mathrm {3} \lambda {,}\ \mathrm {...} \qquad d\ \mathrm {=} \ \mathrm {Abstand\ zw.\ den\ Gitterebenen} }
Foto-Effekt
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{\displaystyle W_{phot}\ \mathrm {=} \ h\;\cdot \;f\qquad \left[J=h\cdot Hz=J\cdot sec\cdot {1 \over sec}\right]\qquad \mathrm {Energie=\ Plank'sche\,Konst.\ \cdot \ Frequenz} }
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{\displaystyle W_{e^{-}}\ \mathrm {=} \ W_{phot}\ \mathrm {=} \ e\;\cdot \;U\ \mathrm {=} \ h\;\cdot \;f_{max}\qquad \left[coul\cdot V=h\cdot Hz=J\right]\qquad Ladung\;\cdot \;Spannung\ =\ h\;\cdot \;Freq.}
Energieniveaus und Spektrallinien
Energie in der n-ten Bahn
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{\displaystyle W_{n}\ =\ -{m_{e}\cdot e^{4} \over \mathrm {8} \,\epsilon _{0}^{\;2}\,\cdot h^{2}}\cdot {\mathrm {1} \over n^{2}}\qquad m_{e}\mathrm {=Elektronenmasse} ;\;e\mathrm {=Elementarladung} ;\;\epsilon _{0}{,}h\mathrm {=const.} ;\;n\in \mathbb {N} }
Sprung von der m-ten Bahn in die n-te Bahn
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{\displaystyle f\mathrm {=} {W_{m}\mathrm {-} W_{n} \over h}\mathrm {=} f_{R}\cdot \left({\mathrm {1} \over n^{2}}\mathrm {-} {\mathrm {1} \over m^{2}}\right)\qquad n,m\in \mathbb {N} }
R )
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{\displaystyle f_{R}\mathrm {=} {m_{e}\cdot e^{4} \over \mathrm {8} \,\epsilon _{0}^{\;2}\,\cdot h^{3}}\mathrm {=3{,}29\cdot 10^{15}Hz} \qquad m_{e}\mathrm {=Elektronenmasse} ;\;e\mathrm {=Elementarladung} ;\;\epsilon _{0}{,}h\mathrm {=const.} }
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{\displaystyle f_{K}\;\mathrm {=} \;(Z\mathrm {-1} )^{2}\cdot f_{R}\cdot \left({\mathrm {1} \over \mathrm {1^{2}} }\mathrm {-} {\mathrm {1} \over n^{2}}\right)\qquad Z\mathrm {=Ordnungszahl} ;\;n\mathrm {>1} ;\;n\in \mathbb {N} }
![{\displaystyle W_{phot}\ \mathrm {=} \ h\;\cdot \;f\qquad \left[J=h\cdot Hz=J\cdot sec\cdot {1 \over sec}\right]\qquad \mathrm {Energie=\ Plank'sche\,Konst.\ \cdot \ Frequenz} }](/media/api/rest_v1/media/math/render/svg/8c0287d66d4e7ebc6766dfc0de5eb1110e808f1f)
![{\displaystyle W_{e^{-}}\ \mathrm {=} \ W_{phot}\ \mathrm {=} \ e\;\cdot \;U\ \mathrm {=} \ h\;\cdot \;f_{max}\qquad \left[coul\cdot V=h\cdot Hz=J\right]\qquad Ladung\;\cdot \;Spannung\ =\ h\;\cdot \;Freq.}](/media/api/rest_v1/media/math/render/svg/17533359a050acbf4fe3d6a3dfad4b91036399ed)
