Formeln für die Arbeit am 14.12.2004
2 d ⋅ sin ϕ = λ , 2 λ , 3 λ , . . . d = A b s t a n d z w . d e n G i t t e r e b e n e n {\displaystyle \mathrm {2} d\cdot \sin \phi \mathrm {\ =\ } \lambda {,}\ \mathrm {2} \lambda {,}\ \mathrm {3} \lambda {,}\ \mathrm {...} \qquad d\ \mathrm {=} \ \mathrm {Abstand\ zw.\ den\ Gitterebenen} }
W p h o t = h ⋅ f [ J = h ⋅ H z = J ⋅ s e c ⋅ 1 s e c ] E n e r g i e = P l a n k ′ s c h e K o n s t . ⋅ F r e q u e n z {\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} }
W e − = W p h o t = e ⋅ U = h ⋅ f m a x [ c o u l ⋅ V = h ⋅ H z = J ] L a d u n g ⋅ S p a n n u n g = h ⋅ F r e q . {\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.}
W n = − m e ⋅ e 4 8 ϵ 0 2 ⋅ h 2 ⋅ 1 n 2 m e = E l e k t r o n e n m a s s e ; e = E l e m e n t a r l a d u n g ; ϵ 0 , h = c o n s t . ; n ∈ N {\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} }
f = W m − W n h = f R ⋅ ( 1 n 2 − 1 m 2 ) n , m ∈ N {\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} }
f R = m e ⋅ e 4 8 ϵ 0 2 ⋅ h 3 = 3 , 29 ⋅ 10 15 H z m e = E l e k t r o n e n m a s s e ; e = E l e m e n t a r l a d u n g ; ϵ 0 , h = c o n s t . {\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.} }
f K = ( Z − 1 ) 2 ⋅ f R ⋅ ( 1 1 2 − 1 n 2 ) Z = O r d n u n g s z a h l ; n > 1 ; n ∈ N {\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)
