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Find the refreactive index of metallic sodium for electrons with kinetic energy T=135 eV. Only one free electron is assumed to correspond to each sodium atom. |
Answer» Solution : The potential energy inside the metal is `-U_(0)` for the ELECTRON and it related to the work function `A` by `U_(0)=E_(F)+A` If `T` is the `K.E` of electron outside the metal, its `K.E` inside the metal will be `(E+U_(0))`. On entering the metal electron canot experience any tangential force so the tangential componet of mometum is unchanged. Then `(2mT)SIN alpha=sqrt(2m(T+U_(0))) sin beta` Hence `(sin alpha)/(sin beta)=sqrt(1+(U_(0))/(T))=n` by DEFINATION ofrefractive index. In sodium with ONE free electron PER `Na` atom `n=2.54xx10^(22) per c.c` `E_(F)= 3.15eV` `A= 2.27eV`(from table) `U_(0)= 5.42eV` `n=1.02` |
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