MCQ
A photon and an electron have equal energy $E$. ${\lambda_{{\rm{photon}}}}/{\lambda _{{\rm{electron}}}}$ is proportional to
- A$\sqrt E $
- ✓$1/\sqrt E $
- C$1/E$
- DDoes not depend upon $E$
✓
Answer
Correct option: B.
$1/\sqrt E $
b
(b)${\lambda _{photon}} = \frac{{hc}}{E}$and ${{\lambda }_{electron}}=\frac{h}{\sqrt{2\,mE}}$
(b)${\lambda _{photon}} = \frac{{hc}}{E}$and ${{\lambda }_{electron}}=\frac{h}{\sqrt{2\,mE}}$
$\Rightarrow \frac{{{\lambda }_{photon}}}{{{\lambda }_{electron}}}=c\sqrt{\frac{2m}{E}}$
$\Rightarrow \frac{{{\lambda }_{photon}}}{{{\lambda }_{electron}}}\propto \frac{1}{\sqrt{E}}$
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