Dual Nature Of Light Question 353
Question: An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is:
Options:
A) $ \frac{1}{c}{{( \frac{E}{2m} )}^{\frac{1}{2}}} $
B) $ {{( \frac{E}{2m} )}^{\frac{1}{2}}} $
C) $ c{{( 2mE )}^{\frac{1}{2}}} $
D) $ \frac{1}{xc}{{( \frac{E}{2m} )}^{\frac{1}{2}}} $
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Answer:
Correct Answer: A
Solution:
[a] For electron De-Broglie wavelength, $ {\lambda_{e}}=\frac{h}{\sqrt{2mE}} $ ; For photon E = pc
$ \Rightarrow $ De-Broglie wavelength, $ {\lambda_{Ph}}=\frac{hc}{E} $
$ \therefore \frac{{\lambda_{e}}}{{\lambda_{Ph}}}=\frac{h}{\sqrt{2mE}}\times \frac{E}{hc}={{( \frac{E}{2m} )}^{1/2}}\frac{1}{c} $
BETA
