Neet Solved Paper 2013 Question 38
Question: The wavelength $ {\lambda_e} $ of an electron and $ {\lambda_p} $ of a photon of same energy E are related by
Options:
A) $ {\lambda _p}\propto \lambda _e^{2} $
B) $ {\lambda _p}\propto {\lambda _e} $
C) $ {\lambda _p}\propto \sqrt{{\lambda _e}} $
D) $ {\lambda _p}\propto \frac{1}{\sqrt{{\lambda _e}}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Wavelength of electron, $ {\lambda_e}=\frac{h}{\sqrt{2mE}} $ and proton $ {\lambda_p}=\frac{hc}{E} $
$ \Rightarrow $ $ \lambda _e^{2}=\frac{h^{2}}{2mE} $ or $ E=\frac{hc}{{\lambda_p}} $
$ \therefore $ $ \lambda _e^{2}=\frac{h^{2}}{2m.\frac{hc}{{\lambda_p}}}\Rightarrow \lambda _e^{2}=\frac{h _2}{2mhc}{\lambda_p} $
$ \Rightarrow $ $ \lambda _e^{2}\propto {\lambda_p} $
