Dual Nature Of Light Question 439

Question: An electron of mass m when accelerated through a potential difference V has de-Broglie wavelength $ \lambda $ . The de-Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be

Options:

A) $ \lambda \frac{m}{M} $

B) $ \lambda \sqrt{\frac{m}{M}} $

C) $ \lambda \frac{M}{m} $

D) $ \lambda \sqrt{\frac{M}{m}} $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ \lambda =\frac{h}{\sqrt{2mE}} $
$ \Rightarrow $ $ \lambda \propto \frac{1}{\sqrt{m}} $ (E = same)