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.

• A. $\lambda\frac{m}{M}$
• B. $\lambda\sqrt{\frac{m}{M}}$
• C. $\lambda\frac{M}{m}$
• D. $\lambda\sqrt{\frac{M}{m}}$

Answer 1

Answer: (B)

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

Answer 2

$\lambda = \frac{h}{\sqrt{2mE}}$ ⇒ $\lambda \propto \frac{1}{\sqrt{m}}$ (E = same)