Question

An electron accelerated under a potential difference \( V \) volt has a certain wavelength \( \lambda \). Mass of proton is some 2000 times the mass of the electron. If the proton has to have the same wavelength \( \lambda \), then it will have to be accelerated under a potential difference of:

• A. \( V \)
• B. 2000 V
• C. \( 2000 \, \text{V} \)
• D. \( 3000 \, \text{V} \)

Hint:

The potential difference required for a proton to have the same wavelength as an electron is proportional to the ratio of their masses.

Answer 1

The Correct Option is C

Step 1: Wavelength and potential difference.
The de Broglie wavelength of a particle is related to its momentum and potential difference: \[ \lambda = \frac{h}{p} \] For the proton to have the same wavelength as the electron, it must be accelerated under a potential difference that gives it the same momentum.
Step 2: Calculate the required potential.
Since the mass of the proton is 2000 times that of the electron, the required potential difference is 2000 V for the proton.
Final Answer: \[ \boxed{2000 \, \text{V}} \]