Question

An electron moving with initial velocity \( \mathbf{V} = V_0 \hat{i} \) is moving in a magnetic field \( \mathbf{B} = B \hat{k} \). Then its de-Broglie wavelength:

• A. increases with time
• B. first increases and then decreases
• C. decreases with time
• D. remains constant

Hint:

The de-Broglie wavelength of a particle depends on its momentum, which remains unchanged in a magnetic field if no work is done on the particle.

Answer 1

The Correct Option is D

Step 1: De-Broglie Wavelength Formula.
The de-Broglie wavelength \( \lambda \) of a particle is given by: \[ \lambda = \frac{h}{p} \] where \( h \) is Planck's constant and \( p \) is the momentum of the electron. Since the magnetic force does not work on the electron (it only changes the direction of the velocity), the speed and hence the momentum of the electron remains constant. Therefore, the de-Broglie wavelength remains constant.
Step 2: Final Answer.
Thus, the de-Broglie wavelength remains constant.