Question

An electron is moving with an initial velocity $\vec{v} = v_0 \hat{i}$ and is in a magnetic field $\vec{B} = B_0 \hat{j}$. Then its de Broglie wavelength

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

Answer 1

Answer: (A)

Here, $\vec{v} = v_0 \hat{i}, \vec{B} = B_0 \hat{j}$
Force on moving electron due to magnetic field is
$\vec{F} = - e \left(\vec{v}\times\vec{B}\right)$
$ = -e\left(v_{0} \hat{i} \times B_{0}\hat{j}\right) = - e v_{0}B_{0} \hat{k} $
As this force is perpendicular to $\vec{v}$ and $\vec{B}$ , so the magnitude of $\vec{v}$ will not change, i.e., momentum $(= mv)$ will remain constant in magnitude.
Therefore, de Broglie wavelength, $\lambda ( = \frac{h}{mv})$ remains constant.