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.