Question

An electron is moving with an initial velocity $\overline{v}=v_0\hat{i}$ and is in a magnetic field $\overline{B}=B_0\hat{j}$ 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)

remains constant

The magnetic force on moving electron is given as,

$F=-e\left(v_0\overrightarrow{i}\times B_0\overrightarrow{j}\right)$

$=-e{v}_0{B}_0\overrightarrow{k}$

Since the force is perpendicular to $\overrightarrow{v}$ and $\overrightarrow{B}$, so the magnitude of $v$ will not change that’s means the momentum will remain constant.

De Broglie wavelength is given as,

$\lambda =\frac{h}{mv}$

Thus, if the momentum will remain constant, then de Broglie wavelength will remain constant.