Question

An electron is moving with an initial velocity $\overrightarrow{v} = v_{0}\widehat{i}$ and is in a magnetic field $\overrightarrow{B} = B_{0}\widehat{j}$ Then it’s 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

Answer 2

: Here $\overset{\rightarrow}{v} = v_{0}î,\overset{\rightarrow}{B} = B_{0}\widehat{j}$

Force on moving electron due to magnetic field is

$\overrightarrow{F} = - e(\overrightarrow{v} \times \overrightarrow{B}) = - e(v_{0}î \times B_{0}\widehat{j}) = - ev_{0}B_{0}\widehat{k}$

As this force is perpendicular to $\overrightarrow{v}$and $\overrightarrow{B}$, so the magnitude of $\overrightarrow{v}$ will not change. i.e. momentum $( = mv)$ will remain constant in magnitude

Therefore, de Broglie wavelength $\lambda\left( = \frac{h}{mv} \right)$remains constant