An electron is moving with an initial velocity $\vec{v}=v_0 \hat{i}$ and is in a magnetic field $\ve

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

Professor PC Thomas Classes · 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(\vec{v} 	imes \vec{B})=-e\left(v_0 \hat{i} 	imes B_0 \hat{j}ight)=-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 $(=m v)$ will remain \  constant in magnitude. \ Therefore, de-Broglie wavelength, \  $\lambda\left(=\frac{h}{m v}ight)$ remains constant.