question_answer

An electron is moving with an initial velocity \[v={{v}_{0}}\overset{}{\mathop{i}}\,\] and is in a magnetic field \[B={{B}_{0}}\overset{}{\mathop{j}}\,\]. Then, its de-Broglie wavelength

A) remains constant.

B) increases with time.

C) decreases with time.

D) increases and decreases periodically.

Correct Answer: A

Solution :

Option [a] is correct.

Explanation: Given, \[v={{v}_{0}}\overset{}{\mathop{i}}\,\]and \[B={{B}_{0}}\overset{}{\mathop{j}}\,\] Magnetic   force   on   moving   electron\[=-e[{{v}_{0}}i\times {{B}_{0}}j]=-e{{v}_{0}}{{B}_{0}}k\]

So, the force is perpendicular to v and B both as the force is perpendicular to the velocity. So, the magnitude will not change v or mv \[(p=mv\ \operatorname{momentum})\]so, the de-Broglie wavelength remains same.