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Question

(D) The de-Broglie wavelength is given by $\lambda = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass of the electron,and $v$ is its speed

Vedclass · Accepted Answer

$\lambda_1 > \lambda_2$ or $\lambda_1 < \lambda_2$

Vedclass · Answer

(D) The de-Broglie wavelength is given by $\lambda = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass of the electron,and $v$ is its speed.When an electron enters a uniform electric field,the electric force $F = qE$ acts on it,which can either accelerate or decelerate the electron depending on the direction of the field. Thus,the speed $v_1$ changes,causing $\lambda_1$ to change.When an electron enters a uniform magnetic field,the magnetic force $F = q(v 	imes B)$ acts perpendicular to the velocity. This force changes the direction of motion but does not change the magnitude of the speed. Thus,the speed $v_2$ remains constant,and $\lambda_2$ remains constant.Since the speed $v_1$ in the electric field can either increase or decrease relative to the initial speed,$\lambda_1$ can be either smaller or larger than $\lambda_2$.

Two electrons are moving with the same speed $v$. One electron enters a region of uniform electric field while the other enters a region of uniform magnetic field. After some time,if the de-Broglie wavelengths of the two are $\lambda_1$ and $\lambda_2$,then:

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