Two electrons are moving with the same speed | vedclass

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(D) The de-Broglie wavelength is given by $\lambda = \frac{h}{p} = \frac{h}{mv}$.Since the mass $m$ is constant,the wavelength depends on the speed $v

Vedclass · Accepted Answer

Depends on the direction of the electric field

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(D) The de-Broglie wavelength is given by $\lambda = \frac{h}{p} = \frac{h}{mv}$.Since the mass $m$ is constant,the wavelength depends on the speed $v$ of the electron.In 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 velocity. Thus,the speed remains $v$ and the wavelength remains constant.In a uniform electric field,the electric force $F = qE$ acts on the electron. This force can change the magnitude of the velocity (speed) depending on the direction of the field relative to the motion of the electron.If the electric field accelerates the electron,the speed increases,and $\lambda$ decreases. If it decelerates the electron,the speed decreases,and $\lambda$ increases.Therefore,the relationship between ${\lambda _1}$ and ${\lambda _2}$ depends on the direction of the electric field relative to the electron's velocity.

List-$I$	List-$II$
$A$. $E = hv$	$I$. de Broglie wavelength
$B$. Diffraction and Interference	$II$. Particle nature of light
$C$. $\lambda = h/p$	$III$. Wave nature of light
$D$. Compton effect	$IV$. Energy of photon

Two electrons are moving with the same speed $v$. One electron enters a region of a uniform electric field,while the other enters a region of a uniform magnetic field. If the de-Broglie wavelengths of the two electrons after some time are ${\lambda _1}$ and ${\lambda _2}$ respectively,then:

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