A monochromatic light is incident on a metallic plate having work...

A monochromatic light is incident on a metallic plate having work function

\phi

. An electron, emitted normally to the plate from a point

A

with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point

B

. The distance between A and B is :
(Given : The magnitude of charge of an electron is e and mass is

\mathrm{m}, \mathrm{h}

is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

Options

A $\sqrt{2 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} / \mathrm{eB}$
B $\sqrt{\mathrm{m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} / \mathrm{eB}$
C $\sqrt{8 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} / \mathrm{eB}$
D $2 \sqrt{\mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} / \mathrm{eB}$

Correct answer

C. $\sqrt{8 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} / \mathrm{eB}$

Step-by-step solution

\begin{aligned} & \mathrm{KE}_{\max }=\frac{\mathrm{hc}}{\lambda}-\phi \\ & \mathrm{p}=\sqrt{2 \mathrm{mK}_{\max }} \\ & \mathrm{p}=\sqrt{2 \mathrm{~m}\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)} \\ & \mathrm{d}_{\mathrm{A}-\mathrm{B}}=2 \mathrm{R} \\ & =2\left[\frac{\mathrm{p}}{\mathrm{qB}}\right]\end{aligned}

\mathrm{d}_{\mathrm{AB}}=\frac{2 \sqrt{2 \mathrm{~m}\left(\frac{\mathrm{\text{ hc }}}{\lambda}-\phi\right)}}

{\mathrm{eB}}=\frac{\sqrt{8 \mathrm{~m}

\left(\frac{\mathrm{hc}}{\lambda}-\phi\right)}}{\mathrm{eB}}

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