A monochromatic light is incident on a metallic plate having work… - Vidyadip

MCQ

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

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

✓

Answer

Correct option: C.

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

(C) $\sqrt{8 m\left(\frac{ hc }{\lambda}-\phi\right)} / eB$
Explanation: $KE _{\max }=\frac{ hc }{\lambda}-\phi$
$p =\sqrt{2 mK _{\max }}$
$p =\sqrt{2 m\left(\frac{ hc }{\lambda}-\phi\right)}$
$d_{A-B}=2 R$
$=2\left[\frac{ p }{ qB }\right]$
$d _{ AB }=\frac{2 \sqrt{2 m\left(\frac{ hc }{\lambda}-\phi\right)}}{ eB }=\frac{\sqrt{8 m\left(\frac{ hc }{\lambda}-\phi\right)}}{ eB }$

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