A monochromatic light is incident on a metallic plate having work function . An electron, emitted normally to the plate from a point A with maximum kinetic energy, enterss a constant magnetic field, perpendicular to the initial velocity of electron. The e

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Solution

Q.
A monochromatic light is incident on a metallic plate having work function $ϕ$ . An electron, emitted normally to the plate from a point A with maximum kinetic energy, enterss 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) [2025]

1 $\sqrt{2 m (\frac{h c}{λ} - ϕ)} / e B$

2 $\sqrt{m (\frac{h c}{λ} - ϕ)} / e B$

3 $\sqrt{8 m (\frac{h c}{λ} - ϕ)} / e B$

4 $2 \sqrt{m (\frac{h c}{λ} - ϕ)} / e B$

Ans.
(3)

${KE}_{\max} = \frac{h c}{λ} - ϕ$

$p = \sqrt{2 m K_{\max}}$

$p = \sqrt{2 m (\frac{h c}{λ} - ϕ)}$

$d_{A B} = 2 R = 2 [\frac{p}{q B}]$

$d_{A B} = \frac{2 \sqrt{2 m (\frac{h c}{λ} - ϕ)}}{e B} = \frac{\sqrt{8 m (\frac{h c}{λ} - ϕ)}}{e B}$

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