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Light of wavelength $λ$ is incident on a spherical zinc ball of radius 10m. The ball has a charge of 1 nC. The ball is in vacuum. The work function of zinc is 4 eV.

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If $λ$ = 250 nm, electrons will come out of the ball but all of them will re-enter the ball.

If $λ$ = 350 nm, electrons will not come out of the ball.

If $λ$ = 300 nm, electrons will come out of the ball but all of them will reenter the ball.

If $λ$ = 155 nm, electrons will come out of the ball but some of them will never re-enter the ball.

answer is B, C, D.

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Detailed Solution

$\begin{array}{l} V = \frac{k Q}{R} = \frac{9}{10} = 0.9 V \\ V_{S_{1}} = \frac{h C}{ℓ λ} - ϕ = \frac{1240}{250} - 4 = 0.96 > 0.9 \end{array}$

$\Rightarrow$ same will escape.

$V_{S_{2}} = \frac{1240}{300} - 4 < 0 \Rightarrow No electrons will come out .$

$V_{S_{3}} = \frac{1240}{300} - 4 = 0.13 V \Rightarrow Electrons come out & re enter$

$V_{S_{3}} = \frac{1240}{155} - 4 = 4 V \Rightarrow Many will escape.$

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