JEE Advanced 2016 · Paper 2 · Physics Q8

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PhysicsMultiple correct+4 / -2Question 8 of 54

Light of wavelength $\lambda_{ph}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $\phi$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. A potential difference $V$ is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is $\lambda_e$ , which of the following statement(s) is(are) true?

An evacuated tube with a cathode plate on the left and a wire-mesh anode on the right; light (wavy arrow) falls on the cathode, and electrons travel to the mesh and pass through it. A battery of voltage V (negative to the cathode, positive to the anode) is connected across the electrodes.

\lambda_e

decreases with increase in

\phi

and

\lambda_{ph}

\lambda_e

is approximately halved, if

d

is doubled

For large potential difference

(V\gg\phi/e)

\lambda_e

is approximately halved if

V

is made four times

\lambda_e

increases at the same rate as

\lambda_{ph}

for

\lambda_{ph}<hc/\phi

Answer and worked solution

Official answer: C

Fastest electrons. They leave the cathode with $\frac{hc}{\lambda_{ph}}-\phi$ and gain $eV$ , so at the anode
$K=\frac{hc}{\lambda_{ph}}-\phi+eV,\qquad\lambda_e=\frac h{\sqrt{2mK}}.$

(A) Increasing $\phi$ or $\lambda_{ph}$ lowers $K$ , so $\lambda_e$ increases. False.
(B) $K$ does not depend on $d$ . False.
(C) For $eV\gg\phi$ , $K\approx eV$ and $\lambda_e\propto V^{-1/2}$ . Making $V$ four times halves $\lambda_e$ . True.
(D) $\lambda_e$ is not proportional to $\lambda_{ph}$ . False.

(C)

Topics:de Broglie waves Photoelectric effect

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JEE Advanced 2016 · Paper 2, Physics question 8