JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Modern Physics

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Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be

(A) $1 : 2$
(B) $1 : 3$
(C) $2 : 3$ ✓ Correct
(D) $3 : 2$

Answer: (C)

Solution

Using Einstein's photoelectric equation:

K . E . = E - ϕ

.

For the first stream:

\frac{1}{2} m v_{1}^{2} = 5 ϕ - ϕ = 4 ϕ

.

For the second stream:

\frac{1}{2} m v_{2}^{2} = 10 ϕ - ϕ = 9 ϕ

.

Taking the ratio:

\frac{v _{1}^{2}}{v _{2}^{2}} = \frac{4}{9}

, so

\frac{v _{1}}{v _{2}} = \frac{2}{3}

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Single correct option

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