JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Modern Physics

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Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is

x : y

. The value of x is ____

Answer: 1

Solution

Einstein's photoelectric equation puts the maximum kinetic energy at the excess of the photon energy over the work function, so for the two beams

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

Dividing,

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

, so

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

. The ratio of maximum velocities is

1 : 3

, giving

x = 1

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Integer answer

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