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 em

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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

TestHub · Accepted Answer

Using Einstein's photoelectric equation,
Maximum kinetic energy, $K E_{m a x} = E - ϕ$ , where, $E$ is energy of photon and $ϕ$ is work function.
For two cases,
$\frac{1}{2} m v_{1}^{2} = 5 ϕ - ϕ = 4 ϕ$ and $\frac{1}{2} m v_{2}^{2} = 10 ϕ - ϕ = 9 ϕ$
Thus, the ratio $\frac{v_{1}}{v_{2}} = \frac{4}{9} = \frac{2}{3} = 2 : 3$

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