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Q.

Two streams of photons, possessing energies equal to thrice and nine 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 where x and y are co-prime integers. The value of y is

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answer is 2.

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Detailed Solution

${KE}_{\max} = hv - ϕ \frac{1}{2} {mv}^{2} = hv - ϕ V = \sqrt{\frac{2 (hv - ϕ)}{m}} Given {hv}_{1} = 3 ϕ {hv}_{2} = 9 ϕ ∴ \frac{V_{1}}{V_{2}} = \sqrt{\frac{{hv}_{1} - ϕ}{{hv}_{2} - ϕ}} \frac{V_{1}}{V_{2}} = \sqrt{\frac{3 ϕ - ϕ}{9 ϕ - ϕ}} = \frac{1}{2}$

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