Let K 1 and K 2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ 1 and λ 2 , respectively are incident on a metallic surface. If λ 1 = 3 λ 2 then

Question

Let K 1 and K 2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ 1 and λ 2 , respectively are incident on a metallic surface. If λ 1 = 3 λ 2 then :

TestHub · Accepted Answer

According to Einstein's photoelectric equation

$\frac{h c}{λ} = ϕ_{0} + {KE}_{max}$ , where $ϕ_{0}$ is a work function of a metal

$∴ K_{1} = \frac{h c}{λ_{1}} - ϕ_{0} \dots (i)$

$K_{2} = \frac{h c}{λ_{2}} - ϕ_{0} \dots (i i)$

$or K_{1} - K_{2} = h c [\frac{1}{λ_{1}} - \frac{1}{λ_{2}}]$

$= h c [\frac{1}{{3 λ}_{2}} - \frac{1}{λ_{2}}] = - \frac{2 h c}{3 λ_{2}} (Given λ_{1} = 3 λ_{2})$

$= - \frac{2}{3} (K_{2} + ϕ_{0}) (Using (ii))$

$or K_{1} = K_{2} - \frac{2}{3} K_{2} - \frac{2}{3} ϕ_{0} = \frac{K_{2}}{3} - \frac{2}{3} ϕ_{0}$

$or K_{1} < \frac{K_{2}}{3}$

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