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A light source of wavelength $λ$ illuminates a metal and ejects photo electrons with ${(K . E)}_{m a x} = 1 e v$ Another light source of wavelength $= \frac{λ}{3}$ ,Another light source of wavelength ${(K . E)}_{m a x} = 4 e v$ find the value of work function ?

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1 eV

2 eV

4 eV

0.5 eV

answer is D.

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Detailed Solution

$hϑ = {hϑ}_{0} + KE$

$\frac{hc}{λ} = \frac{h c}{λ_{0}} + 1$

$\frac{3 hc}{λ} = \frac{h c}{λ_{0}} + 4$

$3 [\frac{hc}{λ_{0}} + 1] = \frac{h c}{λ_{0}} + 4$

$\frac{2 hc}{λ_{0}} + 3 = \frac{h c}{λ_{0}} + 4$

$\frac{2 hc}{λ_{0}} = 1$

$\frac{hc}{λ_{0}} = \frac{1}{2}$

Work function = 0.5eV.

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