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Radius of a beam of radiation of wavelength 5000Å is 10–3m. Power of the beam is 10–3 W. 

This beam is normally incident on a metal of work function 1.9 eV. The charge emitted by the metal per unit area in unit time is……….Assume that each incident photon emits one electron. (h = 6.625 × 10–34 J.s) 

(A) 1.282 C 

(B) 12.82 C 

(C) 128.2 C 

(D) 1282 C

1 Answer

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Best answer

The correct option is (C) 128.2 C.

Explanation:

power of beam = 10–3 W and r = radius = 10–3 m

∴ amount of energy incident in unit time = 10–3 J

 ∴ E = {(nhc) / λ} = 10–3 hence n = {(10–3 λ) / hc}

∴ n = [{10–3 × 5000 × 10–10} / {6.625 × 10–34 × 3 × 108}]---(λ = 5000Å)

= 251.57 × 1013

n' = no of photons per unit area in one second

= [{251.57 × 1013} / {π(10–3)2}] = 80.11 × 1019

each photon emits 1 electron.

∴ amount of charge emitted per unit area in unit times is ɸ and ɸ = n' e

= 80.11 × 1019 × 1.6 × 10–19

 = 128.18 C

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