A beam of light has three wave lengths 4144 Å, 4972 Å and 6216 Å with a total intensity of 3.6 × 10^–3 W

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A beam of light has three wave lengths 4144 Å, 4972 Å and 6216 Å with a total intensity of 3.6 × 10–3 W equally distributed among the three wavelengths. This beam is incident on a area of 1 cm2 on a clean metal surface of work function 2.3 eV. It is given that each capable photon ejects one electron. The number of phoelectrons liberated in (Assume there is no loss of light due to reflection).

(1) 5.5 ×1011

(2) 11×1011

(3) 11×1012

(4) 11×1010

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Correct option : (1) 5.5×1011

Explanation :

The threshold wavelength will be given by

Hence light of wavelength 6216 Å will not emit photoelectrons from the metal surface. Since the total intensity of light is equally distributed among the wavelengths, the intensity which each wavelength will have is

Power incident on the surface due to each wavelength is

1.2×10–3 × 10–4 J/s (A = 10–4)

Power incident on 1 cm2 = P1 = 1.2×10–3×10–4 = 1.2×10–7 J/s

∴ The number of electrons emitted by λ1 = number of photon incident

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