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A photon of wavelength 4 x 10-7 m strikes on metal surface, the work function of the metal being 2.13 eV. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy of the emission and (iii) the velocity of the photoelectron (1 eV = 1.6020 x 10-19 J).

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Wavelength of the photon, λ = 4 x 10-7 m

Work function of the metal, W = 2.13 eV = 2.13 x 1.6020 x 10-19 J

= 3.14 x 10-19 J

(i) Energy of photon = ch/λ = {3 x 108 ms-1 x 6.626 x 10-34 Js}/{4 x 10-7 m}

= 4.97 x 10-19 J

= {4.97 x 10-19 J}/{1.6020 x 10-19 J/eV} = 3.10 eV

(ii) Kinetic energy of the emission = Ephoton - W

= 4.97 x 10-19 J - 3.41 x 10-19 J

= 1.56 x 10-19 J

= 3.10 eV - 2.13 eV = 0.97 eV

(iii) Kinetic energy of the emitted photoelectron = 1/2 m x v2

or,

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