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The surface of a metal is illuminated alternately with photons of energies E 1 = 4   eV and E 2 = 2 . 5   eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2 . The work function of the metal in ( eV ) is..........

Correct answer

2

Step-by-step solution

Given, Energy of two photons are E 1 = 4   eV and E 2 = 2 . 5   eV The ratio of maximum speeds of the photoelectrons emitted in the two cases is v 1 v 2 = 2 Using Einstein equation of photoelectric effect, K E m a x = 1 2 m v 2 = E - ϕ     . . . ( 1 ) Where, ϕ is the work function of metal and E is the energy of photon Now using equation for both the cases we get, 1 2 m v 1 2 = 4 - ϕ    … ( 2 ) 1 2 m v 2 2 = 2 . 5 - ϕ     . . . ( 3 ) Dividing equatio

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