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A silver ball of radius 4.8 cm is suspended by a thread in a vacuum chamber. UV light of wavelength 200 nm is incident on the ball for some time during which total energy of 1 × 10 – 7 J falls on the surface. Assuming that on an average, one out of 10 3 photons incident on the ball is able to eject an electron, then the potential of the sphere will be

Options

  1. A1   V
  2. B2   V
  3. C3 V
  4. Dzero

Correct answer

C. 3 V

Step-by-step solution

The total number of photons striking the surface of the ball is n p = E λ h c = 1   ×   10 - 7 × 200 × 10 - 9 6 .6 × 10 - 34 × 3 × 10 8 = 1 × 10 11 The total number of electrons ejected is n e = 1 0 11 1 0 3 = 1 0 8 ∴ V = q 4 πε 0 r = 10 8 × 1 .6 × 10 - 19 × 9 × 10 9 4 .8 × 10 - 2 = 3   V

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