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The velocity of the electrons liberated by electromagnetic radiation of wavelength λ = 18 . 0 nm , from stationary He + ions in the ground state, is

Options

  1. A2 . 3 × 10 6 ms - 1
  2. B1 . 3 × 10 6 ms - 1
  3. C2 . 3 × 10 5 ms - 1
  4. D1 . 3 × 10 3 ms - 1

Correct answer

A. 2 . 3 × 10 6 ms - 1

Step-by-step solution

Step I : Determine binding energy of electron : As we know E ⁡ = - 1 3 . 6 Z 2 n 2 = - 1 3 . 6 2 2 1 2 For ground state = – 54.4 eV ∴ The binding energy of electron is E b = – E = 54.4 eV Step II : Determine kinetic energy of electron. ∴ T e ⁡ = h ⁡ c λ - E ⁡ b = 1 2 4 2 n meV 1 8 n m ⁡ - 5 4 . 4 eV = (69 – 54.4) eV = 14.6 eV = 23.36 × 10 –19 joule ∴ T ⁡ e ⁡ = 1 2 mv 2 v ⁡ = 2 T e ⁡ m ⁡ = 2 × 2 3 . 3 6 × 1 0 - 1 9 9 . 1 × 1 0 - 3 1 m/s = 2 . 3 × 1 0 6 m/s

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