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A hydrogen atom initially in the ground state absorbs a photon which excites it to n = 4 state. The frequency of the photon is

Options

  1. A3 . 1 x 10 15 Hz
  2. B3 . 1 × 10 14 Hz
  3. C9 . 7 × 10 15 Hz
  4. D9 . 7 × 10 14 Hz

Correct answer

A. 3 . 1 x 10 15 Hz

Step-by-step solution

For ground state n 1 = 1 to n 2 = 4 Energy absorbed by photon, E = E 2 - E 1 = + 13.6 1 n 1 2 - 1 n 2 2 × 1.6 × 10 - 19 J = 13.6 1 1 - 1 4 2 × 1.6 × 10 - 19 = 13.6 × 1.6 × 10 - 19 15 16 = 2 . 4 × 10 - 19 or E = h v = 20 . 4 x 10 - 19 J Frequency v = 20.4 × 10 - 19 h = 20.4 × 10 - 19 6.63 × 10 - 34 = 3 . 076 × 10 15 = 3 . 1 × 10 15 Hz

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