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MHT CET202519 Apr 2025Morning ShiftPhysicsAtomic PhysicsActual

The ratio of the wavelength of the last line of Paschen series to that of Balmer series is

Options

  1. A9 4
  2. B3 2
  3. C2 3
  4. D4 9

Correct answer

A. 9 4

Step-by-step solution

The wavelength of spectral lines in the hydrogen atom follows the Rydberg formula: 1 = R ( 1 n_f^2 - 1 n_i^2 ) , where R is the Rydberg constant, n_f is the final quantum number, and n_i is the initial quantum number. For the Balmer series, n_f = 2 , and the last line corresponds to n_i = . Its wavelength is _B = 4 R . For the Paschen series, n_f = 3 , and the last line also corresponds to n_i = , yielding _P = 9 R . The ratio is _P _B = 9/ R 4/ R = 9 4 . Answer: A

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