If an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength . When it jumps from the second to the first orbit, the corresponding wavelength of the photon will be

Step-by-step solution

The Rydberg formula for the wavelength of a photon emitted during an electronic transition in a hydrogen atom is given by 1 = R ( 1 n_f^2 - 1 n_i^2 ) , where R is the Rydberg constant. For the transition from the third orbit ( n_i = 3 ) to the second orbit ( n_f = 2 ), the wavelength is given by: 1 = R ( 1 2^2 - 1 3^2 ) = R ( 1 4 - 1 9 ) = R ( 9 - 4 36 ) = 5R 36 For the transition from the second orbit ( n_i = 2 ) to the first orbit ( n_f = 1 ), let the wavelength be ' . Then: 1 ' = R ( 1 1^2 - 1 2^2 ) = R ( 1 - 1