The wavelength of radiation emitted is ' ' when an electron jumps from second to first orbit of hydrogen atom. For the electron to jump from third to first orbit of hydrogen atom, the wavelength of radiation emitted will be

Step-by-step solution

Using the Rydberg formula for the wavelength of emitted radiation: 1 = R ( 1 n₁^2 - 1 n₂^2 ) For the transition from the second to the first orbit ( n₂ = 2 , n₁ = 1 ): 1 = R ( 1 1^2 - 1 2^2 ) = R ( 1 - 1 4 ) = 3R 4 For the transition from the third to the first orbit ( n₂ = 3 , n₁ = 1 ), let the wavelength be ' : 1 ' = R ( 1 1^2 - 1 3^2 ) = R ( 1 - 1 9 ) = 8R 9 Dividing the two equations: ' = 3R 4 8R 9 = 3 4 9 8 = 27 32 ' = 27 32 Answer: 27 32