The wavelength of the radiation emitted is ₀ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be (20 ₀/x) . The value of x is

Step-by-step solution

For the first transition, the electron jumps from the second excited state ( n=3 ) to the first excited state ( n=2 ). Using the Rydberg formula: 1 ₀ = R ( 1 2^2 - 1 3^2 ) = R ( 1 4 - 1 9 ) = 5R 36 R = 36 5 ₀ For the second transition, the electron jumps from the third excited state ( n=4 ) to the second orbit ( n=2 ). The wavelength is given by: 1 = R ( 1 2^2 - 1 4^2 ) = R ( 1 4 - 1 16 ) = 3R 16 = 16 3R Substituting the value of R from the first equation: = 16 3 ( 36 5 ₀ ) = 16 5 ₀ 3 36 = 80 ₀ 108 = 20 ₀ 27 Compar