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

Step-by-step solution

The Rydberg formula gives the wavelength of emitted radiation when an electron transitions between energy levels in a hydrogen atom: 1 = R ( 1 n_f^2 - 1 n_i^2 ) where R is the Rydberg constant. First transition: Second excited state ( n_i = 3 ) to first excited state ( n_f = 2 ). 1 = R ( 1 4 - 1 9 ) = R ( 5 36 ) Second transition: Third excited state ( n_i = 4 ) to second orbit ( n_f = 2 ). 1 ' = R ( 1 4 - 1 16 ) = R ( 3 16 ) Given ' = 20 x , substitute the expressions for and ' : 16 3R = 20 x 36 5R Cancel R and si