BITSAT Physics Question (2024) — Solution

Step-by-step solution

Let the transition of electron in hydrogen atom (Z=1) gives wavelength _1 for transition from n_2 to n_1, then 1 =R Z^2 ( 1 m^2 - 1 n^2 ) Here, = _1, Z=1, m=n_1, n=n_2 1 _1 =R(1)^2 ( 1 n_1^2 - 1 n_2^2 )=R ( 1 n_1^2 - 1 n_2^2 ) Now, if electron makes transition in He ^ + ion from n_4 to n_3 and gives wavelength _2, then aligned 1 _2 & =R(2)^2 ( 1 n_3^2 - 1 n_4^4 ) \\ & =R [ 1 ( n_3 2 )^2 - 1 ( n_4 2 )^2 ] aligned Given that, _1= _2 R ( 1 n_1^2 - 1 n_2^2 )=R [ 1 ( n_3 2 )^2 - 1 ( n_4 2 )^2 ] On comparing beth sides, we get n_1= n_3 2 and n_2= n_4 2 The value of n_1, n_2, n_3 and n_4 must be an integer, as they denote principal quantum number. If n_3=2 and n_4=4, then the given condition is satisfied.