In a certain electronic transition in the hydrogen atoms from an initial state (1) to the final state (2), the difference in the orbital radius `(r_1 - r_2)` is 24 times the first Bohr radius. Identify the transition.

Options

A. `5 to 1`
B. `25 to 1`
C. `8 to 3`
D. `6 to 5`

Answer

A

Explanation

The radius of `n^(th)` orbit of the hydrogen atom `(Z = 1) r_n = r_0 xx n^2`
Where `r_0 = 0.529 Å` is constant and it is the Bohr radius of hydrogen in the ground state `r_1`
By given condition,
`r_(n_1)-r_(n_2) = 24 xx r_1`
`n_1^2xx r_0 - n_2^2xxr_0 = 24 xx r_0`
`implies n_1^2 -n_2^2 = 24`
By putting the different values of `n_1 and n_2` we check the set which can satisfy this.
When `n_1 = 5 and n_2 = 1 " then " 5^2 - 1^2 = 24`
So, the given relation satisfies for the transition of the initial state `n_1 = 5 " and final state " n_2 = 1`.