The electron in hydrogen atom makes a transition `n_(1)ton_(2)` where `n_1` and `n_2` are the principal quantum number of two states. Assuming the Bohr model to be valid, the time period of the electron in the initial state is eight times that in the final state. The possible value of `n_1` and `n_2` are:

Options

A. `n_1=4,n_2=2`
B. `n_1=8,n_2=2`
C. `n_1=8,n_2=1`
D. `n_1=6,n_2=2`

Answer

A

Explanation

In the `n^(th)` orbit , let `r_n=` radius and `v_n=` speed of electron.
Time period , `T_n=(2pir_n)/(v_n)prop (r_n)/(v_n)`
Now, `r_npropn^2` and `v_nprop(1)/(n)therefore (r_n)/(v_n)propn^3` or `T_npropn^3`.
Here, `8=((n_1)/(n_2))^3` or `(n_1)/(n_2)=2 ` or `n_1-2n_2`