Question

The electron in hydrogen atom makes a transition from $n=n_1\text{to}n=n_2$ state. The time period of the electron in the initial state is eight times that in the final state. The possible values are

• A. $n_1=4,n_2=2$
• B. $n_1=8,n_2=2$
• C. $n_1=8,n_1=2$
• D. $n_1=6,n_2=2$

Answer 1

The correct option is A

$n_1=4,n_2=2$

$T=\frac{2\pi r}{v}\text{and}r\propto n^2,v\propto 1/n\Rightarrow T\propto n^3\frac{T_1}{T_2}={\left(\frac{n_1}{n_2}\right)}^{3}8={\left(\frac{n_1}{n_2}\right)}^{3}or\frac{n_1}{n_2}=2$