Question

The time period for revolution of electron in a Hydrogen atom state $n_1$ is $T_1$ and time period for revolution of electron in higher orbit $n_2$ is $T_2$. If $\frac{T_2}{T_1}=27$. Which values of $n_1$ and $n_2$ are not possible?

• A. $n_1=2,n_2=6$
• B. $n_1=3,n_2=6$
• C. $n_1=3,n_2=9$
• D. $n_1=4,n_2=12$

Answer 1

The correct option is B $n_1=3,n_2=6$

We know, period of revolution $T\propto \frac{n^3}{Z^2}$
where n is the orbit number and Z is the atomic number.
Since, Z = 1 for Hydrogen
So, $\frac{T_2}{T_1}={\left(\frac{n_2}{n_1}\right)}^3=27$ where $n_1$ and $n_2$ are the orbit numbers.

$\Rightarrow \frac{n_2}{n_1}=3$