The electron in a hydrogen atom makes a transition from $n = n_{1}$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 of $n_{1}$and $n_{2}$ are

Question

Dr. Abubacker · Accepted Answer

(b) According to Kepler’s 3rd law.
$T^{2} \propto r^{3}$
$	herefore\ \frac{T_{1}}{T_{2}} = \left( \frac{r_{1}}{r_{2}} ight)^{3/2} = 8$
$\frac{r_{1}}{r_{2}} = 8^{2/3} = 4$
According to Bohr atom model, $r \propto n^{2}$
$	herefore\ \frac{n_{1}^{2}}{n_{2}^{2}} = \frac{r_{1}}{r_{2}} = 4;\ \frac{n_{1}}{n_{2}} = 2$
If $n_{1} = 2$, then $n_{2} = 1$

Q. The electron in a hydrogen atom makes a transition from $n = n_{1}$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 of $n_{1}$and $n_{2}$ are

Explanation

Reviewed by Dr. Abubacker

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