Question

The time period of revolution of electron inits ground state orbit in a hydrogen atom is $1 .6 \times 10^{- 16}$ s. The frequency of revolution of the electron in its first excited state (in $s ^{- 1}$) is :

• A. $56 \times 10^{12}$
• B. $1.6 \times 10^{14}$
• C. $7.8 \times 10^{14}$
• D. $6.2 \times 10^{15}$

Answer 1

Answer: (C)

$T\,\propto\, \frac{r}{v}\propto \, \frac{n^{2}}{z}\times\frac{n}{z}\propto \, \frac{n^{3}}{z^{2}}$
$\frac{T_{1}}{T_{2}}=\frac{n^{3}_{1}}{n^{3}_{3}}=\frac{1}{8}$
$T_{2}=8T_{1}$
$=8\times1.6\times10^{-16}=12.8\times10^{-16}$
$f_{2}=\frac{1}{12.8\times10^{-16}} \approx7.8\times10^{14}$