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)

$T\propto \frac{r}{v}\propto \frac{n^2}{z}\times \frac{n}{z}\propto \frac{n^3}{z^2}$
$\frac{T_1}{T_2}=\frac{n_1^3}{n_3^3}=\frac{1}{8}$
$T_2=8T_1$
$=8\times 1.6\times 10^{-16}=12.8\times 10^{-16}$
$f_2=\frac{1}{12.8\times 10^{-16}}\approx 7.8\times 10^{14}$