The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 × 10–16 s. The frequency of revolution of the electron in its first excited state (in s

Engineering

Physics

Spectrum of Hydrogen and Hydrogen Like Atoms

Question

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 × 10^–16 s. The frequency of revolution of the electron in its first excited state (in s^–1) is :

1.6 × 10¹⁴

5.6 × 10¹²

7.8 × 10¹⁴

6.2 × 10¹⁵

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$T \propto \frac{r}{v} \propto \frac{n^{2}}{z} \times \frac{n}{z} \propto \frac{n^{3}}{z^{2}}$

$\frac{T_{1}}{T_{2}} = \frac{n_{1}^{3}}{n_{2}^{3}} = \frac{1}{8}$

T₂ = 8T₁

= 8 × 1.6 × 10^–16 = 12.8 × 10^–16

^{$f_{2} = \frac{1}{12 .8 \times 10^{- 16}} \approx 7 .8 \times 10^{14}$}