Question

For Hydrogen atom the ratio of time required to complete $1$ revolution of electron in $I^{st},I{I}^{nd}$ and $II{I}^{rd}$ orbit respectively is:

• A. $1:8:27$
• B. $1:4:9$
• C. $1:2:3$
• D. $1:16:81$

Answer 1

The correct option is A $1:8:27$

Time required to complete $1$ revolution $=\frac{2\pi r}{v}$

$\because r\propto n^2$ and $v\propto \frac{1}{n}$

$\therefore$ $Time$ $required\propto n^3$

$\therefore$Ratio of time required in $I^{st},I{I}^{nd}$ and $II{I}^{rd}$ orbit is, $(1{)}^3:(2{)}^3:(3{)}^3$ i.e. $1:8:27$