Question

What is the ratio of time periods in the second orbit of the hydrogen atom $\left(T_H\right)$ to the fourth orbit of $H{e}^{+}$ ion $\left(T_{He}\right)$?

• A. $1:2$
• B. $2:1$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is A $1:2$

We know that,
$\text{Time period T}\propto \frac{n^3}{Z^2}$
where n = shell number and Z = atomic number of the element

$T_H/T_{He}=\frac{n_1^3{Z}_2^2}{n_2^3{Z}_1^2}$

$(\text{where},n_1=2,Z_1=1\&n_2=4,Z_2=2)$

$=\frac{\left(2{)}^3\right(2{)}^2}{\left(4{)}^3\right(1{)}^2}=\frac{32}{64}=\frac{1}{2}$
Hence,
$T_H/T_{He}=1:2$