Question

What is the ratio of time periods $\left(T_1/T_2\right)$ in second orbit of hydrogen atom to third orbit of $H{e}^{+}$ ion?

• A. $\frac{8}{27}$
• B. $\frac{32}{27}$
• C. $\frac{27}{32}$
• D. $\frac{16}{27}$

Answer 1

The correct option is B $\frac{32}{27}$

We know that the time period $T\propto \frac{n^3}{Z^2}$
$\therefore \frac{T_1}{T_2}=\frac{n_1^3}{Z_1^2}\times \frac{Z_2^2}{n_2^3}=\frac{2^3}{1}\times \frac{2^2}{3^3}=\frac{32}{27}$