Chemistry - Atomic Structure Question with Solution | TestHub

For hydrogen atom : 

For Lyman series ${\mathrm{n}}_1=1 \& {\mathrm{n}}_2=\infty$

$\frac{1}{{\mathrm{\lambda }}_{\mathrm{H}}}=Rr\left[\frac{1}{1}-\frac{1}{\infty }\right] \text{ So, } \mathrm{\lambda }=\frac{1}{{\mathrm{R}}_{\mathrm{H}}}$

For ${\mathrm{He}}^{+}\text{ion }$

Balmer series ${\mathrm{n}}_1=2 \& {\mathrm{n}}_2=3$

$\frac{1}{{\mathrm{\lambda }}_{{\mathrm{He}}^{+}}}={\mathrm{R}}_{\mathrm{H}}\times {\mathrm{Z}}^2\left[\frac{1}{4}-\frac{1}{9}\right]$

$\frac{1}{{\mathrm{\lambda }}_{{\mathrm{He}}^{+}}}={\mathrm{R}}_{\mathrm{H}}\times 4\times \frac{5}{36}$

$\frac{1}{{\mathrm{\lambda }}_{{\mathrm{He}}^{+}}}=\frac{5}{9}{\mathrm{R}}_{\mathrm{H}}=\left(\frac{5}{9}\right)\frac{1}{\mathrm{\lambda }}$

$\left({\mathrm{\lambda }}_{{\mathrm{He}}^{+}}\right)=\frac{9}{5}\mathrm{\lambda }$