Question

The wavelength of the first line of the Balmer series of $H{e}^{+}$ ion is x times the last line . x is

Answer 1

Balmer series can be resulted in transitions from $(n_2=3,4,5,6etc)$ to $n_1=2$
The first line corresponds to transition from $n_2=3$ to $n_1=2$
The last line corresponds to transition from $n_2=\infty$ to $n_1=2$

$\frac{1}{{\lambda }_{\text{1}}}=4R(\frac{1}{4}-\frac{1}{9})$
$\frac{1}{{\lambda }_{\infty }}=4R(\frac{1}{4}-\frac{1}{{\infty }^2})$

$\frac{{\lambda }_1}{{\lambda }_{\infty }}=\frac{36}{20}=1.8$