Chemistry - Atomic Structure Question with Solution | TestHub

$\frac{\frac{1}{{\mathrm{\lambda }}_2}={\mathrm{R}}_{\mathrm{H}}\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)}{\frac{1}{{\mathrm{\lambda }}_1}={\mathrm{R}}_{\mathrm{H}}\left(\frac{1}{{\mathrm{m}}_1^2}-\frac{1}{{\mathrm{m}}_2^2}\right)}$

As for shortest wavelengths,${\mathrm{n}}_2$and${\mathrm{m}}_2$is$\mathrm{\infty }$.
$\therefore \mathrm{ }\mathrm{ }\frac{{\mathrm{\lambda }}_1}{{\mathrm{\lambda }}_2}=\frac{9}{1}=\frac{{\mathrm{m}}_1^2}{{\mathrm{n}}_1^2}$

Now if${\mathrm{m}}_1=3$and${\mathrm{n}}_1=1$it will justify the statement hence Lyman and Paschen$\left(\mathrm{B}\right)$is correct.