NEET 2023, Physics Q23: The Line Spectra of the Hydrogen Atom

The shortest wavelength of a series corresponds to the transition from $n=\infty$ to the lower level.

Balmer (final $n=2$): $\frac{1}{\lambda }=R\left(\frac{1}{4}-0\right)=\frac{R}{4}$.

Bracket (final $n=4$): $\frac{1}{{\lambda }^{\prime }}=R\left(\frac{1}{16}-0\right)=\frac{R}{16}$.

Dividing: $\frac{{\lambda }^{\prime }}{\lambda }=4\Rightarrow {\lambda }^{\prime }=4\lambda$.