d
Wavelength of emitted photon from \(n^{\text {th }}\) state to the ground state, \(\frac{1}{\Lambda_{\mathrm{n}}}=R Z^{2}\left(\frac{1}{1^{2}}-\frac{1}{\mathrm{n}^{2}}\right)\)

\(\Lambda_{\mathrm{n}}=\frac{1}{R Z^{2}}\left(1-\frac{1}{\mathrm{n}^{2}}\right)^{-1}\)

since \(n\) is very large, using binomial theorem 

\(\Lambda_{n}=\frac{1}{R Z^{2}}\left(1+\frac{1}{n^{2}}\right)\)

\(\Lambda_{\mathrm{n}}=\frac{1}{R Z^{2}}+\frac{1}{R Z^{2}}\left(\frac{1}{\mathrm{n}^{2}}\right)\)

As we know, \(\lambda_{\mathrm{n}}=\frac{2 \pi \mathrm{r}}{\mathrm{n}}=2 \pi\left(\frac{\mathrm{n}^{2} \mathrm{h}^{2}}{4 \pi^{2} \mathrm{m} \mathrm{Ze}^{2}}\right) \frac{1}{\mathrm{n}} \propto \mathrm{n}\)

\(\Lambda_{\mathrm{n}} \approx \mathrm{A}+\frac{\mathrm{B}}{\lambda_{\mathrm{n}}^{2}}\)