Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this ?
Given: Rydberg constant $\left.{\mathrm{R}}_{\mathrm{H}}={10}^5{\mathrm{cm}}^{-1},\mathrm{h}=6.6\times {10}^{-34}\mathrm{Js},\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}\right)$

$\begin{array}{l}\lambda =900\mathrm{nm} \text{ H-atom }(\mathrm{Z}=1)\\ =9\times {10}^{-5}\mathrm{cm}\\ {\mathrm{R}}_{\mathrm{H}}={10}^5{\mathrm{cm}}^{-1}\\ \text{ Ryderg eq. }=\frac{1}{\lambda }={\mathrm{R}}_{\mathrm{H}}{\mathrm{Z}}^2\times \left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)\\ \Rightarrow \frac{1}{\lambda \times {\mathrm{R}}_{\mathrm{H}}}=\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\\ \Rightarrow \frac{1}{9\times {10}^{-5}\mathrm{cm}\times {10}^5{\mathrm{cm}}^{-1}}=\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)\\ \Rightarrow \frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}=\frac{1}{9}\end{array}$

It is possible when n₁ = 3, n₂ =∞
Possible series : ∞→3