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 $\mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1},$ $\mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s},$ $\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}$

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Aicharya · Accepted Answer

$\begin{aligned}
& \lambda=900 \mathrm{~nm} \quad \text { H-atom }(\mathrm{Z}=1) \\
& =9 \times 10^{-5} \mathrm{~cm} \\
& \mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1} \\
& \text { Ryderg eq. }=\frac{1}{\lambda}=\mathrm{R}_{\mathrm{H}} \mathrm{Z}^2 \times\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\
& \Rightarrow \frac{1}{\lambda \times \mathrm{R}_{\mathrm{H}}}=\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2} \\
& \Rightarrow \frac{1}{9 \times 10^{-5} \mathrm{~cm} \times 10^5 \mathrm{~cm}^{-1}}=\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\
& \Rightarrow \frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}=\frac{1}{9}
\end{aligned}$
It is possible when $\mathrm{n}_1=3, \mathrm{n}_2=\infty$
Possible series : $\infty \rightarrow 3$

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H…

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