Heat treatment of muscular pain involves radiation of wavelength of...

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}

)

Options

ABalmer series, $\infty \rightarrow 2$
BLyman series, $\infty \rightarrow 1$
CPaschen series, $\infty \rightarrow 3$
DPaschen series, $5 \rightarrow 3$

Correct answer

C. Paschen series, $\infty \rightarrow 3$

Step-by-step solution

\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

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