JEE MAIN - Chemistry (2025 - 23rd January Morning Shift - No. 19)
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 $\left.\mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$
Explanation
$$\begin{array}{ll} \lambda=900 \mathrm{~nm} & \text { H-atom }(\mathrm{Z}=1) \\ =9 \times 10^{-5} \mathrm{~cm} \\ \mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1} & \end{array}$$
$$\begin{aligned} & \text { Ryderg eq. }=\frac{1}{\lambda}=\mathrm{R}_{\mathrm{H}} \mathrm{Z}^2 \times\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\ & \Rightarrow \frac{1}{\lambda \times \mathrm{R}_{\mathrm{H}}}=\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2} \\ & \Rightarrow \frac{1}{9 \times 10^{-5} \mathrm{~cm} \times 10^5 \mathrm{~cm}^{-1}}=\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\ & \Rightarrow \frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}=\frac{1}{9} \end{aligned}$$
It is possible when $n_1=3, n_2=\infty$
Possible series: $\infty \rightarrow 3$
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