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

🧠 The Infrared Match 900 nm is in the Infrared region. In the Hydrogen spectrum, transitions ending at $n=1$ (Lyman) are UV, and those ending at $n=2$ (Balmer) are mostly Visible. For muscular pain (heat treatment), we need Infrared, which corresponds to the Paschen series ($n=3$).

🗺️ The Calculation Verification

1. Given $R_H$: $1 \times 10^5 \text{ cm}^{-1} = 10^7 \text{ m}^{-1}$ (This is an approximation for $1.097 \times 10^7$).
2. Testing Paschen Limit ($n = \infty \to 3$): $\bar{\nu} = R \left( \frac{1}{3^2} - 0 \right) = \frac{10^5}{9} \text{ cm}^{-1}$
3. Wavelength: $\lambda = \frac{9}{10^5} \text{ cm} = 9 \times 10^{-5} \text{ cm} = 900 \text{ nm}$ This matches the criteria exactly.

⚡ The "Heat = IR" Logic In competitive exams, remember:

• Lyman = Sterilization/UV
• Balmer = Vision/Light
• Paschen/Brackett = Muscular Pain/Remotes/Heat/Infrared The "900 nm" value is a huge hint. 700+ nm is IR. Paschen starts there.

⚠️ Common Traps Don't get tricked into calculating the frequency! The question gives $\lambda = 900$ nm. Use the Rydberg formula in its wave number form directly. Using the given simplified $R_H$ value is critical; using $1.097$ would give $\sim 820$ nm, which might make you doubt your answer.

$\boxed{\text{Answer: (A)}}$