Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of hydrogen atom is suitable for this?

Hydrogen Spectral Line for Heat Treatment | JEE Mains PYQ | Structure of Atom

Q. Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of hydrogen atom is suitable for this?

Given:
Rydberg constant, R_H = 10⁵ cm⁻¹
h = 6.6 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s

Choose the correct answer from the options given below:

A. Lyman series, ∞ → 1

B. Balmer series, ∞ → 2

C. Paschen series, 5 → 3

D. Paschen series, ∞ → 3

Explanation

Step 1: Identify wavelength region

Given wavelength ≈ 900 nm lies in the infrared region.

Step 2: Hydrogen spectral series

Lyman series → Ultraviolet (n = 1)
Balmer series → Visible (n = 2)
Paschen series → Infrared (n = 3)

Step 3: Series limit calculation

For Paschen series (∞ → 3):
1/λ = R_H (1/3² − 0) = R_H/9

λ = 9 / R_H = 9 × 10⁻⁵ cm = 900 nm

✔ This exactly matches the required wavelength.

Correct Answer = Paschen series, ∞ → 3

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