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Question:

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

Lyman,∞→1

Paschen,5→3

Paschen,∞→3

Balmer,∞→2

Solution:

We have, 1/λ = RZ²(1/nl² - 1/nf²)
Here if nl=3 and nf = ∞
1/λ = 109677 cm⁻¹ × 1²(1/3² - 1/∞²) = 109677/9 cm⁻¹ = 12186.33 cm⁻¹
λ = 1/12186.33 cm⁻¹ = 8.208 × 10⁻⁵ cm = 820.8 nm ≈ 900 nm
So, the correct option is Paschen, ∞→3