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 R_H=10⁵ cm⁻¹, h=6.6 × 10⁻³⁴ J s, c=3 × 10⁸ m / s)

Solution

Chemistry ma’am · 3 steps

Put each transition into the Rydberg formula and see which one gives exactly 900 nm.

1. Rydberg formula. For a hydrogen electron falling from level n₂ to level n₁, the wavenumber of the emitted line is given below. You do not need h or c here, because the question asks only for a wavelength.

   1/λ = R_H(1/n₁²-1/n₂²), R_H = 10⁵ cm⁻¹

2. Unit check. Since 1 cm = 10⁷ nm, a wavelength of 10⁻⁵ cm is 100 nm. For n₂ = ∞, the term 1/n₂² becomes zero.

   Option	1/λ (cm⁻¹)	λ	Region
   (a) ∞ → 1	10⁵ × 1	100 nm	ultraviolet
   (b) ∞ → 2	10⁵ × 1/4	400 nm	edge of visible
   (c) 5 → 3	10⁵ × 16/225	about 1406 nm	infrared
   (d) ∞ → 3	10⁵ × 1/9	900 nm	near infrared

3. So. Only the Paschen series limit, ∞ → 3, gives λ = 9 × 10⁻⁵ cm = 900 nm. The answer is (d).

The idea to keep. Lyman lines lie in the UV, Balmer lines in the visible and Paschen lines in the infrared. Within a series, the ∞ transition gives the shortest wavelength, λ = n₁²/R_H.

Answer from the NTA final answer key. Solution by PrepWiser.