Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H-atom is suitable for this purpose? $[\mathrm{R}_{\mathrm{H}}=1 \times 10^{5} \mathrm{~cm}^{-1}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}]$

(A) Paschen, $\infty \rightarrow 3$

(C) Balmer, $\infty \rightarrow 2$

(D) Lyman, $\infty \rightarrow 1$

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Atomic Structure

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

[R_{H} = 1 \times 1 0^{5} cm^{- 1}, h = 6.6 \times 1 0^{- 34} Js, c = 3 \times 1 0^{8} ms^{- 1}]

Answer: (A)

A wavelength of

900 nm = 9000 \overset{˚}{A}

lies in the infrared, the home of the Paschen series with transitions ending at

n = 3

. Its wavenumber is

\frac{1}{λ} = \frac{1}{9 \times 1 0 ^{- 5} cm} = 1.11 \times 1 0^{4} cm^{- 1}

. In the Rydberg relation

\frac{1}{λ} = R_{H} (\frac{1}{9} - \frac{1}{n _{2}^{2}})

with

R_{H} = 1 0^{5} cm^{- 1}

, the right side equals

1 0^{5} \times \frac{1}{9} = 1.11 \times 1 0^{4} cm^{- 1}

only when

\frac{1}{n _{2}^{2}} \to 0

, i.e.

n_{2} \to \infty

. The suitable line is the Paschen series limit, the transition from

\infty

3

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option