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 [2025]

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Q.
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 $R_{H} = 10^{5} {cm}^{- 1},$ $h = 6.6 \times 10^{- 34} Js,$ $c = 3 \times 10^{8} m/s$ [2025]

1 Lyman series, $\infty \to 1$

2 Balmer series, $\infty \to 2$

3 Paschen series, $5 \to 3$

4 Paschen series, $\infty \to 3$

Ans.
(4)

$λ = 900 nm = 900 \times 10^{- 9} m$

$= 900 \times 10^{- 9} m \times 100 cm = 9 \times 10^{- 5} cm$

$R_{H} = 10^{5} {cm}^{- 1}$

By Rydberg’s equation:

$\frac{1}{λ} = R_{H} Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

$\frac{1}{9 \times 10^{- 5} cm} = 10^{5} {cm}^{- 1} \times {(1)}^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$

$(\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) = \frac{1}{9}$

$n_{1} = 3, n_{2} = \infty$

Solution

Q.
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 $R_{H} = 10^{5} {cm}^{- 1},$ $h = 6.6 \times 10^{- 34} Js,$ $c = 3 \times 10^{8} m/s$ [2025]

1 Lyman series, $\infty \to 1$

2 Balmer series, $\infty \to 2$

3 Paschen series, $5 \to 3$

4 Paschen series, $\infty \to 3$

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Solution

Q. 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 RH=105 cm-1, h=6.6×10-34Js, c=3×108m/s [2025]

1 Lyman series, ∞→1

2 Balmer series, ∞→2

3 Paschen series, 5→3

4 Paschen series, ∞→3

Ans. (4) λ=900 nm=900×10-9m =900×10-9m×100 cm=9×10-5cm RH=105cm-1 By Rydberg’s equation: 1λ=RHZ2(1n12-1n22) 19×10-5cm=105cm-1×(1)2(1n12-1n22) (1n12-1n22)=19 n1=3, n2=∞

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Q.
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 $R_{H} = 10^{5} {cm}^{- 1},$ $h = 6.6 \times 10^{- 34} Js,$ $c = 3 \times 10^{8} m/s$ [2025]

1 Lyman series, $\infty \to 1$

2 Balmer series, $\infty \to 2$

3 Paschen series, $5 \to 3$

4 Paschen series, $\infty \to 3$