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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 purpose?
$[R_{H} = 1 \times 10^{5} {cm}^{- 1}, h = 6 .6 \times 10^{- 34} Js, c = 3 \times 10^{8} {ms}^{- 1}]$

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a

Paschen, $5 \to 3$

b

Balmer, $\infty \to 2$

c

Paschen, $\infty \to 3$

d

Lyman, $\infty \to 1$

answer is B.

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Detailed Solution

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$\frac{1}{λ} = R_{H} Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

= $10^{5} \times 1^{2} [\frac{1}{3^{2}} - \frac{1}{\infty^{2}}]$

$λ$ = 9 x 10^-5 cm = 9 x 10^-5 cm x 10⁷nm/cm = 900 nm

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Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H-atom is suitable for this purpose?[RH=1×105 cm−1, h=6.6×10−34 Js, c=3×108 ms−1]