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  4. 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]

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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 ?
$[R_H = 1 \times 10^5 \; cm^{-1}, h = 6.6 \times 10^{-34} \; Js, c = 3 \times 10^8 \; ms^{-1}]$

JEE MainJEE Main 2019Structure of Atom

Solution:

We have,
$\frac{1}{\lambda}=R Z^{2}\left(\frac{1}{n_{l}{ }^{2}}-\frac{1}{n_{f}{ }^{2}}\right)$
Here if $n _{l}=3$ and $n _{ f }=\infty$
$\frac{1}{\lambda}=10^{-7} \times 1^{2}\left(\frac{1^{2}}{3}-\frac{1}{\infty^{2}}\right)=\frac{10^{-7}}{9}=900\, mm$