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

We need to find which spectral line of the hydrogen atom produces radiation of wavelength about 900 nm. The Rydberg formula is:

$$ \frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) $$

Given: $$\lambda = 900$$ nm $$= 9 \times 10^{-5}$$ cm, $$R_H = 10^5$$ cm$$^{-1}$$. Therefore,

$$ \frac{1}{\lambda} = \frac{1}{9 \times 10^{-5}} = \frac{10^5}{9} \text{ cm}^{-1} $$

For the Paschen series (where $$n_1 = 3$$) in the limit $$n_2 \to \infty$$, the formula gives

$$ \frac{1}{\lambda} = R_H \left(\frac{1}{9} - 0\right) = \frac{10^5}{9} \text{ cm}^{-1} $$

Since this matches the calculated value of $$\frac{1}{\lambda}$$, the wavelength 900 nm corresponds to the series limit of the Paschen series ($$\infty \to 3$$). The correct answer is Option 3: Paschen series, $$\infty \rightarrow 3$$.