Final answer:
The infrared radiation used for heat treatment of muscular pain at 900 nm is within the near-infrared spectrum and could be matched to the Balmer series of the hydrogen atom but normally comes from a broad spectrum source, not a specific spectral line.
Step-by-step explanation:
The heat treatment of muscular pain using infrared radiation at a wavelength of about 900 nm correlates to the use of electromagnetic energy for therapeutic purposes. When determining which spectral line of the hydrogen atom is suitable for emitting a wavelength of 900 nm, one needs to consider the different series of the hydrogen spectrum, such as the Lyman, Balmer, Paschen, Brackett, and Pfund series. For a wavelength of 900 nm, the Balmer series, specifically the transition from higher energy levels to the second energy level, would be suitable because the Balmer series corresponds to visible and near-infrared light, which includes wavelengths greater than 656 nm (the longest wavelength Balmer line, H-alpha) up to about 3646 nm (the series limit).
Using the Rydberg formula and the Rydberg constant (RH = 1\u00d7105 cm-1), one can calculate the energy levels associated with the spectral lines and their corresponding wavelengths. However, human-made devices like heat lamps and medical equipment often don't rely on specific spectral lines of hydrogen or other elements but instead use broader bands of IR radiation tuned to specific therapeutic wavelengths, like 900 nm.