Paschen series

The Paschen series is the set of emission lines from atomic hydrogen gas, due to electrons descending from an electron shell of number n greater than 3 down to that of n = 3, or the analogous absorption lines when absorbed electromagnetic radiation (EMR) makes electrons do the opposite. It is one of the hydrogen line series, such as the Lyman series and Balmer series, and is named after Friedrich Paschen. The lines are within near infrared and some are within atmospheric windows, so given no redshift, some of the lines in astronomical sources may be viewed from ground telescopes while others are blocked. Lines:

• 4 -> 3: 1875 nm
• 5 -> 3: 1282 nm
• 6 -> 3: 1094 nm
• 7 -> 3: 1005 nm
• 8 -> 3: 995 nm
• 9 -> 3: 923 nm
• ...
• infinity -> 3: 820 nm

Formula for wavelengths:

1/wavelength = RH ( 1/9 - 1/n² )

• wavelength is that of a Paschen series line.
• R_H is the Rydberg constant for hydrogen, 1.0973731568160 × 10⁷m^-1 ≈ 13.6 eV / (hc)
• n is the higher electron shell number.
• h - Planck constant.
• c - speed of light in a vacuum.