Brackett series

The Brackett series is the set of emission lines from atomic hydrogen gas, due to electrons descending from an electron shell of number n greater than 4 down to that of n = 4, 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 Frederick Sumner Brackett. The lines are within 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:

• 5 -> 4: 4051 nm
• 6 -> 4: 2625 nm
• 7 -> 4: 2166 nm
• 8 -> 4: 1944 nm
• 9 -> 4: 1817 nm
• ...
• infinity -> 4: 1458 nm

Formula for the wavelengths:

1/wavelength = RH ( 1/16 - 1/n² )

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