Question

What is the longest wavelength of light that can be absorbed by a hydrogen atom that is initially in the first excited state?

Answer 1

The energy differences between levels in the Bohr model, and hence the wavelengths of emitted/absorbed photons, is given by the Rydberg formula:^[3]

=R -- ( ) R-1.097373 × 107 m-1

where n is the upper energy level, n? is the lower energy level, and R is the Rydberg constant.^[4] Meaningful values are returned only when n is greater than n? and the limit of one over infinity is taken to be zero.

Balmer series (n? = 2)[edit]

Main article: Balmer series

n	? (nm)
3	656.3
4	486.1
5	434.0
6	410.2
7	397.0
$\infty$	365

Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict the Balmer series, in 1885. Balmer lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen.^[7] Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen.