Balmer series

[1] There are several prominent ultraviolet Balmer lines with wavelengths shorter than 400 nm.

The series continues with an infinite number of lines whose wavelengths asymptotically approach the limit of 364.5 nm in the ultraviolet.

After Balmer's discovery, five other hydrogen spectral series were discovered, corresponding to electrons transitioning to values of n other than two.

The transitions are named sequentially by Greek letter: n = 3 to n = 2 is called H-α, 4 to 2 is H-β, 5 to 2 is H-γ, and 6 to 2 is H-δ.

Although physicists were aware of atomic emissions before 1885, they lacked a tool to accurately predict where the spectral lines should appear.

The Balmer equation predicts the four visible spectral lines of hydrogen with high accuracy.

Balmer's equation inspired the Rydberg equation as a generalization of it, and this in turn led physicists to find the Lyman, Paschen, and Brackett series, which predicted other spectral lines of hydrogen found outside the visible spectrum.

In true-colour pictures, these nebula have a reddish-pink colour from the combination of visible Balmer lines that hydrogen emits.

Later, it was discovered that when the Balmer series lines of the hydrogen spectrum were examined at very high resolution, they were closely spaced doublets.

Balmer noticed that a single wavelength had a relation to every line in the hydrogen spectrum that was in the visible light region.

Where In 1888 the physicist Johannes Rydberg generalized the Balmer equation for all transitions of hydrogen.

The equation commonly used to calculate the Balmer series is a specific example of the Rydberg formula and follows as a simple reciprocal mathematical rearrangement of the formula above (conventionally using a notation of m for n as the single integral constant needed):

where λ is the wavelength of the absorbed/emitted light and RH is the Rydberg constant for hydrogen.

The Rydberg constant is seen to be equal to ⁠4/B⁠ in Balmer's formula, and this value, for an infinitely heavy nucleus, is ⁠4/3.6450682×10−7 m⁠ = 10973731.57 m−1.

[3] The Balmer series is particularly useful in astronomy because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the universe, and therefore are commonly seen and relatively strong compared to lines from other elements.

Other characteristics of a star that can be determined by close analysis of its spectrum include surface gravity (related to physical size) and composition.

This has important uses all over astronomy, from detecting binary stars, exoplanets, compact objects such as neutron stars and black holes (by the motion of hydrogen in accretion disks around them), identifying groups of objects with similar motions and presumably origins (moving groups, star clusters, galaxy clusters, and debris from collisions), determining distances (actually redshifts) of galaxies or quasars, and identifying unfamiliar objects by analysis of their spectrum.

The "visible" hydrogen emission spectrum lines in the Balmer series. H-alpha is the red line at the right. Four lines (counting from the right) are formally in the visible range . Lines five and six can be seen with the naked eye , but are considered to be ultraviolet as they have wavelengths less than 400 nm.
In the simplified Rutherford Bohr model of the hydrogen atom , the Balmer lines result from an electron jump between the second energy level closest to the nucleus, and those levels more distant. Shown here is a photon emission. The 3→2 transition depicted here produces H-alpha , the first line of the Balmer series. For hydrogen ( Z = 1) this transition results in a photon of wavelength 656 nm (red).
Two of the Balmer lines (α and β) are clearly visible in this emission spectrum of a deuterium lamp