TheBalmer series, orBalmer lines inatomic physics, is one of a set ofsix named series describing thespectral line emissions of thehydrogen atom. The Balmer series is calculated using the Balmer formula, anempirical equation discovered byJohann Balmer in 1885.
The visiblespectrum oflight fromhydrogen displays fourwavelengths, 410 nm, 434 nm, 486 nm, and 656 nm, that correspond to emissions ofphotons byelectrons in excited states transitioning to the quantum level described by theprincipal quantum numbern equals 2.[1] There are several prominentultraviolet 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 otherhydrogen spectral series were discovered, corresponding to electrons transitioning to values ofn other than two.
The Balmer series is characterized by theelectron transitioning fromn ≥ 3 ton = 2, wheren refers to theradial quantum number orprincipal quantum number of the electron. The transitions are named sequentially by Greek letter:n = 3 ton = 2 is called H-α, 4 to 2 is H-β, 5 to 2 is H-γ, and 6 to 2 is H-δ. As the first spectral lines associated with this series are located in the visible part of theelectromagnetic spectrum, these lines are historically referred to as "H-alpha", "H-beta", "H-gamma", and so on, where H is the element hydrogen.
| Transition ofn | 3→2 | 4→2 | 5→2 | 6→2 | 7→2 | 8→2 | 9→2 | ∞→2 |
|---|---|---|---|---|---|---|---|---|
| Name | H-α / Ba-α | H-β / Ba-β | H-γ / Ba-γ | H-δ / Ba-δ | H-ε / Ba-ε | H-ζ / Ba-ζ | H-η / Ba-η | Balmer break |
| Wavelength (nm, air) | 656.279[2] | 486.135[2] | 434.0472[2] | 410.1734[2] | 397.0075[2] | 388.9064[2] | 383.5397[2] | 364.5 |
| Energy difference (eV) | 1.89 | 2.55 | 2.86 | 3.03 | 3.13 | 3.19 | 3.23 | 3.40 |
| Color | Red | Cyan | Blue | Violet | (Ultraviolet) | (Ultraviolet) | (Ultraviolet) | (Ultraviolet) |
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 theRydberg equation as a generalization of it, and this in turn led physicists to find theLyman,Paschen, andBrackett series, which predicted other spectral lines of hydrogen found outside thevisible spectrum.
The redH-alpha spectral line of the Balmer series of atomic hydrogen, which is the transition from the shelln = 3 to the shelln = 2, is one of the conspicuous colours of theuniverse. It contributes a bright red line to the spectra ofemission or ionisation nebula, like theOrion Nebula, which are oftenH II regions found in star forming regions. 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. This splitting is calledfine structure. It was also found that excited electrons from shells withn greater than 6 could jump to then = 2 shell, emitting shades of ultraviolet when doing so.
Balmer noticed that a single wavelength had a relation to every line in the hydrogen spectrum that was in the visiblelight region. That wavelength was364.50682 nm. When any integer higher than 2 was squared and then divided by itself squared minus 4, then that number multiplied by364.50682 nm (see equation below) gave the wavelength of another line in the hydrogen spectrum. By this formula, he was able to show that some measurements of lines made in his time byspectroscopy were slightly inaccurate, and his formula also predicted lines that had not yet been observed but were found later. His number also proved to be the limit of the series.The Balmer equation could be used to find thewavelength of the absorption/emission lines and was originally presented as follows (save for a notation change to give Balmer's constant asB):Where
In 1888 the physicistJohannes Rydberg generalized the Balmer equation for all transitions of hydrogen. The equation commonly used to calculate the Balmer series is a specific example of theRydberg formula and follows as a simple reciprocal mathematical rearrangement of the formula above (conventionally using a notation ofm forn as the single integral constant needed):
whereλ is the wavelength of the absorbed/emitted light andRH is theRydberg constant for hydrogen. The Rydberg constant is seen to be equal to4/B in Balmer's formula, and this value, for an infinitely heavy nucleus, is4/3.6450682×10−7 m =10973731.57 m−1.[3]
The Balmer series is particularly useful inastronomy because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in theuniverse, and therefore are commonly seen and relatively strong compared to lines from other elements. The first two Balmer lines correspond to theFraunhofer lines C and F.
Thespectral classification of stars, which is primarily a determination of surface temperature, is based on the relative strength of spectral lines, and the Balmer series in particular is very important. Other characteristics of a star that can be determined by close analysis of its spectrum includesurface gravity (related to physical size) and composition.
Because the Balmer lines are commonly seen in the spectra of various objects, they are often used to determineradial velocities due todoppler shifting of the Balmer lines. This has important uses all over astronomy, from detectingbinary stars,exoplanets, compact objects such asneutron stars andblack holes (by the motion of hydrogen inaccretion 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 (actuallyredshifts) of galaxies orquasars, and identifying unfamiliar objects by analysis of their spectrum.
Balmer lines can appear asabsorption oremission lines in a spectrum, depending on the nature of the object observed. Instars, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000kelvins (spectral type A). In the spectra of most spiral and irregular galaxies,active galactic nuclei,H II regions andplanetarynebulae, the Balmer lines are emission lines.
In stellar spectra, the H-epsilon line (transition 7→2, 397.007 nm) is often mixed in with another absorption line caused by ionizedcalcium known as "H" (theoriginal designation given byJoseph von Fraunhofer). H-epsilon is separated by 0.16 nm from Ca II H at 396.847 nm, and cannot be resolved in low-resolution spectra. The H-zeta line (transition 8→2) is similarly mixed in with a neutralhelium line seen in hot stars.