Balmer series

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Two of the balmer lines (α and β) are clearly visible in this emission spectrum of a deuterium lamp.

The Balmer series or Balmer lines in atomic physics, is the designation of one of a set of six different named series describing the spectral line emissions of the hydrogen atom.

The Balmer series is calculated using the Balmer formula, an empirical equation discovered by Johann Balmer in 1885. The visible spectrum of light from hydrogen displays four wavelengths, 410 nm, 434 nm, 486 nm, and 656 nm, that reflect emissions of photons by electrons in excited states transitioning to the quantum level described by the principal quantum number n equals 2.

1 Overview
2 Balmer's formula
3 Role in astronomy
4 See also
5 External links

[edit] Overview

The Balmer series is characterized by the electron transitioning from n ≥ 3 to n = 2, where n refers to the radial quantum number or principal quantum number of the electron. 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. As the spectral lines associated with this series are located in the visible part of the electromagnetic spectrum, these lines are historically referred to as H-alpha, H-beta, H-gamma and H-delta where H is the element hydrogen.

Balmer Series (Second) (visible light) n=2 limit = 365 nm

n = 3, λ = 656.3 nm, α, color emitted: red

n = 4, λ = 486.1 nm, β, color emitted: bluegreen

n = 5, λ = 434.1 nm, γ, color emitted: violet

n = 6, λ = 410.2 nm, δ, color emitted: violet

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 absorption/emission lines of hydrogen with high accuracy. Balmer's equation led physicists to find the Lyman, Paschen, and Brackett series which predicted other absorption/emission lines found outside the visible spectrum.

The familiar red H-alpha line of hydrogen which is the transition from the shell n=3 to the Balmer series shell n=2 is one of the conspicuous colors of the universe contributing a bright red line to the spectra of star forming regions.

Later, it was discovered that when the spectral lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely-spaced doublets. This splitting is called fine structure. It was also found that excited atoms could jump to the Balmer series n=2 from orbitals where n was greater than 6 emitting shades of violet.

[edit] Balmer's formula

Balmer noticed that a single number had a relation to every line in the hydrogen spectrum that was in the visible light region. That number was 364.56 nm. When any integer higher than 2 was squared and then divided by itself minus 4, then that number multiplied by 364.56 gave a wavelength of another line in the visible hydrogen spectrum. By this formula he was able to show that certain measurements of lines made in his time by spectroscopy were slightly inaccurate measurements and his formula predicted lines that were later found although had not yet been observed. His number also proved to be the limit of the series.

The formula discovered by Balmer could be used to find the wavelength of the absorption/emission lines and was originally presented as follows:

$\lambda\ = \frac{ hm^2 }{ (m^2 - n^2) }$

Where

λ

is the wavelength.

h is a constant with the value of 3.6456×10^-7 m or 364.56 nm.

n is equal to 2

m is an integer such that m > n.

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 is as follows:

$\frac{1}{\lambda} = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right), n=3,4,5,...$

where λ is the wavelength of the absorbed/emitted light and R_H is the Rydberg constant for hydrogen. The Rydberg constant for an infinitely heavy nucleus is 10,973,735.3 m⁻¹.

[edit] Role in astronomy

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. Astrophysicists are able to use the Balmer lines to help determine the age of stars because younger stars are composed almost entirely of hydrogen, while older stars have greater quantities of heavier elements due to nuclear fusion. All elements have unique spectral lines, so careful analysis of the absorption/emission lines can give clues to the relative age of stars.

Balmer lines can appear in absorption or emission. In stars they are absorption lines, and they are "strongest" when radiating from a star with a temperature in excess of 10,000 kelvins. In AGNs, H II regions and planetary nebulae, they are emission lines.