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Analysis and Interpretation of Astronomical Spectra 42
10 Wavelength and Energy
10.1 Planck’s Energy Equation
In the above wavelength-calibrated Sirius spectrum we want to calculate the
corresponding photon energies of the hydrogen lines. This is possible with
the familiar and simple equation of Max Planck (1858 – 1947):
Radiation Energy in Joule [J]
Planck’s Quantum of Action [6.626 10-34 J s]
(Greek: „nu“) Radiation frequency [s-1] of the spectral line.
The Radiation frequency of the spectral line is simply related to the wave-
length [m] ( = light speed 3 108 m/s):
Insert {9} into {8}:
The most important statement of formulas {8} and {10}: The radiation energy is propor-
tional to the radiation frequency and inversely proportional to the wavelength .
10.2 Units for Energy and Wavelength
To express such extremely low amounts of energy in Joules [J] is very impractical and not
easy to interpret. Joule has been defined to be applied in traditional mechanics. In quantum
mechanics and therefore also in spectroscopy, the units of electron volts [eV] is in use [5].
Further in the optical spectral domain also the wavelengths are extremely small and there-
fore in astronomy usually measured in angstroms [Å] or nanometres [nm]. One should be
aware that 1Å corresponds about to the diameter of an atom, including its electron shells!
In the infrared range also [μm] is in use:
,, ,,
Rather rarely, the frequency is also expressed as “Wavenumber” . This is the reciprocal
value of the wavelength , usually expressed somewhat “special” in number of waves
within
In the optical spectral domain, the wavelength is usually based on the standard atmos-
phere (atmospheric pressure 1013.25 hPa, temperature 15° C). The program SpectroTools
[413] by Peter Schlatter, enables also to convert vacuum wavelengths to this atmospheric
standard (or vice versa) and to demonstrate the temperature dependency of a measure-
ment. So it becomes clear why the calibration spectrum should, as quick as possible, be re-
corded immediately prior to, and/or after the object spectrum!
The following simple formulas, suitable for pocket calculators, allow to convert the wave-
length [Å] into energy [eV] and vice versa,:
