K.E. Johansson

Stockholm House of Science and Department of Physics, Stockholm University and 

 Department of Astronomy, Stockholm University 

Analysis of the temperature of the photosphere and determine the temperature by students using CCD spectrometers.

The main process responsible for the energy production in the Sun is the proton-proton chain reactions. In these reactions, four hydrogen nuclei are fused into a helium nucleus. The sum of the masses of the four hydrogen nuclei is slightly larger than the mass of the final helium nucleus, and this mass is turned into energy described by Einstein's equation, E = mc

 . The mass difference between four protons and one helium nucleus, 4.6 10

  kg, is transformed into 27 MeV of energy including the annihilation of the two positrons created in the process. Each second about 4 million tonnes of matter is converted into 2 10

  MeV of energy in the Sun, most of it in the form of gamma-rays. 

House of Science has six CCD spectrometers Avantes AvaSpec-2048 from Azpect Photonics, with which the radiation from the Sun is studied. The CCD has an array of 2048 pixels and covers the wavelength range 200–1100 nm. The observed sunlight comes from a thin layer of the solar atmosphere, the photosphere. The thickness of the photosphere is only 400 km which is very thin compared to the 700,000 km radius of the Sun. 

Sun radiates almost as a blackbody, that is the radiation spectrum is determined by the temperature. Using Wien's displacement law:  

where λm is the wavelength at which the Planck curve has its maximum, it is possible to determine the temperature (T) of the photosphere. From their observations, the students estimate the value of λm either by visual inspection or with the help of the AvaSoft software which comes with the CCD spectrometers. Usually, the students find a value of the temperature of around 5800 K. 

There are several absorption lines superimposed on the blackbody spectrum. These lines originate from the upper parts of the photosphere. By determining the wavelength for these lines it is possible to identify the elements in the solar atmosphere that are causing them. It is important to go through the energy level diagram of hydrogen and how absorption lines arise, particularly the Balmer lines emerging from transitions from the second energy level in the hydrogen atom. The Balmer lines are emitted in the optical region of the spectrum and are detectable with the spectrometer. The students identify them in their observed spectrum and also can identify lines from other elements in the solar atmosphere like calcium, magnesium, and iron. The sunlight also passes through the Earth's atmosphere and strong absorption lines from H

 molecules in the Earth's atmosphere can be seen. 

As a complement to the solar observations, the students study the spectrum from a hydrogen lamp. This spectrum is an emission spectrum containing both hydrogen and oxygen lines. The difference between absorption and emission lines is discussed with the students. They easily identify at least six components of the Balmer series. By accurately determining the wavelengths of the Balmer lines (quantum numbers n = 2 and m = 3,4,5..) with the spectrometer software the students are able to calculate Rydberg's constant (RH) from Bohr's formula: 

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K.E. Johansson

Articles

Observing the Solar Spectrum at House of Science