Black-body spectrum

Figure 2.3 An almost-perfect black body spectrum for the cosmic background radiation. Figure courtesy of NASA/COBE Science Team...

This is a similar value to the temperature of the Sun derived optically or from A.max in the black body spectrum. In a colder star the Balmer series is weaker still, but in a hotter star the Balmer series lines are stronger. In very hot stars the Balmer series may become weaker again due to collisional ionisation of H atoms, removing the electrons from the atoms completely. 

That part of the black body spectrum coincident with the atomic transition frequencies leads to the transitions which redistribute the population. In contrast, all the energy of the black body radiation contributes to the shift of the energy levels. The energy shift is a second order ac Stark shift, and for state n the shift AWb is given by10... 

The major selling point of standard cosmology is the observed isotropic microwave background radiation, with black-body spectrum. In a closed universe it needs no explanation. Radiation, which accumulates in any closed cavity, tends, by definition, to an equilibrium wavelength distribution according to Planck s formula (Figure 2.5). 

The function Fb(XT) defines the fraction of total energy in the black-body spectrum which lies below XT and is a unique function of XT. For purposes of digital computation, the following series expansion for Fb(XT) proves especially useful. 

The Sun delivers a spectral irradiance at the Earth s surface at AM 1.0 (air mass), without concentrator, of 1.16 W m nm at 2 = 700 nm [2]. The solid angle represented by the Sun seen from the Earth is Q = 6.8 x 10 steradian. From Eq. (10), one calculates in this case Tr = 5500 K, and from Eq. (12) with T = 298 K one obtains rj = 0.946. If the solar spectrum were that of a black body, all wavelengths would lead to the same values of Jr and Figure 1 shows that this condition is fulfilled only if the receiver is outside the atmosphere. At the Earth s surface, absorption by atmospheric oxygen, ozone, water, and carbon dioxide makes the structured solar irradiance spectrum deviate significantly from the ideal black-body spectrum and requires rR(A) to be calculated for each wavelength. 

One of the pillars of standard cosmology is the so-called black-body spectrum of the universal microwave background. It is precisely such an observation that also led to the first recognition of a quantum effect by Max Planck in 1901. 

From Planck s radiation formula, other relationships for a black body spectrum can be derived. The Stefan Boltzmann law gives the total radiance emitted (pbb) black body as a function of the black body temperature ... 

The tenn black body may be somewhat misleading, because a black body is not necessarily black. In fact the radiation spectrum of our sun measured above the atmosphere is very closely a black body spectrum. Here we merely deal with the temperature dependence of the total energy density of a black body. The spectrum is calculated in Sect. 5.2. 

This was later confirmed experimentally by Millikan (1916), and led to a value of h which agreed to within 0.5 per cent with the value derived by fitting equation (1.3) to the black-body spectrum. With this clarification of the quantum aspects of the interaction of light and matter, the stage was then set for further advances in the field of atomic spectroscopy. 

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