Figure: The extraterrestrial solar spectrum compared to the blackbody spectrum (Planck's law)

This figure shows the extraterrestrial solar radiation, or what an observer would see from a vantage point just above Earth's atmosphere. The irregularities result from processes in the sun's interior and on its surface. For reference, the distribution of equivalent blackbody radiation at 5800 K is also shown.

Blackbody Radiation

As shown in the figure, the sun behaves approximately like a blackbody -- a perfect radiator -- at a temperature of about 5800K. It is of interest to understand the source of the blackbody radiation curve shown along with the measured extraterrestrial insolation in this figure. The calculations are based on Planck's law, first published in 1901.

E = (2πhc²λ^-5)/[exp(hc/λkT) - 1] Δλ

where E is radiated power per unit area in the wavelength interval Δλ; λ is wavelength in meters; c is the speed of light, 2.9979 · 10⁸ m/s; h is Planck's constant, 6.6261 · 10^-34 Joule·s; k is Boltzmann's constant, 1.38065 · 10^-23 Joule/K; T is temperature in Kelvins.

The total power radiated in the interval Δλ is 4πr²E, where the sun's radius r is about 6.96 · 10⁸ m. At the average Earth-sun radius R, the extraterrestrial radiation in the interval Δλ is E(r²/R²) W/m², where R is about 1.5 · 10¹¹ m.

Planck derived this famous equation in an attempt to reconcile the behavior of blackbody radiation as then described by the 19th century Rayleigh-Jeans and Wien's laws. The Rayleigh-Jeans law explained blackbody radiation at long wavelengths, but not at short wavelengths. Wien's law worked for shorter wavelengths, but not for longer wavelengths. The Rayleigh-Jeans law had a firm foundation in electromagnetic theory as it was understood at the time, so its breakdown at short wavelengths (the "ultraviolet catastrophe") was profoundly disturbing to physicists.

When Planck searched for a mathematical description that would work for all wavelengths, he found that the available data on blackbody radiation could be explained by assuming that radiation is emitted only in discrete packets with an energy proportional to the inverse of wavelength: energy = hc/λ. Planck considered this assumption to be only a "fudge factor" that provided an empirical explanation of blackbody radiation. However, other physicists soon realized that this assumption must, in fact, have a physical basis that required a fundamentally new theory of electromagnetic radiation. In 1905, Einstein published a Nobel-prize-winning paper showing that the well known photoelectric effect, in which light striking certain surfaces causes a small current to flow, cannot be explained by classical theories of electromagnetic radiation, but can be explained by assuming that light energy is quantized -- transmitted only in discrete units by what are now called photons. However, the new explanation of the photoelectric effect appeared to be inconsistent with well known optical effects such as interference patterns. Such effects are completely consistent with classical theory, which attributes wavelike properties to light and other forms of electromagnetic radiation. The realization that electromagnetic radiation must have both wavelike and particle-like properties, no matter how counterintuitive such a conclusion seemed, revolutionized physics and led to the development of what is now known as quantum mechanics.

Text and image Credit: David R. Brooks, Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, USA.

http://www.pages.drexel.edu/~brooksdr/DRB_web_page/papers/UsingTheSun/using.htm