INTERACTIVE EXAMPLE© Copyright, Department of Physics, University of Illinois at Urbana-Champaign Comments

## Sunspots

The surface temperature of the Sun is 5900 K, but sunspots are only about 4300 K. Above is a photograph of the Sun followed by a close-up of a sunspot.

Consider two hydrogen atoms, one located on the sunspot, the other on the hotter surface of the Sun. The energy levels of the hydrogen atom are given by the equation

En = -13.6 eV /n2 ( n = 1, 2, 3,...).

Define P2(surface, 5900 K) to be the probability of the hydrogen atom being in the first excited state (n=2) on the Sun's surface.
Define P2(sunspot, 4300 K) to be the probability of the hydrogen atom being in the first excited state (n=2) on a sunspot.

Calculate the ratio P2(surface, 5900 K) / P2(sunspot, 4300 K). Assume that you can ignore energy states higher than the first excited state, n=2 (why?). Also, ignore any degeneracy: assume that the hydrogen atom has one and only one state for each energy level.

Note: In such problems it is helpful to use the Boltzmann constant in electron-volt units, k = 8.617×10-5 eV/K.

P2(surface, 5900 K) / P2(sunspot, 4300 K) =