Consider two stars with effective temperatures Teff = 5800 K and radius 1 RSun , and...

Consider two stars with effective temperatures T_eff = 5800 K and radius 1 R_Sun , and T_eff = 20,000 K and radius 3.5 R_Sun. Assuming blackbody spectra, what is the ratio of the number of Hydrogen - ionizing photons (hν > 13.6eV) that they produce?

Solutions

Expert Solution

The number density of photons that have energy above Q is

where c1 is a constant.

In the limit

the result simplifies to

The total number is given by the number density multiplied by the volume of the star

In the problem

is the ionization energy of hydrogen

The Boltzmann constant is

Now consider the first star with

This gives

For the second star

This gives

The ratio of these numbers is

genius_generous answered 1 year ago

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