An Introduction to Modern Astrophysics · Problem 9.3

The Interiors of Stars — Carroll & Ostlie

Physics — Astrophysics · blackbody-photon-average-energy

Problem

(a) Use the results of Problem 9.2 to find the total number density,

n

, of blackbody photons of all wavelengths. Also show that the average energy per photon,

u/n

, is

\frac{u}{n} = \frac{\pi^4 kT}{15(2.404)} = 2.70kT. \tag{9.65}

(b) Find the average energy per blackbody photon at the center of the Sun, where

T = 1.57 \times 10^7

K, and in the solar photosphere, where

T = 5777

K. Express your answers in units of electron volts (eV).