Page 25 - 83 basic knowledge of astronomy

θ
φ

Figure 22: Thermal radiation from a surface of a black body.

Therefore, the total power F of the blackbody radiation from a spherical
star with radius R is equal to:
4
2
2
F = 4πR S ? = 4πR σT .
The power flux density of the thermal radiation which we receive from a star
or a cloud of solid angle Ω, surface temperature T, and distance r, is from
equation (32):
ΩσT 4
S = Ω I = ,
π
2
2
which, for the spherically symmetric case where Ω = πR /r , is reduced to
R 2 R 2 F
4
S = σT = S ? = ,
r 2 r 2 4πr 2
as expected.

9.7 Universality of the Relationship among Einstein’s
Coefficients

We derived equations (21) and (25), giving the following relationships among
Einstein’s coefficients:
n
m
g m β m = g n β ,
n
α m = 2hν 3 ,
n
β n m c 3
or, equivalently,
m
g m B n = g n B ,
n
m
A m 8πhν 3
n
B m = c 3 ,
n
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