Question

The mean free path of photons in stars is of the order of 0.2 cm. Show that the time
taken for a photon to reach the surface of a star of radius 4 Ro is of the order of one
million year.

Answer 1

Answer on Question #69703 – Physics - Astronomy | Astrophysics

The mean free path of photons in stars is of the order of 0.2 cm. Show that the time taken for a photon to reach the surface of a star of radius $4R_{\odot}$ is of the order of one million year.

Solution. The distance $d$ moved by a photon that random walks through $N$ steps:

$$4R_{\odot} = l\sqrt{N},$$

where $l = 0.2\,cm$.

We have then the following number of steps

$$N = \frac{16R_{\odot}^2}{l^2}$$

and the following total time spent

$$t = Nt_1 = \frac{16R_{\odot}^2}{lc} = \frac{16 \times (695700\,km)^2}{0.2 \times 10^{-5}\,km \times 299792\, \frac{km}{s}} \approx 1.3 \times 10^{13}\,s \approx 0.41 \times 10^6\, \text{years}$$

Answer. $0.41 \times 10^6$ years.

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