Question

For the following two ionized regions, determine the mean separation between particles, r, and the mean free path for a photon, l. Indicate whether the region should be considered an ideal gas and also whether it is in LTE. For simplicity, assume a pure hydrogen gas, that the most likely interaction for the photon is scattering from a free electron , and that the effective particle size is its geometrical size.

(a) The center of the Sun (T = 15.8 × 10^6 K, n_e = 6.4 × 10^25 cm^−3 )

(b) A diffuse region in the Galaxy of diameter, D = 1 pc (T = 10^5 K, ne = 0.001 cm^−3 )

Answer 1

Mean seperation between particles, r is given as

where n is the number density

(a) 0.25 10^-10 m, (0.25 Angstrom)

(b) 10 cm

Mean free path $\lambda$ is given by
$\lambda = \frac{1}{\sigma_T n_e}$

where $\sigma_T$ is Thomson cross-section with value 6.6524*10^-29 m^2

(a) 2.3*10^8 m

b) 1.5 *10^37 m