Question

Estimate the average thermal energy of a helium atom at (i) room temperature (27°C), (ii) the temperature on the surface of the Sun (6000 K), (iii) the temperature of 10 million Kelvin (the typical core temperature in the case of a star).

Answer 1

The average thermal energy of an atom

is E = 3/2 k_BT

where k_B = 1.38 x 10^-23 JK^-1

is the Boltzmann's const.

(i) At room temperature, T = 27°C = 27 + 273 = 300 K

E = 3/2 x 1.38 x 10^-23 x 300 = 6.21 x 10^-21 J

(ii) At the temperature on the surface of the sun, i.e., T = 6000 K

E = 3/2 x 1.38 x 10^-23 x 6000 = 1.24 x 10^-19 J

(iii) At T = 10 million Kelvin = 10 x 10⁶ K

E = 3/2 x 1.38 x 10^-23 x 10 x 10⁶ = 2.1 x 10^-16 J