This problem can be solved using the relation between kinetic energy and temperature i.e. average thermal energy = (3/2)k_BT per atom.

(i) Average thermal energy of a helium atom at room temperature (27 °C)

At room temperature (T) = 27°C = 300 K

Average thermal energy (E_Th) = (3/2)k_BT

(Where k_B is Boltzmann constant = 1.38 × 10^–23 m² kg s^–2 K^–1 )

∴ E_Th = (3/2)k_BT

⇒ E_Th = (3/2) 1.38 × 10^–23 × 300

⇒ E_Th = 6.21 × 10^–21J

The average thermal energy of a helium atom at room temperature is 6.21 × 10^–21 J.

(ii) The surface of the sun has T = 6000 K

∴ E_Th = (3/2)k_BT

⇒ E_Th = (3/2) × 1.38 × 10^-23 × 6000

⇒ E_Th = 1.241 × 10 ^-19 J

Hence, the average thermal energy of a helium atom on the surface of the sun is 1.241 × 10^–19 J.

(iii) The temperature of 10 million

kelvin Average thermal energy = (3/2)k_BT

⇒ E_Th = (3/2) × 1.38 × 10^-23 × 10⁷

⇒ E_Th = 2.07 × 10^-16 J

Hence, the average thermal energy of a helium atom (the typical core temperature in the case of a star) is 2.07 × 10^–16 J.