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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 -

(i) At room temperature, T = 270┬аC= 300 K

Average thermal energy = (3 / 2) kT

Where,

k is the Boltzmann constant = 1.38 x 10-23┬аm2┬аkg s-2┬аK-1

Hence,

(3 / 2) kT = (3 / 2) x 1.38 x 10-23┬аx300

On calculation, we get,

= 6.21 x 10-21┬аJ

Therefore, the average thermal energy of a helium atom at roomtemperature of 270┬аC is 6.21 x 10-21┬аJ

(ii) On the surface of the sun, T = 6000 K

Average thermal energy = (3 / 2) kT

= (3 / 2) x 1.38 x 10-23┬аx6000

We get,

= 1.241 x 10-19┬аJ

Therefore, the average thermal energy of a helium atom on thesurface of the sun is 1.241 x 10-19┬аJ

(iii) At temperature, T = 107┬аK

Average thermal energy = (3 / 2) kT

= (3 / 2) x 1.38 x 10-23┬аx107

We get,

= 2.07 x 10-16┬аJ

Therefore, the average thermal energy of a helium atom at thecore of a star is 2.07 x 10-16┬аJ

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