#### Question

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

#### Solution

Given:-

Average thermal energy, E = 1.5 kT

Point of coulomb potential energy = 2 fm

Potential energy is given by

`U = (Kq_1q_2)/r ......(1)`

Here , `K = 1/(4pi∈_0) = 9 xx 10^9`

Charge , `q_1 = q_2 = 2 xx 1.6 xx 10^-19 C`

Average kinetic energy (E) is given by

`E = 3/2 kT ....(2)`

Here, k = Boltzman constant

T = Temperature

Equating equation (1) and (2) , we get

`(kq_1q_2)/r = 3/2kT`

`⇒ T = (2Kq_1q_2)/(3kr)`

`= (2 xx 9 xx 10^9 xx 4 xx (1.6 xx 10^-19)^2)/(3 xx 1.38 xx 10^-23 xx 2 xx 10^-15)`

`= 2.23 xx 10^10 "K"`

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Solution Consider the Fusion in Helium Plasma. Find the Temperature at Which the Average Thermal Energy 1.5 Kt Equals the Coulomb Potential Energy at 2 Fm. Concept: Nuclear Energy - Nuclear Fusion – Energy Generation in Stars.