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.

Answer 1

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"`