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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.
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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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