Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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# 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. - Physics

ConceptNuclear Energy Nuclear Fusion – Energy Generation in Stars

#### 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.
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