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

Explanation:

It is given:

Average thermal energy, E = 1.5 kT

Coulomb potential energy’s point = 2 fm

Potential energy is shown as U = Kq1q2r   …..(1)

Here,$K=14 \pi \varepsilon 0=9 \times 10^{\circ}$

Charge, $q 1=q 2=2 \times 1.6 \times 10-19$

Average kinetic energy, E is shown as E = 32kT     …..(2)

Here, T = Temperature, k = Constant of Boltzman

When the equation (1) and equation (2) is equated, we obtain,  

$\mathrm{kq} 1 \mathrm{q} 2 \mathrm{r}=32 \mathrm{kT}$

$\Rightarrow \mathrm{T}=2 \mathrm{Kq} 1 \mathrm{q} 23 \mathrm{kr}=2.23 \times 10^{10} \mathrm{K}$