Question

Consider fusion of $He$ plasma. At what temperature fusion at a distance $2$ $fm$ is possible

• A. $2.23\times {10}^9$ $K$
• B. $22.3\times {10}^9$ $K$
• C. $2.23\times {10}^8$ $K$
• D. none of these

Answer 1

Answer: (B)

$22.3\times {10}^9$ $K$

Applying energy balance : thermal energy = potential energy
$\frac{3KT}{2}=\frac{K{q}_1{q}_2}{r}$
$\frac{3}{2}$ $kT$ = $\frac{(2e{)}^2}{4\pi {\epsilon }_{0}r}$
$\Rightarrow$$T$ = $\frac{8\times (1.6\times {10}^{-19}{)}^2\times 9\times {10}^9}{3\times 1.38\times {10}^{-23}\times 2\times {10}^{-15}}$$=2.23\times {10}^{10}$ $K$