Question

Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy $1.5kT$, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature $T$ required for them to reach a separation of $4\times {10}^{-15}$ m is in the range

• A. $1.0\times {10}^{9}K<T<2.0\times {10}^{9}K$
• B. $2.0\times {10}^{9}K<T<3.0\times {10}^{9}K$
• C. $3.0\times {10}^{9}K<T<4.0\times {10}^{9}K$
• D. $4.0\times {10}^{9}K<T<5.0\times {10}^{9}K$

Answer 1

The correct option is A $1.0\times {10}^{9}K<T<2.0\times {10}^{9}K$

Conservation of energy:
$KE=PE$
$2\left(1.5kT\right)=\frac{e^2}{4\pi {ϵ}_{o}d}$
$3kT=\frac{(1.6\times {10}^{-19}{)}^2}{4\pi (8.84\times {10}^{-12}(4\times {10}^{-15}}$

$T=1.4\times {10}^{9}K$