Modern Physics 5 Question 19
21. Assume that two deuteron nuclei in the core of fusion reactor at temperature $T$ are moving towards each other, each with kinetic energy $1.5 kT$, 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
(2009)
(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) $4.0 \times 10^{9} K<T<5.0 \times 10^{9} K$
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Answer:
Correct Answer: 21. (b, c)
Solution:
- From conservation of mechanical energy, we have
$$ \begin{aligned} U _i+K _i & =U _f+U _f \\ 0+2(1.5 k T) & =\frac{1}{4 \pi \varepsilon _0} \cdot \frac{(e)(e)}{d}+0 \end{aligned} $$
Substituting the values, we get
$$ T=1.4 \times 10^{9} K $$
