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For the fusion process ²₁H + ³₁H → ⁴₂He + n, if the electrostatic repulsion energy between the two nuclei is about 7.7 × 10⁻¹⁴ J, then the gas must be heated to approximately what temperature to start the reaction? [Take Boltzmann’s constant k = 1.38 × 10⁻²³ J/K]

1. 10⁷ K
2. 10⁵ K
3. 10³ K
4. 10⁹ K

Correct answer: 10⁹ K

Solution

The correct option is 10⁹ K because the thermal energy needed to overcome the electrostatic repulsion between the nuclei is given by the equation E = kT. To achieve the required energy of approximately 7.7 × 10⁻¹⁴ J, the temperature must be extremely high, around 10⁹ K, which is typical for fusion reactions.

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