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At what temperature will a proton in hydrogen gas possess sufficient thermal energy to surmount an energy barrier of 4.14 × 10^−14 J? (Take Boltzmann constant = 1.38 × 10^−23 J K^−1)

1. 2 × 10⁸ K
2. 10⁹ K
3. 6 × 10⁹ K
4. 3 × 10⁹ K

Correct answer: 3 × 10⁹ K

Solution

Equating thermal energy to the barrier, T = E/k = 4.14*10^-14 / 1.38*10^-23 = 3*10^9 K.

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