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If the fission of one U-235 nucleus liberates 200 MeV of energy, how many fissions per second are needed to generate a power output of 1 kW? (Take 1 eV = 1.6 × 10⁻¹⁹ J)
- 3.125 × 10¹³
- 3.125 × 10¹⁴
- 3.125 × 10¹⁵
- 3.125 × 10¹⁶
Correct answer: 3.125 × 10¹³
Solution
To find the number of fissions needed to produce 1 kW of power, we first convert 1 kW to joules per second (1 kW = 1000 J/s). Since each fission of U-235 releases 200 MeV, we convert that to joules (200 MeV = 3.2 × 10⁻¹¹ J). Dividing the power output by the energy per fission gives the required number of fissions per second, which calculates to 3.125 × 10¹³.
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