To generate a power of 3.2 mega watt, the number of fissions of U₂₃₅ per minute is. (Energy released per fission = 200 MeV, 1 eV = 1.6 × 10⁻¹⁹ J).

• A. 6 × 10¹⁸
• B. 6 × 10¹⁷
• C. 10 × 10¹⁷
• D. 6 × 10¹⁶

To find the number of fissions of U-235 needed to generate 3.2 megawatts of power, we can follow these steps:

Step 1: Convert Power to Watts

3.2 megawatts is equal to:

• 3.2 MW = 3.2 × 10⁶ W

Step 2: Calculate Energy Released per Fission

The energy released per fission of U-235 is given as 200 MeV. We need to convert this to joules:

• 200 MeV = 200 × 1.6 × 10^-19 J = 3.2 × 10^-14 J

Step 3: Determine the Number of Fissions per Second

To find the number of fissions required to produce 3.2 × 10⁶ W, we use the formula:

• Power (W) = Energy per fission (J) × Number of fissions per second

Rearranging gives:

• Number of fissions per second = Power / Energy per fission

Substituting the values:

• Number of fissions per second = (3.2 × 10⁶ W) / (3.2 × 10^-14 J) = 1 × 10²⁰ fissions/second

Step 4: Convert to Fissions per Minute

To find the number of fissions per minute, multiply by 60:

• Number of fissions per minute = 1 × 10²⁰ fissions/second × 60 seconds = 6 × 10²¹ fissions/minute

Final Answer

None of the options provided (A, B, C, D) match the calculated value of 6 × 10²¹ fissions per minute. Please check the options again or the values used in the calculations.