How do you calculate the value of reactivity with keff?

How do you calculate the value of reactivity with keff?

• A. ((keff - 1)/keff) * 100
• B. ((keff - 1)/1) * 100
• C. ((1 - keff)/keff) * 100
• D. (keff - 1) * 100

Answer: (A)

Reactivity in percent measures how far the reactor is from critical, scaled to the current multiplication factor keff. The correct way to express this is to take the difference keff minus 1, divide by keff, and multiply by 100. This normalization ensures the percentage reflects the actual departure from unity relative to the reactor’s current state. For example, if keff is 1.002, reactivity = (1.002 − 1)/1.002 × 100 ≈ 0.20%. If keff is 0.995, reactivity = (0.995 − 1)/0.995 × 100 ≈ −0.50%. Why the other forms aren’t correct: dividing by 1 would ignore the current keff and give an incorrect, generally larger value; using (1 − keff)/keff flips the sign of the result; and multiplying by 100 without dividing by keff overstates or understates the departure, especially as keff moves away from 1.

Reactivity in percent measures how far the reactor is from critical, scaled to the current multiplication factor keff. The correct way to express this is to take the difference keff minus 1, divide by keff, and multiply by 100. This normalization ensures the percentage reflects the actual departure from unity relative to the reactor’s current state.

For example, if keff is 1.002, reactivity = (1.002 − 1)/1.002 × 100 ≈ 0.20%. If keff is 0.995, reactivity = (0.995 − 1)/0.995 × 100 ≈ −0.50%.

Why the other forms aren’t correct: dividing by 1 would ignore the current keff and give an incorrect, generally larger value; using (1 − keff)/keff flips the sign of the result; and multiplying by 100 without dividing by keff overstates or understates the departure, especially as keff moves away from 1.