Question

Energy released in the fission of a single \( {}_{92}\text{U}^{235} \) nucleus is 200 MeV. The fission rate of a \( {}_{92}\text{U}^{235} \) fueled reactor operating at a power level of 5W is:

• A. \( 1.56\times10^{11}\,\text{s}^{-1} \)
• B. \( 1.56\times10^{10}\,\text{s}^{-1} \)
• C. \( 1.56\times10^{16}\,\text{s}^{-1} \)
• D. \( 1.56\times10^{17}\,\text{s}^{-1} \)

Hint:

Always convert electron-volts to Joules first. A handy benchmark value to memorize is that a standard \( 1~\text{W} \) power output requires roughly \( 3.1\times10^{10} \) uranium fissions per second to sustain it.

Answer 1

The Correct Option is A

Concept: The operating power level \( P \) of a nuclear reactor represents the total amount of energy generated per second, which can be expressed as: \[ P = R \cdot E_{\text{fission}} \] where \( R \) is the total number of fission events occurring per second, and \( E_{\text{fission}} \) is the energy released during a single fission event converted into standard Joules units (\( 1~\text{MeV} = 1.6\times10^{-13}~\text{J} \)).

Step 1: Converting single-fission energy into standard Joules.
Given value: \( E = 200\,\text{MeV} \). \[ E = 200 \times 1.6\times10^{-13}~\text{J} = 3.2\times10^{-11}~\text{J} \]

Step 2: Isolating the rate of fission events \( R \).
Given operating power level: \( P = 5\,\text{W} = 5\,\text{J/s} \). \[ R = \frac{P}{E} = \frac{5}{3.2\times10^{-11}} \]

Step 3: Evaluating the numerical rate.
\[ R = 1.5625\times10^{11}~\text{fissions/sec} \] Thus, the fission rate is approximately \( 1.56\times10^{11}\,\text{s}^{-1} \).