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

Step 1: Connect power to fission rate.
A reactor's power is the energy it produces each second. If $R$ fissions happen per second and each releases energy $E$, then: \[ P = R\,E \]
Step 2: Convert the fission energy to joules.
Each fission gives $200$ MeV, and $1\ \text{MeV} = 1.6\times10^{-13}$ J: \[ E = 200\times1.6\times10^{-13} = 3.2\times10^{-11}\ \text{J} \]
Step 3: Write the power in SI units.
The power is $P = 5$ W $= 5$ J/s.
Step 4: Rearrange for the rate.
\[ R = \frac{P}{E} = \frac{5}{3.2\times10^{-11}} \]
Step 5: Do the division.
\[ R = 1.5625\times10^{11}\ \text{fissions per second} \]
Step 6: State the answer.
\[ \boxed{R \approx 1.56\times10^{11}\ \text{s}^{-1}} \]