Consider the fission of ${}^{235}\text{U}$ induced by a thermal neutron: ${}^{235}\text{U}{+}^1\text{n}{\to }^{92}\text{Kr}{+}^{141}\text{Ba}+3{}^1\text{n}$ Atomic masses (in u) are: $m{(}^{235}\text{U})=235.0439$, $m{(}^1\text{n})=1.008665$, $m{(}^{92}\text{Kr})=91.9262$, $m{(}^{141}\text{Ba})=140.9144$.\n(a) Calculate the Q‑value (energy released) per fission reaction in MeV.\n(b) If $0.5\text{g}$ of ${}^{235}\text{U}$ undergoes complete fission, find the total energy released in joules. (Use $1\text{u}=931.5\text{MeV}$ and $1\text{MeV}=1.602\times 10^{-13}\text{J}$.)\n(c) How many fissions per second are required to produce a thermal power of $500\text{MW}$?

Step-by-step solution

1. Total mass of reactants: $m_{\text{react}}=m{(}^{235}\text{U})+m{(}^1\text{n})=235.0439+1.008665=236.052565\text{u}$.
2. Total mass of products: $m_{\text{prod}}=m{(}^{92}\text{Kr})+m{(}^{141}\text{Ba})+3m{(}^1\text{n})$.
3. Compute product mass: $m_{\text{prod}}=91.9262+140.9144+3(1.008665)=91.9262+140.9144+3.025995=235.866595\text{u}$.
4. Mass defect: $\Delta m=m_{\text{react}}-m_{\text{prod}}=236.052565-235.866595=0.185970\text{u}$.
5. Convert to energy: $Q=0.185970\times 931.5=173.2\text{MeV}$ (rounded to one decimal).
6. Typical textbooks give $\approx 200\text{MeV}$; using the given masses we obtain $173\text{MeV}$. We'll keep $173\text{MeV}$ for the calculation.
7. Number of ${}^{235}\text{U}$ nuclei in $0.5\text{g}$: $N=\frac{0.5\text{g}}{235{\text{g mol}}^{-1}}\times N_A=\frac{0.5}{235}\times 6.022\times 10^{23}=1.28\times 10^{21}$.
8. Total energy released: $E=N\times Q\times 1.602\times 10^{-13}\text{J}$.
9. Substitute: $E=1.28\times 10^{21}\times 173\times 1.602\times 10^{-13}=3.54\times 10^{10}\text{J}$ (approx).
10. For part (c), power $P=500\text{MW}=5.0\times 10^8\text{J/s}$.
11. Energy per fission in joules: $E_f=173\text{MeV}\times 1.602\times 10^{-13}=2.77\times 10^{-11}\text{J}$.
12. Fissions per second required: $\frac{P}{E_f}=\frac{5.0\times 10^8}{2.77\times 10^{-11}}=1.8\times 10^{19}\text{fissions/s}$.

Concept tested: Energy release in nuclear fission

Published 19 September 2026 · How this solution was prepared and checked