Fission vs. Fusion

a) Reaction: $^{235}U\to ^{117}Sn\to ^{118}Sn$ Calculate the energy released per fission and the energy release per atomic mass of fuel. b) Reaction: $^2H + ^3H \to ^4He+n$ Calculate the energy released per fusion and the energy released per atomic mass unit of fuel.

Here’s a full breakdown of both reactions, including energy released per event and per atomic mass unit of fuel:

🔬 a) Fission: $^{235}\text{U} \to ^{117}\text{Sn} \to ^{118}\text{Sn}$

This is a stylized representation of uranium-235 undergoing fission and producing tin isotopes. In reality, U-235 fission yields a wide range of products, but the average energy released per fission is well established:

✅ Energy Released per Fission

~200 MeV per fission event

⚖️ Energy per Atomic Mass Unit of Fuel

Atomic mass of U-235 ≈ 235 u
Energy per atomic mass unit:
$\frac{200 \, \text{MeV}}{235 \, \text{u}} \approx 0.851 \, \text{MeV/u}$

⚛️ b) Fusion: $^2\text{H} + ^3\text{H} \to ^4\text{He} + n$

This is the deuterium-tritium fusion reaction, the most efficient known fusion process.

✅ Energy Released per Fusion

17.6 MeV total:
- 14.1 MeV carried by the neutron
- 3.5 MeV by the helium nucleus

⚖️ Energy per Atomic Mass Unit of Fuel

Combined mass of reactants: $^2\text{H} + ^3\text{H} = 5 \, \text{u}$
Energy per atomic mass unit:
$\frac{17.6 \, \text{MeV}}{5 \, \text{u}} = 3.52 \, \text{MeV/u}$

📊 Comparison Summary

Reaction Type	Energy per Event	Energy per u of Fuel
Fission (U-235)	~200 MeV	~0.851 MeV/u
Fusion (D-T)	17.6 MeV	~3.52 MeV/u

Fusion releases less energy per event, but more energy per unit mass, making it more efficient by weight.