Nuclear Reactions

Nuclear reactions involve rearrangements of nucleons between nuclei, releasing or absorbing energy quantified by the Q-value. Fission (splitting heavy nuclei) and fusion (combining light nuclei) are both exothermic and form the basis of nuclear power and weapons.

Key Concepts

Q-value: energy released Q = (m_i - m_f)c²
Fission: heavy nucleus splits releasing ~200 MeV
Fusion: light nuclei combine releasing ~17 MeV (D-T reaction)
Cross section σ measured in barns (1 b = 10⁻²⁴ cm²)
Reaction rate: R = nσΦ where Φ is neutron flux

Key Equations

Q-value

Q = (\sum m_i - \sum m_f)c^2

D-T fusion

{}^2_1H + {}^3_1H \to {}^4_2He + n + 17.6\text{ MeV}

Fission Q-value

{}^{235}U + n \to {}^{141}Ba + {}^{92}Kr + 3n + \sim 200\text{ MeV}

Reaction rate

R = N\sigma\Phi

Worked Example

Example Problem

Problem

Find the Q-value for D-T fusion: ²H + ³H → ⁴He + n. Masses: m(²H)=2.01410 u, m(³H)=3.01605 u, m(⁴He)=4.00260 u, m(n)=1.00866 u.

Solution

Δm = (2.01410+3.01605) - (4.00260+1.00866) = 5.03015 - 5.01126 = 0.01889 u. Q = 0.01889×931.5 = 17.59 MeV.

Practice

Exercises

7 problems

1 of 7

Find Q for the p+p → d+e⁺+ν_e reaction. Masses: m_p=938.272 MeV/c², m_d=1875.613 MeV/c², m_e=0.511 MeV/c². Use Q=(2m_p - m_d - m_e)c² (ignoring ν mass).

Your answer

MeV

2 of 7

The fission of ²³⁵U releases about 200 MeV per fission. Find the energy release from 1.0 gram of ²³⁵U in MJ.

Your answer

3 of 7

A nuclear reactor has thermal power P=3000 MW. If each fission gives 200 MeV, find the fission rate in fissions/s.

Unlock Exercise 3