Nuclear reactions and the conservation laws they obey
In a nuclear reaction, nuclei change and new elements form. Mass number, atomic number (charge), mass-energy and momentum are all conserved.
Chemical and nuclear reactions
| Feature | Chemical reaction | Nuclear reaction |
|---|---|---|
| What takes part | Outer (valence) electrons of atoms | Nuclei |
| New elements? | No: atoms only regroup | Yes: one element can change into another (transmutation) |
| Energy per reaction | A few eV (4.08 eV for C + O₂ → CO₂) | Millions of eV (MeV) |
| Change of mass | About 10⁻³⁵ kg: far too small to measure | Large enough to measure |
| What balances | Number of atoms of each element | Mass number and atomic number |
Starting a nuclear reaction
A nucleus is surrounded by a strong electric field. A charged projectile, such as a proton or an alpha particle, is repelled as it comes near. This repulsion is the Coulomb barrier: about 3 MeV for carbon and 20 MeV for lead. A projectile with less energy bounces back without any reaction. Neutrons have no charge, so they feel no repulsion. Even slow thermal neutrons (about 0.025 eV) can enter a nucleus. That is why neutrons are the best projectiles.
Conservation laws in every nuclear reaction
Check them with Rutherford's 1919 reaction: ⁴₂He + ¹⁴₇N → ¹⁷₈O + ¹₁H.
- 1Mass number is conserved: 4 + 14 = 17 + 1 = 18.
- 2Atomic number (charge) is conserved: 2 + 7 = 8 + 1 = 9.
- 3Mass-energy is conserved: the mass of the reactants plus their kinetic energy equals the mass of the products plus their kinetic energy.
- 4★Linear momentum is conserved, which decides how the kinetic energy is shared among the products.
★ key step
Worked example: completing reaction equations
Find the missing particle: (a) ¹⁴₇N + ¹₀n → ¹⁴₆C + ?; (b) ¹⁰₅B + ¹₀n → ⁷₃Li + ?; (c) ⁹₄Be + ⁴₂He → ¹²₆C + ?
- (a) A: 14 + 1 = 14 + A, so A = 1. Z: 7 + 0 = 6 + Z, so Z = 1. The particle is a proton, ¹₁H.
- (b) A: 10 + 1 = 7 + A, so A = 4. Z: 5 + 0 = 3 + Z, so Z = 2. The particle is ⁴₂He, an alpha particle.
- (c) A: 9 + 4 = 12 + A, so A = 1. Z: 4 + 2 = 6 + Z, so Z = 0. The particle is a neutron, ¹₀n.
(a) ¹₁H, a proton; (b) ⁴₂He, an alpha particle; (c) ¹₀n, a neutron
Worked example: energy released in a reaction
Find the energy released in ¹⁰₅B + ¹₀n → ⁷₃Li + ⁴₂He. (Masses: ¹⁰B = 10.01294 u, ¹₀n = 1.00867 u, ⁷Li = 7.01600 u, ⁴He = 4.00260 u; 1 u = 931 MeV)
- Mass before = 10.01294 + 1.00867 = 11.02161 u.
- Mass after = 7.01600 + 4.00260 = 11.01860 u.
- Mass lost Δm = 11.02161 − 11.01860 = 0.00301 u.
- Q = 0.00301 × 931 MeV = 2.80 MeV. Q is positive, so the reaction is exothermic.
About 2.8 MeV is released (exothermic)
Boron absorbs neutrons by the reaction ¹⁰B + n → ⁷Li + ⁴He. That is why boron and cadmium rods are pushed into a reactor to slow the chain reaction, and why boron is used in neutron detectors.
2 marks: “Distinguish between a chemical reaction and a nuclear reaction, giving one example of each.” Chemical: valence electrons rearrange, no new element, a few eV (C + O₂ → CO₂ + 4.08 eV). Nuclear: nuclei change and new elements form, MeV energies (⁴₂He + ¹⁴₇N → ¹⁷₈O + ¹₁H).
2 marks: “Which quantities are conserved in every nuclear reaction?” Conservation of mass number, atomic number (charge), mass-energy and linear momentum.
1 marks: “Why are neutrons the best projectiles for nuclear reactions?” They have no charge, so the Coulomb barrier does not repel them.
A, Z, E, p: mass number, atomic number, mass-energy and momentum balance in every nuclear reaction.