4.4 - Nuclear Decay Equations

Balancing a nuclear equation

• A nuclear equation shows radioactive decay using nuclide symbols.
• It's written with the nucleus before decay on the left, an arrow, then the nucleus after decay plus the radiation emitted:

nucleus before decay → nucleus after decay + radiation emitted

Every equation must balance

• Charge and mass are conserved, so the totals can't change across the arrow.
• The total mass number (top numbers) on the left equals the total mass number on the right.
• The total atomic number (bottom numbers) on the left equals the total atomic number on the right.

Alpha decay

• In alpha decay the nucleus emits an alpha particle - two protons and two neutrons (a helium nucleus).
• Because two protons and two neutrons leave the nucleus:
  • The mass number decreases by 4
  • The atomic number decreases by 2
• Losing two protons changes the nucleus into a different element.
• In a nuclear equation the alpha particle is written as a helium nucleus:

$${}_Z^A\text{X}\to {}_{Z-2}^{A-4}\text{Y}+{}_2^4\text{He}$$

Worked example - Balancing an alpha decay

Uranium-238 decays by alpha emission to thorium. Write the balanced equation.

Beta decay and gamma emission

Beta decay

• A neutron in the nucleus changes into a proton and emits a fast-moving electron - the beta particle.
• The nucleus loses a neutron and gains a proton, so:
  • The mass number stays the same
  • The atomic number increases by 1
• The extra proton means a different element is formed.
• A beta particle is written as ${}_{-1}^0\text{e}$ in a nuclear equation.

Gamma emission

• A nucleus with excess energy releases it as a gamma ray.
• This removes energy only, so the mass number and the atomic number both stay the same and the element does not change.

Worked example - Balancing a beta decay

Carbon-14 decays by beta emission to nitrogen. Write the balanced equation.

Positron emission (beta-plus decay)

• In positron emission (also called beta-plus decay), a proton in the nucleus changes into a neutron and emits a positron.
• The nucleus loses a proton and gains a neutron, so:
  • The mass number stays the same
  • The atomic number decreases by 1
• The positron carries away the positive charge lost by the nucleus, so the totals still balance.

Example - Fluorine-18

Fluorine-18 undergoes positron emission:

$${}_9^{18}\text{F}\to {}_8^{18}\text{O}+{}_{+1}^0\text{e}$$

• Mass numbers: 18 = 18 + 0
• Atomic numbers: 9 = 8 + 1

Neutron emission

• In neutron emission the nucleus gives out a single neutron.
• A neutron has a mass number of 1 and no charge, so:
  • The mass number decreases by 1
  • The atomic number stays the same
• Because the atomic number is unchanged, the element is the same but becomes a lighter isotope.

Example - Helium-5

Helium-5 emits a neutron to become helium-4:

$${}_2^5\text{He}\to {}_2^4\text{He}+{}_0^1\text{n}$$

The mass numbers (5 = 4 + 1) and the atomic numbers (2 = 2 + 0) both balance.