Physics

22.2 - Nuclear Decay Equations

8 min

Alpha decay equations

Beta decay equations

Gamma emission

Neutron emissionOutside your course

note 1 of 6

Balancing a nuclear equation

A nuclear equation shows radioactive decay using nuclide notation.
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 nucleon number (top numbers) on the left equals the total nucleon number on the right.
The total proton number (bottom numbers) on the left equals the total proton number on the right.

note 2 of 6

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 nucleon number decreases by 4
- The proton 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:

$_{Z}^{A} X \to_{Z - 2}^{A - 4} Y +_{2}^{4} He$

note 3 of 6

Worked example - Balancing an alpha decay

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

Step 1 - Apply the alpha decay changes

The alpha particle is $_{2}^{4} He$ , so the nucleon number falls by 4 and the proton number falls by 2:

$_{92}^{238} U \to_{90}^{234} Th +_{2}^{4} He$

Step 2 - Check the totals balance

Nucleon numbers: 238 = 234 + 4
Proton numbers: 92 = 90 + 2

Both totals match across the arrow, so the equation is balanced.

note 4 of 6

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 nucleon number stays the same
- The proton number increases by 1
The extra proton means a different element is formed.
A beta particle is written as $_{- 1}^{0} β$ in a nuclear equation.

Gamma emission

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

note 5 of 6

Worked example - Balancing a beta decay

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

Step 1 - Apply the beta decay changes

The beta particle is $_{- 1}^{0} β$ . The nucleon number is unchanged and the proton number rises by 1:

$_{6}^{14} C \to_{7}^{14} N +_{- 1}^{0} β$

Step 2 - Check the totals balance

Nucleon numbers: 14 = 14 + 0
Proton numbers: 6 = 7 + (−1)

Both totals match across the arrow, so the equation is balanced.

note 6 of 6

Why nuclei decay

An unstable nucleus decays to move towards a more stable state.
Each decay mode does this differently:
- Alpha decay - Removes two protons and two neutrons, reducing the size of very heavy nuclei
- Beta decay - Turns a neutron into a proton, reducing an excess of neutrons
- Gamma emission - Releases excess energy without changing the particles in the nucleus

key terms

TermDefinition

Alpha particleA particle made of two protons and two neutrons that is emitted from a nucleus during alpha decay.

Beta particleA fast-moving electron emitted from a nucleus when a neutron changes into a proton.

Gamma rayVery high-frequency electromagnetic radiation, usually given out by an unstable nucleus as it loses energy. Giving it out does not change the number of protons or neutrons.

end of notes

Key points to remember

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22.3 - Radioactive Decay & Half-LifeNext up