Physics

5.4 - Nuclear Decay Equations

8 min

Alpha decay equations

Beta decay equations

Gamma emission

Neutron emission

note 1 of 6

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.

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 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:

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

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 mass number falls by 4 and the atomic number falls by 2:

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

Step 2 - Check the totals balance

Mass numbers: 238 = 234 + 4
Atomic 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 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 $_{- 1}^{0} e$ 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.

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 $_{- 1}^{0} e$ . The mass number is unchanged and the atomic number rises by 1:

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

Step 2 - Check the totals balance

Mass numbers: 14 = 14 + 0
Atomic numbers: 6 = 7 + (−1)

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

note 6 of 6

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:

$_{2}^{5} He \to_{2}^{4} He +_{0}^{1} n$

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

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

Physics

5.4 - Nuclear Decay Equations

8 min

Alpha decay equations

Beta decay equations

Gamma emission

Neutron emission

note 1 of 6

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.

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 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:

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

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 mass number falls by 4 and the atomic number falls by 2:

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

Step 2 - Check the totals balance

Mass numbers: 238 = 234 + 4
Atomic 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 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 $_{- 1}^{0} e$ 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.

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 $_{- 1}^{0} e$ . The mass number is unchanged and the atomic number rises by 1:

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

Step 2 - Check the totals balance

Mass numbers: 14 = 14 + 0
Atomic numbers: 6 = 7 + (−1)

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

note 6 of 6

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:

$_{2}^{5} He \to_{2}^{4} He +_{0}^{1} n$

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

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