Symbols for nuclear particles

Particles emitted in radioactive decay are written in the same way as nuclei, with a top number and a bottom number.
The top number shows the mass number, which is the relative mass in nucleons.
The bottom number shows the relative charge, which for a nucleus is its atomic number.
An alpha particle is written $24He{}^{4}_{2}\text{He}$ or $24α{}^{4}_{2}\alpha$ , because it has a mass of $4$ and a charge of $+ 2$ .
A beta particle is written $−10e{}^{0}_{-1}\text{e}$ or $−10β{}^{0}_{-1}\beta$ , because its mass is almost zero and its charge is $- 1$ .
A gamma ray is written $00γ{}^{0}_{0}\gamma$ , because it has no mass and no charge.
A neutron is written $01n{}^{1}_{0}\text{n}$ , because it has a mass of $1$ and no charge.
A proton is written $11p{}^{1}_{1}\text{p}$ , or $11H{}^{1}_{1}\text{H}$ because it is the nucleus of hydrogen-1.

Writing a decay equation

Definition

Decay equation

An equation that shows an unstable parent nucleus changing into a daughter nucleus and the radiation it emits.

A decay equation shows the parent nucleus on the left of an arrow and the daughter nucleus and the emitted radiation on the right.
Every nucleus and particle in the equation is written with its symbol, mass number and charge.
A decay equation is written in four steps.
1. Write the symbol for the parent nucleus, followed by an arrow.
2. Write the symbol for the emitted particle on the right of the arrow.
3. Work out the mass number and atomic number of the daughter nucleus from the change caused by the particle.
4. Use the atomic number to find the chemical symbol of the daughter nucleus from the periodic table, or from the data in the question.
The two sides of the equation must match in total mass number and in total charge, because nucleons and charge are neither created nor destroyed.

Common decay equations

Uranium-238 emits an alpha particle and becomes thorium-234, so $92238U→90234Th+24He{}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}$ .
Radium-226 emits an alpha particle and becomes radon-222, so $88226Ra→86222Rn+24He{}^{226}_{88}\text{Ra} \rightarrow {}^{222}_{86}\text{Rn} + {}^{4}_{2}\text{He}$ .
Americium-241 emits an alpha particle and becomes neptunium-237, so $95241Am→93237Np+24He{}^{241}_{95}\text{Am} \rightarrow {}^{237}_{93}\text{Np} + {}^{4}_{2}\text{He}$ .
Carbon-14 emits a beta particle and becomes nitrogen-14, so $614C→714N+−10e{}^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\text{e}$ .
Iodine-131 emits a beta particle and becomes xenon-131, so $53131I→54131Xe+−10e{}^{131}_{53}\text{I} \rightarrow {}^{131}_{54}\text{Xe} + {}^{0}_{-1}\text{e}$ .
Cobalt-60 emits a beta particle and a gamma ray and becomes nickel-60, so $2760Co→2860Ni+−10e+00γ{}^{60}_{27}\text{Co} \rightarrow {}^{60}_{28}\text{Ni} + {}^{0}_{-1}\text{e} + {}^{0}_{0}\gamma$ .

Example

Writing an alpha decay equation

Polonium-210, $84210Po{}^{210}_{84}\text{Po}$ , decays by emitting an alpha particle, and the element with atomic number $82$ is lead.
The parent nucleus and the alpha particle are written first.

{}^{210}_{84}\text{Po} \rightarrow \text{daughter} + {}^{4}_{2}\text{He}

The daughter nucleus has a mass number of $210 - 4 = 206$ and an atomic number of $84 - 2 = 82$ .
An atomic number of $82$ means the daughter nucleus is lead.

{}^{210}_{84}\text{Po} \rightarrow {}^{206}_{82}\text{Pb} + {}^{4}_{2}\text{He}

Example

Writing a beta decay equation

Strontium-90, $3890Sr{}^{90}_{38}\text{Sr}$ , decays by emitting a beta particle, and the element with atomic number $39$ is yttrium.
The parent nucleus and the beta particle are written first.

{}^{90}_{38}\text{Sr} \rightarrow \text{daughter} + {}^{0}_{-1}\text{e}

The daughter nucleus keeps a mass number of $90$ , and its atomic number rises to $38 + 1 = 39$ .
An atomic number of $39$ means the daughter nucleus is yttrium.

{}^{90}_{38}\text{Sr} \rightarrow {}^{90}_{39}\text{Y} + {}^{0}_{-1}\text{e}

Common Mistake

Do not write the beta particle as $+10e{}^{0}_{+1}\text{e}$ or $−11e{}^{1}_{-1}\text{e}$ , because its charge is $- 1$ and its mass number is $0$ .
Do not keep the parent symbol for the daughter nucleus after alpha or beta decay, because the change in atomic number makes it a new element.
Do not put the emitted particle on the left of the arrow, because it is a product of the decay.

Exam technique

Completing decay equations

Write all four numbers for every particle, because a symbol such as $α\alpha$ with no numbers often loses the mark.
Take the daughter element from the atomic number, using the periodic table or the list of elements given in the question.
Either $24He{}^{4}_{2}\text{He}$ or $24α{}^{4}_{2}\alpha$ is allowed for an alpha particle, and either $−10e{}^{0}_{-1}\text{e}$ or $−10β{}^{0}_{-1}\beta$ is allowed for a beta particle.

Self review

What does the bottom number of a particle in a decay equation represent?
How is a beta particle written in a decay equation?
What symbol is used for a gamma ray?
Write the symbol for a neutron.
What is the daughter nucleus when radium-226 emits an alpha particle?

Symbols for nuclear particles

Particles emitted in radioactive decay are written in the same way as nuclei, with a top number and a bottom number.
The top number shows the mass number, which is the relative mass in nucleons.
The bottom number shows the relative charge, which for a nucleus is its atomic number.
An alpha particle is written $24He{}^{4}_{2}\text{He}$ or $24α{}^{4}_{2}\alpha$ , because it has a mass of $4$ and a charge of $+ 2$ .
A beta particle is written $−10e{}^{0}_{-1}\text{e}$ or $−10β{}^{0}_{-1}\beta$ , because its mass is almost zero and its charge is $- 1$ .
A gamma ray is written $00γ{}^{0}_{0}\gamma$ , because it has no mass and no charge.
A neutron is written $01n{}^{1}_{0}\text{n}$ , because it has a mass of $1$ and no charge.
A proton is written $11p{}^{1}_{1}\text{p}$ , or $11H{}^{1}_{1}\text{H}$ because it is the nucleus of hydrogen-1.

Writing a decay equation

Definition

Decay equation

An equation that shows an unstable parent nucleus changing into a daughter nucleus and the radiation it emits.

A decay equation shows the parent nucleus on the left of an arrow and the daughter nucleus and the emitted radiation on the right.
Every nucleus and particle in the equation is written with its symbol, mass number and charge.
A decay equation is written in four steps.
1. Write the symbol for the parent nucleus, followed by an arrow.
2. Write the symbol for the emitted particle on the right of the arrow.
3. Work out the mass number and atomic number of the daughter nucleus from the change caused by the particle.
4. Use the atomic number to find the chemical symbol of the daughter nucleus from the periodic table, or from the data in the question.
The two sides of the equation must match in total mass number and in total charge, because nucleons and charge are neither created nor destroyed.

Common decay equations

Uranium-238 emits an alpha particle and becomes thorium-234, so $92238U→90234Th+24He{}^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}$ .
Radium-226 emits an alpha particle and becomes radon-222, so $88226Ra→86222Rn+24He{}^{226}_{88}\text{Ra} \rightarrow {}^{222}_{86}\text{Rn} + {}^{4}_{2}\text{He}$ .
Americium-241 emits an alpha particle and becomes neptunium-237, so $95241Am→93237Np+24He{}^{241}_{95}\text{Am} \rightarrow {}^{237}_{93}\text{Np} + {}^{4}_{2}\text{He}$ .
Carbon-14 emits a beta particle and becomes nitrogen-14, so $614C→714N+−10e{}^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\text{e}$ .
Iodine-131 emits a beta particle and becomes xenon-131, so $53131I→54131Xe+−10e{}^{131}_{53}\text{I} \rightarrow {}^{131}_{54}\text{Xe} + {}^{0}_{-1}\text{e}$ .
Cobalt-60 emits a beta particle and a gamma ray and becomes nickel-60, so $2760Co→2860Ni+−10e+00γ{}^{60}_{27}\text{Co} \rightarrow {}^{60}_{28}\text{Ni} + {}^{0}_{-1}\text{e} + {}^{0}_{0}\gamma$ .

Example

Writing an alpha decay equation

Polonium-210, $84210Po{}^{210}_{84}\text{Po}$ , decays by emitting an alpha particle, and the element with atomic number $82$ is lead.
The parent nucleus and the alpha particle are written first.

{}^{210}_{84}\text{Po} \rightarrow \text{daughter} + {}^{4}_{2}\text{He}

The daughter nucleus has a mass number of $210 - 4 = 206$ and an atomic number of $84 - 2 = 82$ .
An atomic number of $82$ means the daughter nucleus is lead.

{}^{210}_{84}\text{Po} \rightarrow {}^{206}_{82}\text{Pb} + {}^{4}_{2}\text{He}

Example

Writing a beta decay equation

Strontium-90, $3890Sr{}^{90}_{38}\text{Sr}$ , decays by emitting a beta particle, and the element with atomic number $39$ is yttrium.
The parent nucleus and the beta particle are written first.

{}^{90}_{38}\text{Sr} \rightarrow \text{daughter} + {}^{0}_{-1}\text{e}

The daughter nucleus keeps a mass number of $90$ , and its atomic number rises to $38 + 1 = 39$ .
An atomic number of $39$ means the daughter nucleus is yttrium.

{}^{90}_{38}\text{Sr} \rightarrow {}^{90}_{39}\text{Y} + {}^{0}_{-1}\text{e}

Common Mistake

Do not write the beta particle as $+10e{}^{0}_{+1}\text{e}$ or $−11e{}^{1}_{-1}\text{e}$ , because its charge is $- 1$ and its mass number is $0$ .
Do not keep the parent symbol for the daughter nucleus after alpha or beta decay, because the change in atomic number makes it a new element.
Do not put the emitted particle on the left of the arrow, because it is a product of the decay.

Exam technique

Completing decay equations

Write all four numbers for every particle, because a symbol such as $α\alpha$ with no numbers often loses the mark.
Take the daughter element from the atomic number, using the periodic table or the list of elements given in the question.
Either $24He{}^{4}_{2}\text{He}$ or $24α{}^{4}_{2}\alpha$ is allowed for an alpha particle, and either $−10e{}^{0}_{-1}\text{e}$ or $−10β{}^{0}_{-1}\beta$ is allowed for a beta particle.

Self review

What does the bottom number of a particle in a decay equation represent?
How is a beta particle written in a decay equation?
What symbol is used for a gamma ray?
Write the symbol for a neutron.
What is the daughter nucleus when radium-226 emits an alpha particle?

6.1.6 Representing radioactive decay

Symbols for nuclear particles

Writing a decay equation

Common decay equations

Writing an alpha decay equation

Writing a beta decay equation

Completing decay equations

Review 6.1.6 Representing radioactive decay by teaching Genie

6.1.6 Representing radioactive decay

Symbols for nuclear particles

Writing a decay equation

Common decay equations

Writing an alpha decay equation

Writing a beta decay equation

Completing decay equations

Review 6.1.6 Representing radioactive decay by teaching Genie

6.1.6 Representing radioactive decay

Symbols for nuclear particles

Writing a decay equation

Common decay equations

Writing an alpha decay equation

Writing a beta decay equation

Completing decay equations

Review 6.1.6 Representing radioactive decay by teaching Genie

6.1.6 Representing radioactive decay Revision Guide

6.1.6 Representing radioactive decay

Symbols for nuclear particles

Writing a decay equation

Common decay equations

Writing an alpha decay equation

Writing a beta decay equation

Completing decay equations

Review 6.1.6 Representing radioactive decay by teaching Genie

6.1.6 Representing radioactive decay Revision Guide