9.2 Radioactive Decay Processes

There are various types of decay processes that radioactive (unstable) nuclei may undergo to increase their stability. As you peruse these examples, notice the mass-balance of the nuclear equations (both mass number and atomic number). It is important to understand the types of particles involved in a nuclear reaction.

9.2.1 Particles involved in nuclear reactions

Alpha Particle
- \(^{4}_{2}\mathrm{He}\) or \(^{4}_{2}\alpha\)
- helium nucleus
- has a +2 charge
Beta Particle
- \(^{\phantom{-}0}_{-1}e\) or \(^{\phantom{-}0}_{-1}\beta\)
- electron
- negatively charged
Positron
- \(^{\phantom{+}0}_{+1}e\) or \(^{\phantom{+}0}_{+1}\beta\)
- same mass as electron but with a positive charge
Proton
- \(^{1}_{1}\mathrm{H}\) or \(^{1}_{1}\mathrm{p}\)
- a hydrogen nucleus
- has a positive charge
Neutron
- \(^{1}_{0}\mathrm{n}\)
- no charge
- approximately the mass of a proton
Gamma Ray
- \(\gamma\)
- high-energy electromagnetic radiation

9.2.2 Alpha (α) Decay

An α particle is emitted.

In the following example, an unstable uranium-238 nucleus undergoes an alpha decay (converting into thallium-234) and an alpha particle is emitted.

\[^{238}_{\phantom{0}92}\mathrm{U} \longrightarrow ^{234}_{\phantom{0}90}\mathrm{Th} +^{4}_{2}\mathrm{He}\]

\[^{238}_{\phantom{0}92}\mathrm{U} \longrightarrow ^{234}_{\phantom{0}90}\mathrm{Th} +^{4}_{2}\mathrm{\alpha}\]

9.2.3 Beta (β^–) Decay

A β^– particle is emitted.

In the following example, an unstable radium-228 nucleus undergoes an beta decay (converting into the heavier actinium-228) and a beta particle is emitted.

\[^{228}_{\phantom{0}88}\mathrm{Ra} \longrightarrow ^{228}_{\phantom{0}89}\mathrm{Ac} + ^{\phantom{-}0}_{-1}e\]

\[^{228}_{\phantom{0}88}\mathrm{Ra} \longrightarrow ^{228}_{\phantom{0}89}\mathrm{Ac} + ^{\phantom{-}0}_{-1}\beta\]

Note that the atomic number changed (+1 proton) but the mass number did not (–1 neutron). One can rationalize that a neutron been converted into a proton and an electron such that

\[^{1}_{0}\mathrm{n} \longrightarrow ^{1}_{1}\mathrm{p} + ^{\phantom{-}0}_{-1}e\]

though this is a bit misleading as an electron antineutrino is also created (and its discussion lies beyond the scope of this course).

9.2.4 Positron Emission (β⁺ Decay)

A positron emission (i.e. a β⁺ decay) emits a positron.

Here, oxygen-15 decays into nitrogen-15.

\[^{15}_{\phantom{1}8}\mathrm{O} \longrightarrow ^{15}_{\phantom{1}7}\mathrm{N} + ^{\phantom{+}0}_{+1}e\]

\[^{15}_{\phantom{1}8}\mathrm{O} \longrightarrow ^{15}_{\phantom{1}7}\mathrm{N} + ^{\phantom{+}0}_{+1}\beta\]

Note that the atomic number changed (–1 proton) but the mass number did not change (+1 neutron). One can rationalize that a proton converted into a neutron and a positron (though as discussed above, this is a bit misleading).

\[^{1}_{1}\mathrm{p} \longrightarrow ^{1}_{0}\mathrm{n} + ^{\phantom{+}0}_{+1}e\]

9.2.5 Electron Capture

An electron is captured by the nucleus.

Here, potassium-40 captures an electron in its nucleus and becomes argon-40.

\[^{40}_{19}\mathrm{K} + ^{\phantom{-}0}_{-1}e \longrightarrow ^{40}_{18}\mathrm{Ar}\]

Note that the atomic number decreased (–1 proton) yet the mass number stayed the same (+1 neutron). One can rationalize that a neutron was formed from a proton and an electron (though as discussed above, this is a bit misleading).

\[^{1}_{1}\mathrm{p}+ ^{\phantom{-}0}_{-1}e \longrightarrow ^{1}_{0}\mathrm{n}\]

9.2.6 Gamma Ray Emission

A gamma ray emission process commonly accompanies radioactive decay processes and can be written explicitly. A gamma ray emission occurs when a nucleus is in an excited state and relaxes down to a lower energy state (giving off energy in the form of a gamma ray.)

\[^{238}_{\phantom{0}92}\mathrm{U} \longrightarrow ^{234}_{\phantom{0}90}\mathrm{Th} +^{4}_{2}\mathrm{He} + \gamma\] \[^{40}_{19}\mathrm{K} + ^{\phantom{-}0}_{-1}e \longrightarrow ^{40}_{18}\mathrm{Ar} + \gamma\]

Nuclear Decay Processes Summary

Decay pathway of Uranium-238