Nuclear Equations


Nuclear reactions involve changes in the atomic nuclei such as changes in

  • mass number
  • atomic number

It is important to understand the types of particles involved in a nuclear reaction.

Particles involved in nuclear reactions

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


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).


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.

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

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


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).


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).

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


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).

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


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

Practice


See Example 21.4 in the textbook and Chapter 21 questions.


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