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Decay Equations (CIE A Level Physics)

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Neutrino emission

  • An electron neutrino is a type of subatomic particle with no charge and negligible mass which is emitted from the nucleus
  • The electron anti-neutrino is the antiparticle of an electron neutrino
    • Electron anti-neutrinos are produced during β– decay
    • Electron neutrinos are produced during β+ decay

Electron neutrino and anti-electron neutrino

Neutrino Emission, downloadable AS & A Level Physics revision notes

The anti neutrino is denoted by a line above the symbol

Examiner Tip

One way to remember which particle decays into which depends on the type of beta emission, think of beta ‘plus’ as the ‘proton’ that turns into the neutron (plus an electron neutrino)

Energy of alpha & beta decay

  • When the number of α particles is plotted against kinetic energy, there are clear spikes that appear on the graph
  • This demonstrates that α-particles have discrete energies (only certain values)

Graphs showing energy of alpha and beta particles

 Alpha and beta energy graphs, downloadable AS & A Level Physics revision notes

Alpha particles have discrete energy levels whilst beta particles have a continuous range of energies

  • When the number of β particles is plotted against kinetic energy, the graph shows a curve
  • This demonstrates that beta particles (electrons or positrons) have a continuous range of energies
  • This is because the energy released in beta decay is shared between the beta particles (electrons or positrons) and neutrinos (or anti-neutrinos)
  • This was one of the first clues of the neutrino’s existence
  • The principle of conservation of momentum and energy applies in both alpha and beta emission

α & β decay equations

Alpha decay

  • Alpha decay is common in large, unstable nuclei with too many protons
  • The decay involves a nucleus emitting an alpha particle and decaying into a different nucleus
  • An alpha particle consists of 2 protons and 2 neutrons (the nucleus of a Helium atom)

Alpha decay

 Alpha decay diagram, downloadable AS & A Level Physics revision notes

Alpha decay produces a daughter nucleus and an alpha particle (helium nucleus)

  • When an unstable nucleus (the parent nucleus) emits radiation, the constitution of its nucleus changes
  • As a result, the isotope will change into a different element (the daughter nucleus)
  • Alpha decay can be represented by the following radioactive decay equation:

straight X presubscript straight Y presuperscript straight A space rightwards arrow space straight Y presubscript straight Z minus 2 end presubscript presuperscript straight A minus 4 end presuperscript space plus space straight alpha presubscript 2 presuperscript 4

  • An example would be:

Po presubscript 84 presuperscript 212 space rightwards arrow space straight Y presubscript 82 presuperscript 208 space plus space straight alpha presubscript 2 presuperscript 4

  • When an alpha particle is emitted from a nucleus:
    • The nucleus loses 2 protons: proton number decreases by 2
    • The nucleus loses 4 nucleons: nucleon number decreases by 4

Worked example

The radioactive nucleus Rn presubscript 86 presuperscript 222 undergoes alpha decay into a daughter nucleus Po.

11-1-5-we-alpha-decay-question--cie-new

(a)
Which letter in the diagram represents the daughter product?
(b)
Which is the nucleon and proton number of the final nucleus Po?

Answer: 

(a)

Step 1: Determine the number of neutrons

  • This is alpha decay
  • The nucleon number of the parent nucleus decreases by 4
  • The proton number of the parent nucleus decreases by 2
  • Therefore, the number of neutrons is:

222 space minus space 86 space equals space 136

Step 2: Determine the change in the proton and neutrons

  • A helium nucleus has 2 protons and 2 neutrons
  • The proton and neutron numbers will decrease by 2
  • This reaches the point of the diagram marked C

(b)

Step 1: Write the equation for the alpha decay

11-1-5-we-alpha-decay-answer---cie-new

straight X presubscript straight Z presuperscript straight A space rightwards arrow space straight alpha presubscript 2 presuperscript 4 space plus space straight Y presubscript straight Z minus 2 end presubscript presuperscript straight A minus 4 end presuperscript

Rn presubscript 86 presuperscript 222 space rightwards arrow space straight alpha presubscript 2 presuperscript 4 space plus space Po presubscript 84 presuperscript 218

Step 2: Determine the nucleon and proton numbers of Po

  • Nucleon number = 218
  • Proton number = 84

β- decay

  • A β- particle is a high energy electron emitted from the nucleus
  • β- decay is when a neutron turns into a proton emitting an electron and an anti-electron neutrino

Beta decay

Beta minus decay diagram, downloadable AS & A Level Physics revision notes

In beta-minus decay, a neutron decays into a proton, an electron and an anti-electron neutrino

  • When a β- is emitted from a nucleus:
    • The number of protons increases by 1: proton number increases by 1
    • The total number of nucleons stays the same: nucleon number remains the same

  • The decay equation for beta-minus decay is:

straight X presubscript straight Z presuperscript straight A space rightwards arrow space straight Y presubscript straight Z plus 1 end presubscript presuperscript straight A space plus space straight beta presubscript negative 1 end presubscript presuperscript 0 space plus space scriptbase v with bar on top end scriptbase presubscript 0 presuperscript 0 subscript e

  • An example would be:

straight C presubscript 6 presuperscript 14 space rightwards arrow space straight N presubscript 7 presuperscript 14 space plus space straight beta presubscript negative 1 end presubscript presuperscript 0 space plus space scriptbase stack straight v subscript straight e with bar on top end scriptbase presubscript 0 presuperscript 0

  • The new nucleus formed from the decay is called the “daughter” nucleus (nitrogen in the example above)

β+ decay

  • A β+ particle is a high energy positron emitted from the nucleus
  • β+ decay is when a proton turns into a neutron emitting a positron (anti-electron) and an electron neutrino

Beta-plus decay

Beta plus decay diagram, downloadable AS & A Level Physics revision notes

In beta plus decay, a proton decays into a neutron, a positron and an electron neutrino

  • When a β+ is emitted from a nucleus:
    • The number of protons decreases by 1: proton number decreases by 1
    • The total number of nucleons stays the same: nucleon number remains the same

  • The decay equation for beta-plus decay is:

straight X presubscript straight Z presuperscript straight A space rightwards arrow space straight Y presubscript straight Z minus 1 end presubscript presuperscript straight A space plus space straight beta presubscript plus 1 end presubscript presuperscript 0 space plus space straight v presubscript 0 presuperscript 0 subscript straight e

  • An example of this would be:

straight C presubscript 6 presuperscript 6 space rightwards arrow space straight B presubscript 5 presuperscript 6 space plus space straight beta presubscript plus 1 end presubscript presuperscript 0 space plus space straight v presubscript 0 presuperscript 0 subscript straight e

Worked example

A radioactive substance with a nucleon number of 212 and a proton number of 82 decays by β-plus emission into a daughter product which in turn decays by further β-plus emission into a granddaughter product.

WE - Beta emission question image, downloadable AS & A Level Physics revision notes

State the letter in the diagram that represents the granddaughter product.

Answer: A

  • In β+ decay, a proton decays into a neutron, a positron, and an anti-electron neutrino
  • The number of neutrons is:

212 space minus space 82 space equals space 130

  • The proton number decreases by one and the number of neutrons increases by one
    • This happens twice, so it reaches point A on the diagram

11-1-5-we-beta-emission---cie-new

Examiner Tip

Remember to avoid the common mistake of confusing the number of neutrons with nucleon number. In alpha decay, the nucleon (protons and neutrons) number decreases by 4 but the number of neutrons only decreases by 2.

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Leander

Author: Leander

Expertise: Physics

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.