Radioactive Decay Equations (DP IB Physics) : Revision Note

Katie M

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Katie M

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Radioactive Decay Equations

  • There are four reasons why a nucleus might become unstable, and these determine which decay mode will occur

  1. Too many neutrons = beta-minus emission

  2. Too many protons = beta-plus emission or electron capture

  3. Too many nucleons = alpha emission

  4. Too much energy = gamma emission

If there are too many neutrons...

  • Beta-minus-) emission occurs

  • One of the neutrons in the nucleus changes into a proton and a β- particle (an electron) and antineutrino is released

  • The nucleon number is constant

    • The neutron number (N) decreases by 1

    • The proton number (Z) increases by 1

  • The general decay equation for β- emission is:

X presubscript Z presuperscript A space rightwards arrow space beta presubscript negative sign 1 end presubscript presuperscript 0 space plus space Y presubscript Z plus 1 end presubscript presuperscript A space plus space top enclose italic v subscript e

Beta Minus Decay Graph, downloadable AS & A Level Physics revision notes

Representing beta-minus decay graphically

If there are too many protons...

  • Beta-plus+) emission or electron capture occurs

  • In beta-plus decay:

    • A proton changes into a neutron and a β+ particle (a positron) and neutrino are released

  • In electron capture:

    • An orbiting electron is taken in by the nucleus and combined with a proton causing the formation of a neutron and neutrino

  • In both types of decay, the nucleon number stays constant

    • The neutron number (N) increases by 1

    • The proton number (Z) decreases by 1

  • The general decay equation for β+ emission is:

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

Beta Plus Decay Graph, downloadable AS & A Level Physics revision notes

Representing beta-plus decay graphically

  • The decay equation for electron capture is:

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

If there are too many nucleons...

  • Alpha (α) emission occurs

  • An α particle is a helium nucleus

  • The nucleon number decreases by 4 and the proton number decreases by 2

    • The neutron number (N) decreases by 2

    • The proton number (Z) decreases by 2

  • The general decay equation for α emission is:

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

Alpha Decay Graph, downloadable AS & A Level Physics revision notes

Representing alpha decay graphically

If there is too much energy...

  • Gamma (γ) emission occurs

  • A gamma particle is a high-energy electromagnetic radiation

  • This usually occurs after a different type of decay, such as alpha or beta decay

  • This is because the nucleus becomes excited and has excess energy

Representing Nuclear Processes Graphically

  • In summary, alpha decay, beta decay and electron capture can be represented on an N–Z graph as follows:

NZ Decay Graph, downloadable AS & A Level Physics revision notes

Representing nuclear processes graphically

Worked Example

A nucleus with 84 protons and 126 neutrons undergoes alpha decay. It forms lead, which has the element symbol Pb.

Worked Example Alpha Decay, downloadable IGCSE & GCSE Physics revision notes

Which of the isotopes of lead pictured is the correct one formed during the decay?

Answer:  A

Step 1: Calculate the mass number of the original nucleus

  • The mass number is equal to the number of protons plus the number of neutrons

  • The original nucleus has 84 protons and 126 neutrons

84 + 126 = 210

  • The mass number of the original nucleus is 210

Step 2: Calculate the new atomic number

  • The alpha particle emitted is made of two protons and two neutrons

  • Protons have an atomic number of 1, and neutrons have an atomic number of 0

  • Removing two protons and two neutrons will reduce the atomic number by 2

84 – 2 = 82

  • The new nucleus has an atomic number of 82

Step 3: Calculate the new mass number

  • Protons and neutrons both have a mass number of 1

  • Removing two protons and two neutrons will reduce the mass number by 4

210 – 4 = 206

  • The new nucleus has a mass number of 206

Worked Example

Plutonium-239 is a radioactive isotope that contains 94 protons and emits α particles to form a radioactive isotope of uranium. This isotope of uranium emits α particles to form an isotope of thorium which is also radioactive.

Write two equations to represent the decay of plutonium-239 and the subsequent decay of uranium.

Answer:

Step 1: Write down the general equation of alpha decay

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

Step 2: Write down the decay equation of plutonium into uranium

Pu presubscript 94 presuperscript 239 space rightwards arrow space straight U presubscript 92 presuperscript 235 space plus space straight alpha presubscript 2 presuperscript 4

Step 3: Write down the decay equation of uranium into thorium

straight U presubscript 92 presuperscript 235 space rightwards arrow space Th presubscript 90 presuperscript 231 space plus space straight alpha presubscript 2 presuperscript 4

Neutrinos & Antineutrinos

  • An electron neutrino is a type of subatomic particle with no charge and negligible mass which is also emitted from the nucleus

  • The anti-neutrino is the antiparticle of a neutrino

    • Electron anti-neutrinos are produced during β– decay

    • Electron neutrinos are produced during β+ decay

Neutrino Emission, downloadable AS & A Level Physics revision notes
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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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