Decay Equations (AQA A Level Physics)

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

1. 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 (β^-) 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:

Representing beta-minus decay graphically

If there are too many protons...

• Beta-plus (β⁺) 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:

Representing beta-plus decay graphically

• The decay equation for electron capture is:

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:

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:

Representing nuclear processes graphically

Part (a)

Step 1: Write down the general equation of alpha decay

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

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

Part (b)

• Plutonium, ²³⁹Pu
  • Number of neutrons: 239 – 94 = 145
  • Neutron-nucleon ratio: 145 / 239 = 0.607

• Uranium, ²³⁵U
  • Number of neutrons: 235 – 92 = 143
  • Neutron-nucleon ratio: 143 / 235 = 0.609

• Thorium, ²³¹Th
  • Number of neutrons: 231 – 90 = 141
  • Neutron-nucleon ratio: 141 / 231 = 0.610

• Thorium-231 is neutron-rich compared to uranium-235 and plutonium-239
• Therefore, it must be a β^– emitter

Part (c)

• The key features to draw on an N–Z graph are:
  • Values for neutron number (N) on the vertical axis
  • Values for proton number (Z) on the horizontal axis
  • Labels for the isotopes eg. ²³⁹Pu, ²³⁵U, ²³¹Th
  • Arrows showing the direction of the decay
  • Labels for the type of emission eg. α, β^–