7.1.7 Decay Equations

Changes in N and Z by Radioactive Decay

• There are four reasons why a nucleus might become unstable, and these determine which decay mode will occur
• Too many neutrons
  • Decays through beta-minus (β^-) emission
  • 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:

• Too many protons
  • Decays through beta-plus (β⁺) emission or electron capture
  • 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:

• • The equation for electron capture is:

• Too many nucleons
  • Decays through alpha (α) emission
  • 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:

• Too much energy
  • Decays through gamma (γ) emission
  • 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

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

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

Step 1: Write down the general equation of alpha decayStep 2: Write down the decay equation of plutonium into uraniumStep 3: Write down the decay equation of uranium into thorium

ANSWER: C

ANSWER: A