Balancing Nuclear Equations
- Radioactive decay events can be shown using a decay equation
- A decay equation is similar to a chemical reaction equation, which means:
- The particles present before the decay are shown before the arrow
- The particles produced in the decay are shown after the arrow
- The sum of the mass and atomic numbers before the reaction must be the same as the sum of the mass and atomic numbers after the reaction
- The following decay equation shows polonium-212 undergoing alpha decay
- The polonium nucleus emits an alpha particle (i.e. a helium nucleus)
- This causes both its proton and nucleon numbers to decrease, so it changes into a new element, lead-208
Alpha Decay Equation
- When the alpha particle is emitted from the unstable nucleus, the nucleon number and proton number of the nucleus changes
- The mass number decreases by 4
- The atomic number decreases by 2
Representing Alpha Decay
When a nucleus decays by emitting an alpha particle, both the proton (atomic) and nucleon (mass) numbers decrease
Beta Decay Equation
- During beta decay, an electron is emitted
- Meanwhile, the proton number increases by one, and the nucleon number stays the same
Representing Beta Decay
When a nucleus decays by emitting a beta particle, the proton (atomic) number increases while the nucleon (mass) number stays the same
Gamma Decay
- During gamma decay, a gamma ray is emitted from an unstable nucleus
- The emitted gamma ray has a lot of energy, but no mass or charge
- The process that makes the nucleus less energetic but does not change its structure
Representing Gamma Decay
When a nucleus decays by emitting a gamma ray, both the proton (atomic) and nucleon (mass) numbers stay the same
Worked example
Polonium-210 undergoes alpha decay. It forms lead, which has the element symbol Pb.
What are the nucleon and proton numbers of the lead isotope?
ANSWER: A
Step 1: Recall the nucleon and proton numbers of alpha
- The emitted alpha particle is made of two protons and two neutrons
- The proton number is 2
- The nucleon number is 4
Step 2: Calculate the proton number of lead
- The proton numbers on both sides must add up to the same number
- So, the new proton number will decrease by 2
y = 84 – 2 = 82
- The lead nucleus has a proton number of 82
Step 3: Calculate the nucleon number of the lead isotope
- The nucleon numbers on both sides must add up to the same number
- So, the new nucleon number will decrease by 4
x = 210 – 4 = 206
- The lead isotope has a mass number of 206
Worked example
Sodium-24 undergoes beta decay. It forms magnesium, which has the element symbol Mg.
What are the nucleon and proton numbers of the magnesium isotope?
ANSWER: D
Step 1: Recall the changes that happen during beta decay
- During beta decay, the nucleon number remains the same and the proton number increases by 1
- The proton number can be written −1
- The nucleon number can be written 0
Step 2: Calculate the proton number of magnesium
- The proton numbers on both sides must add up to the same number
- So, the new proton number will increase by 1
y = 11 + 1 = 12
- The magnesium nucleus has a proton number of 12
Step 3: Calculate the nucleon number of the magnesium isotope
- The nucleon numbers on both sides must add up to the same number
- So, the new nucleon number will stay the same
x = 24 + 0 = 24
- The magnesium isotope has a nucleon number of 24
Exam Tip
You are not expected to know the names of the elements produced during radioactive decay, but you do need to be able to calculate the nucleon and proton numbers by making sure they are balanced on either side of the reaction.