Nuclear Decay Equations
Brook Edgar & Hannah Shuter
Teachers
Explainer Video
Nuclear Decay Equations
When a radioactive isotope undergoes alpha or beta decay, the nucleus changes into a different atom (loses two protons in alpha decay, so it changes the atomic number) or a different isotope (same element but different numbers of neutrons in beta minus decay). We can show these changes using nuclear equations, which work similarly to chemical equations but use atomic number and mass number conservation.
An alpha particle can be represented as because it has the same structure as a helium nucleus ( protons and neutrons).
A beta particle can be represented as or because it is a fast-moving electron with negligible mass (so small it can be ignored) and a charge of .
Alpha Decay Equation
An example of an alpha decay would be:
Notice that the mass numbers on the right-hand side add up to the mass number on the left, and the same is true for the atomic numbers. This is because no particles are “lost” during the decay — they must all be accounted for in the nuclear equation.
The mass numbers (top number) on the RHS = the sum of the mass numbers on the LHS
The atomic numbers (bottom number) on the RHS = the sum of the atomic numbers on the LHS
An alpha particle is a nucleus, so its emission causes the original nucleus to:
Lose from it's mass number (loses two protons and two neutrons), reducing it from to
Lose from its atomic number (as lost two protons), reducing it from to .
Beta Decay Equation
An example of a beta decay is shown below:
Again, notice that the mass and atomic numbers balance on both sides of the equation. In beta decay, a neutron in the nucleus converts into a proton, releasing a beta particle (an electron). Because a neutron and a proton have almost the same mass, the mass number stays the same, but the atomic number increases by , as the nucleus now contains one extra proton.
Gamma
Since gamma radiation does not contain any particles (mass zero, charge zero), its emission does not change the mass number or atomic number of the nucleus.
Remember: You do not need to know the atomic or mass numbers of individual elements but you must know the mass and atomic numbers of alpha and beta particles so that you can use them to balance nuclear equations.
Worked Example:
Uranium (U) has protons and undergoes alpha decay.
Write a nuclear equation to show the alpha decay of uranium into thorium ().
Answers:
An alpha particle is released from the nucleus of the uranium atom. The mass number must decrease by because an alpha particle contains particles (two protons and two neutrons), which is how we calculate the top number of thorium. As two protons are released the atomic number also decreases by which is how we know the bottom number of thorium.
Worked Example:
Strontium() is a radioactive isotope that undergoes beta decay.
Write a nuclear equation to show the beta decay of strontium into yttrium ().
Explain why the mass number of the nucleus does not change during beta decay.
Answer:
In beta decay, a neutron changes into a proton and an electron, but only the electron is emitted from the nucleus. This means that the total number of protons and neutrons in the nucleus remains the same, which is why the top number, the mass number, does not change.
Teacher Tip: In beta decay, a common misconception is to subtract the bottom number by one, but as in beta decay a neutron changes into a proton, the proton number increases by one. The RHS is balanced as , the same as the LHS.
Practice Questions
The nucleus of an isotope of thorium undergoes alpha decay.
The isotope is represented by the symbol .
Write the nuclear equation for this alpha decay. Use an for the decay product.
Explain why the atomic number decreases in alpha decay.
State how the mass number changes in alpha decay.
-> Check out Hannah's video explanation for more help.
Answer:
Two protons are removed from the nucleus because the alpha particle contains two protons.
It decreases by .
An isotope of phosphorus undergoes beta decay to form sulphur ().
The isotope is represented by the symbol .
Write the balanced nuclear equation for this beta decay.
Explain why the atomic number increases in beta decay.
State how the mass number changes in beta decay.
-> Check out Hannah's video explanation for more help.
Answer:
A neutron changes into a proton and emits an electron (beta particle), increasing the proton number by one.
It stays the same.