Chemical reactions rearrange atoms. Nuclear reactions turn one element into another.
In every chemical reaction so far, atoms kept their identity. A carbon atom went in as carbon and came out as carbon. Inside an unstable nucleus, that rule breaks. The nucleus changes, and the atom becomes a different element. This page shows how decay, fission and fusion change the nucleus, and how much energy they release.
Core Claims
- Two totals stay the same. In every nuclear change, the total of protons plus neutrons (A) and the total of protons (Z) match on both sides.
- Alpha decay. The nucleus ejects a helium-4 nucleus. A falls by 4 and Z falls by 2 (alpha decay).
- Beta decay. A neutron changes into a proton and an electron leaves. Z rises by 1 and A stays the same (beta decay).
- Gamma radiation. An excited nucleus sheds energy as a photon. A and Z do not change (gamma radiation).
- Half-life. After each half-life, half of the sample remains.
- Fission and fusion. Fission splits a heavy nucleus. Fusion joins light nuclei. Each releases about a million times more energy per atom than a chemical change.
Three kinds of decay
Retrieval Checklist
- State the two totals that stay the same in a nuclear equation.
- Find the product of an alpha decay and of a beta decay.
- Say how much of a sample remains after 1, 2 and 3 half-lives.
- Compare the energy of a nuclear change with the energy of a chemical change.
In a nuclear change, the element can change but two totals cannot.
In a chemical reaction, atoms rearrange their electrons and the nuclei stay untouched. In a nuclear reaction, the nucleus itself changes. We write a nucleus with nuclear notation:
- Mass number (A): the number of protons plus neutrons.
- Atomic number (Z): the number of protons.
A nuclear equation is balanced when two totals match on both sides. The total of A must match. The total of Z must match.
Thinking a nuclear equation keeps the same element on both sides, like a chemical one. In a nuclear change the element can change. Only the totals of A and Z stay the same.
Unstable nuclei decay by alpha, beta or gamma emission.
A nucleus with too many neutrons, or too much mass, is unstable. It decays by ejecting a particle or a photon.
1. Alpha decay: a helium-4 nucleus leaves
Heavy nuclei shed mass by ejecting an alpha particle, which is a helium-4 nucleus.
The mass number falls by 4. The atomic number falls by 2, so uranium becomes thorium.
2. Beta decay: a neutron becomes a proton
In a nucleus with too many neutrons, one neutron changes into a proton. The nucleus ejects an electron and an antineutrino.
The mass number stays at 14. The atomic number rises by 1, so carbon becomes nitrogen.
3. Gamma radiation: a photon leaves
After alpha or beta decay, the new nucleus is often excited. It sheds the extra energy as a high-energy photon.
The mass number and the atomic number do not change. The element stays the same.
Thinking the electron in beta decay was already inside the nucleus. A nucleus holds only protons and neutrons. The electron is made when a neutron changes into a proton.
After each half-life, half of the sample remains.
Hold one atom of carbon-14. You cannot predict when it will decay. It might be in five seconds or in 20,000 years. Now hold a trillion carbon-14 atoms. About half of them decay in every 5,730 years.
The half-life is the time it takes for half of a sample to decay. Heat, pressure and chemical bonding do not change it, so half-lives work as clocks.
Thinking a sample is gone after two half-lives. After one half-life, half remain. After two, a quarter remain, not none. The sample never reaches zero in a few steps.
Watch 100 atoms decay, and stop at each half-life.
Pick an isotope and press Start run. The run stops at 1, 2, 3 and 4 half-lives so you can record the count.
Why can nobody say when one atom will decay, when a whole sample decays on schedule?
The explanation appears after you predict.
- A parent atom that has not decayed
- A daughter atom, after a decay
- An alpha particle (helium-4 nucleus) leaving
- A beta particle (electron) leaving
- Atoms left in this run
- The halving rule: half remain after each half-life
- Run carbon-14. Press Start run. At each stop, press Record, then press Play. Look for: 49 atoms left after 1 half-life (5,730 years), then 25, 12 and 6. Nobody could say which atom goes next.
- Run iodine-131. Load it, press Start run, and press Record at 2 half-lives. Look for: 25 atoms left after 16 days. Carbon-14 took 11,460 years to reach the same count.
- Run uranium-238. Load it, press Start run, and press Record at 1 half-life. Look for: alpha particles leave in place of electrons. 47 atoms are left after 4.47 billion years.
Use your evidence
Fission and fusion change the nucleus and release far more energy than chemical changes.
In nuclear fission, a heavy nucleus splits. A uranium-235 nucleus absorbs a neutron and splits into two smaller nuclei and three neutrons. Nuclear power plants use fission.
In nuclear fusion, light nuclei join. In the Sun, hydrogen nuclei join to make helium (Lesson 5-1a).
In both changes, the total number of protons and neutrons stays the same. In both, the nuclei change, so the elements change.
| Event | Energy |
|---|---|
| One chemical bond forms | 1 to 10 eV |
| One uranium-235 fission | about 200,000,000 eV |
Thinking a nuclear change gives only a little more energy than a chemical one. One fission releases about 200 million eV. Forming a chemical bond releases 1 to 10 eV.
Split one uranium-235 nucleus.
Fire a neutron at one nucleus. Count the protons and neutrons before and after, and compare the energy with a chemical bond.
What happens to the nucleus when one uranium-235 atom splits?
The explanation appears after you predict.
- A neutron
- Uranium-235, and krypton-92 after the split
- Barium-141, and the bar for one fission
- The bar for one chemical bond
- Fire a neutron. Press Fire a neutron, watch the split to the end, and press Record. Look for: 236 protons and neutrons go in, and 236 come out (141 + 92 + 3). Protons: 92 in, and 56 + 36 = 92 out.
- Compare the energy. Look at the bars once the nucleus has split. Look for: one fission releases about 200 million eV. Each step on the bar scale is 1,000 times bigger, and the chemical bond bar stays near the start.
Use your evidence
The half-life equation, the energy of one fission, and chain reactions.
EnrichmentEquation, mass defect and chain reactions
Extra depth. The rest of the lesson works without it.
The half-life equation
After a time t, the number of nuclei left is N. Here N0 is the starting number and t1/2 is the half-life.
After 3 half-lives, N = N0 × (1/2)3 = N0 / 8.
The energy of one fission
Weigh the particles before and after one fission. The products weigh a little less. The missing mass, the mass defect, becomes energy.
- Before: uranium-235 (235.0439 u) + neutron (1.0087 u) = 236.0526 u
- After: barium-141 + krypton-92 + 3 neutrons = 235.8665 u
- Mass defect: 0.1861 u, which is about 173 MeV (2.8 × 10−11 J)
A chain reaction
Each fission releases neutrons. A neutron can split another nucleus, which releases more neutrons. The number k is how many new fissions each fission causes. If k is above 1, the reaction grows. If k is 1, it holds steady. If k is below 1, it dies out.
A reactor holds k at 1 with control rods that absorb neutrons. Dropping every rod at once, called a SCRAM, pushes k far below 1 and stops the chain.
What decides whether a chain reaction grows, holds steady or dies out?
The explanation appears after you predict.
- A fuel pin that is fissioning
- A control rod, which absorbs neutrons
- The fissions in one generation
- A generation that is off the chart (200 or more)
- Hold it steady. Load 50% rods, press Start run, and press Record when it stops. Look for: k is 1.00, and generation 5 has 50 fissions, the same as the start.
- Pull the rods out. Load 30% rods, press Start run, and press Record when it stops. Look for: k is 1.20, and generation 5 has 124 fissions. The bars climb.
- Drop the rods. Load 100% rods, press Start run, and press Record when it stops. Look for: k is 0.50, and generation 5 has 2 fissions. The bars shrink toward nothing.
Use your evidence
Fill the blanks from memory.
Type each blank from memory, then press Check. Press Show answers after your first check if you are stuck.
1. In every nuclear reaction, the total mass number A and the total atomic number stay the same.
2. In alpha decay, the nucleus ejects a helium-4 nucleus with 2 protons and 2 .
3. In beta-minus decay, a neutron changes into a proton and an leaves.
4. A sample of 80.0 g of iodine-131 decays for 3 half-lives. g of it remain.
5. A nuclear change releases about a times more energy per atom than a chemical change.
Heating a reactant speeds up a chemical reaction. But boiling carbon-14 in acid, or squeezing it to 100,000 atmospheres, does not change its half-life of 5,730 years.
Explain why radioactive decay is not affected by heat, pressure or chemical bonding.
Compare the energy of a chemical bond with the energy inside a nucleus. Write your answer first, then compare it with the model answer.
Chemical changes use the electrons of an atom. They involve 1 to 10 eV. Decay happens in the nucleus, where the energies are millions of eV.
Heat, pressure and bonding are tiny on that scale. The electron cloud also shields the nucleus from outside changes. So the half-life stays fixed.
Write your answer first. Then grade yourself.
Give yourself 1 mark for each idea you wrote down.
Archaeologists find a wooden chest in an ancient burial site. They test a 1.00 g carbon sample from the wood. Living trees give 16.0 counts per minute (cpm) for each gram of carbon, from carbon-14. The sample from the chest gives 2.0 cpm. The half-life of carbon-14 (146C) is 5,730 years.
(a) Write the balanced nuclear equation for the beta decay of carbon-14. [1 mark]
(b) Find how many half-lives have passed since the tree was cut. Find the age of the chest. [2 marks]
(c) Explain why carbon-14 cannot date a dinosaur bone that is 68 million years old. Name an isotope that could. [1 mark]
- Equation (1 mark): You write 146C → 147N + 0−1e + ν̄e, with A and Z balanced.
- Half-lives (1 mark): You halve 16.0 to 8.0, 4.0 and 2.0, so 3 half-lives have passed.
- Age (1 mark): You find 3 × 5,730 = 17,190 years.
- Limit (1 mark): You say almost no carbon-14 is left after 68 million years, and name uranium-238.
Doctors use decay to treat cancer. In targeted alpha therapy, an alpha-emitting isotope such as actinium-225 is attached to an antibody that finds cancer cells. An alpha particle travels less than 50 micrometers. It damages the tumor cell it sits in and spares the healthy tissue around it.
Adaptive Competency Practice: HS-PS1-8
Test your understanding of nuclear changes one question at a time. The adaptive engine covers alpha, beta and gamma radiation, balancing decay equations, half-lives, fission and fusion.