Skip to content
Study Hall
Lesson 4 of 5Energy and Society
Unit 3 · Lesson 4 of 5

Nuclear Energy, Half-Life and Energy Sources

Where the energy in a nucleus comes from, how radioactive decay is measured, and the real trade-offs behind Ontario's electricity supply.

5 min read10 practice questionsAsk AI about this →

Key things to remember

  1. 1Fission splits a heavy nucleus and drives every commercial reactor; fusion joins light nuclei and powers stars.
  2. 2Ontario's CANDU reactors use heavy water, run on unenriched uranium, and can be refuelled while operating.
  3. 3Half-life is the time for half the nuclei in a sample to decay. It is fixed for each isotope.
  4. 4 — use the same time unit for and .
  5. 5Each half-life removes half of what remains: after three, one eighth is left, not zero.
  6. 6Ontario's electricity is roughly 50–60% nuclear and about 25% hydroelectric, with coal phased out in 2014.
  7. 7Wind and solar are intermittent, so a grid relying on them needs storage or dispatchable backup.

The energy released when a nucleus splits or fuses dwarfs anything chemistry can offer — roughly a million times more per kilogram than burning coal. That single fact is why nuclear power exists, and why the questions around it are about waste, risk and cost rather than about whether it works.

Fission and fusion

Fission — splitting a heavy nucleusnU-2352–3 nFreed neutrons split more nuclei — a chain reaction.Every power reactor on Earth works this way.Fusion — joining light nucleiHHHeNeeds enormous temperature and pressure.Powers every star. No net-energy plant yet.Both release energy, roughly a million times more per kilogram than burning coal.
Fig 1Splitting a heavy nucleus, and joining two light ones. Both release energy.
AFission — splitting
  • A heavy nucleus (uranium-235) splits into lighter ones
  • Triggered by absorbing a neutron
  • Releases 2–3 more neutrons, enabling a chain reaction
  • The technology every power reactor uses today
  • Produces long-lived radioactive waste
BFusion — joining
  • Two light nuclei (hydrogen isotopes) join into a heavier one
  • Needs enormous temperature and pressure to start
  • Powers the Sun and every star
  • Still experimental — no net-energy power plant yet
  • Waste is far shorter-lived
CANDU — the Canadian design
Ontario's reactors at Darlington, Pickering and Bruce are CANDU units, a Canadian design that uses heavy water as both moderator and coolant. That lets them run on natural, unenriched uranium, and lets them be refuelled while still operating. Bruce is among the largest operating nuclear stations in the world.

In a reactor, the chain reaction is deliberately held at a steady rate. Control rods made of neutron-absorbing material slide in and out to soak up excess neutrons, the moderator slows neutrons so they are more readily absorbed by the fuel, and the coolant carries heat away to make steam. The steam then drives an ordinary turbine and generator — the nuclear part only replaces the furnace.

Radioactive decay and half-life

Unstable nuclei decay at random, but in such vast numbers that the rate is completely predictable. The half-life is the time for half the nuclei in a sample to decay. It is a fixed property of each isotope, unaffected by temperature, pressure or chemistry.

A₀ is the starting amount, t the elapsed time, and h the half-life. Use the same time unit for both.
% lefthalf-lives elapsed100%050%125%212.50%36.25%43.13%5Each half-life removes half of what REMAINS — so the curve approaches zero without ever reaching it.After 3 half-lives an eighth is left, not nothing.
Fig 2Each half-life removes half of what remains — so the curve approaches zero without reaching it.
Halving, not subtracting
After one half-life, half remains. After two, a quarter. After three, an eighth — not zero. Each half-life takes half of what is left, not half of the original. The exponent is simply the number of half-lives that have passed.
IsotopeHalf-lifeUsed for
Carbon-145730 yearsDating organic remains up to ~50 000 years old
Cobalt-605.27 yearsCancer radiotherapy, sterilizing equipment
Technetium-99m6 hoursMedical imaging — short enough to clear the body quickly
Iodine-1318 daysTreating thyroid conditions
Uranium-235704 million yearsReactor fuel
Plutonium-23924 100 yearsThe reason spent fuel needs long-term storage
When the time is a whole number of half-lives
Just halve repeatedly — it is faster and less error-prone than the formula. Three half-lives means , so remains. Reach for the formula only when the exponent is not a whole number.

Where Ontario's electricity comes from

Ontario's electricity — majority nuclear, no coal since 2014.55%24%9%8%Nuclear55%Hydroelectric24%Wind9%Natural gas8%Solar & biomass4%Coal was phased out in 2014 — at the timethe largest single greenhouse-gas reductionmeasure in North America.Percentages vary year to year with demand,water levels and reactor refurbishment.
Fig 3Ontario's generation is unusual: majority nuclear, almost no coal.

Ontario generates roughly half to sixty per cent of its electricity from nuclear, around a quarter from hydroelectric, and the rest from wind, natural gas, solar and biomass. The province closed its last coal plant in 2014 — at the time the largest single greenhouse-gas reduction initiative in North America — which is why Ontario's grid is among the cleanest on the continent.

SourceRenewable?StrengthsCosts and limits
NuclearNoNo greenhouse gases in operation; huge steady output; small land useLong-lived waste; very high build cost; slow to construct
HydroelectricYesReliable, long-lived, storable, no emissions in operationFloods land; disrupts fish and river ecosystems; sites are limited
WindYesNo fuel, no emissions, falling costIntermittent; needs backup or storage; land and wildlife concerns
SolarYesNo fuel or emissions; works on existing rooftopsIntermittent; poor winter output at Ontario's latitude
Natural gasNoFast to start, fills gaps in demandEmits and methane leaks upstream
BiomassYes*Uses waste material; dispatchableEmits when burnt; only near-neutral if regrown
Intermittency is the real engineering problem
Electricity must be generated at the instant it is used. Wind and solar produce when conditions allow rather than when demand appears, so a grid leaning on them needs storage, long-distance transmission, or dispatchable backup. This is the practical reason a grid cannot simply be all-renewable overnight, and it is where most current research money goes.
  • Conservation beats generation. The cheapest and cleanest kilowatt-hour is the one never used — insulation, LED lighting and efficient appliances all cut demand directly.
  • Every source has costs. Hydro floods habitat, wind kills birds and bats, solar panels need mining and eventual recycling, nuclear leaves waste. The comparison is between trade-offs, not between a perfect option and a flawed one.
  • Life-cycle analysis matters. Comparing sources fairly means counting construction, fuel, operation and decommissioning — not just what comes out of the stack while running.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1
A sample contains of a radioactive isotope with a half-life of 6 days. How much remains after 24 days?
Example 2
A sample of cobalt-60 (half-life 5.27 years) is stored for 15 years. How much remains?
Example 3
A wooden artifact has of the carbon-14 found in living wood. Carbon-14's half-life is 5730 years. How old is it?

Where marks get lost

  • Treating half-life as subtraction, so four half-lives means nothing remains. Each one halves what is left.
  • Using different time units for and . Convert one so they match before dividing.
  • Confusing fission with fusion. Fission splits heavy nuclei and is what reactors do; fusion joins light ones and is what stars do.
  • Forgetting to divide by the half-life before applying the exponent. The exponent is , not .
  • Calling every renewable source harmless. All of them have environmental costs; the comparison is between trade-offs.
  • Ignoring intermittency when arguing for an all-wind-and-solar grid. Electricity has to be generated the instant it is used.
  • Assuming a radioactive source becomes completely safe after one or two half-lives.

Flashcards 10

Nuclear fission
Nuclear fusion
CANDU reactor
Control rods
+ 6 more

Practice

1
A sample has a half-life of 3 days. How many grams remain after 12 days?
g
2
After 3 half-lives, what fraction of a radioactive sample remains?
3
Which process powers the Sun?
4
An artifact retains of its original carbon-14. With a half-life of 5730 years, how old is it, in years?
years
5
What is the name of the Canadian-designed nuclear reactor used throughout Ontario?
6
What is the main engineering challenge of relying heavily on wind and solar generation?
7
A sample decays with a half-life of 20 years. How many grams remain after 60 years?
g
8
In what year did Ontario close its last coal-fired electricity plant?
9
Match each energy source to its principal drawback.
Nuclear
Hydroelectric
Wind
Natural gas
10
Order these isotopes from shortest half-life to longest.
  1. 1Iodine-131 (8 days)
  2. 2Plutonium-239 (24 100 years)
  3. 3Cobalt-60 (5.27 years)
  4. 4Technetium-99m (6 hours)

Spot a mistake on this page? Let us know