IB Physics SLTopic 5 — FissionPaper 1 & 2products more tightly bound~8 min read
Energy from Fission
A single uranium fission releases about 200 MeV — tens of millions of times more than burning one atom of coal. That astonishing energy density is why a fingernail of uranium can outmuscle a truckload of fossil fuel. It all comes down to one fact: the fragments left after fission are more tightly bound than the nucleus you started with.
📘 What you need to know
When a heavy nucleus splits, the daughter nuclei have a higher binding energy per nucleon than the parent
This means the products are more tightly bound, so there is a mass defect and energy is released
Energy released = total binding energy of products − total binding energy of the parent
A nucleus’s total binding energy = binding energy per nucleon × nucleon number (A)
Specific energy = energy released per kilogram of fuel (J kg−1)
Energy density = energy released per cubic metre of fuel (J m−3)
Nuclear fuel has by far the highest energy density of any fuel currently available
Why Fission Releases Energy
The key lies in the binding energy per nucleon curve. A heavy nucleus like uranium-235 sits on the gentle right-hand slope, below the peak. When it splits, the two daughter nuclei land closer to the iron peak — higher up the curve — so they have a higher binding energy per nucleon and are more tightly bound. Because the products are held together more efficiently, there is a small mass defect, and by E = Δmc2 that lost mass appears as released energy.
Fission moves a heavy nucleus (blue) up the curve toward iron: the daughter products (green) have a higher binding energy per nucleon, so the extra binding energy is released.
heavy nucleus splits
→ products more tightly bound →
mass defect
→ E = Δmc2 →
energy released
Calculating the Energy Released
The most common exam method uses binding energy per nucleon read off the curve. A nucleus’s total binding energy is its binding energy per nucleon multiplied by its nucleon number. The energy released is then simply how much more tightly bound the products are than the reactant:
Energy released in fissionE = total BE of products − total BE of reactant
Total binding energy of a nucleus
total BE = (BE per nucleon) × A
🧭 Energy released per fission
Read the binding energy per nucleon of the reactant and each product from the curve or table
Multiply each by its nucleon number A to get total binding energies
Add up the products’ total binding energy
Subtract the reactant’s total binding energy — the difference is the energy released
Convert if needed: 1 MeV = 1.6 × 10−13 J
Specific Energy vs Energy Density
Two related quantities describe how much energy a fuel packs, and it’s easy to mix them up. Specific energy is the energy released per kilogram of fuel; energy density is the energy released per cubic metre. One is per unit mass, the other per unit volume.
The two measures
specific energy = energy ÷ mass (J kg−1) · energy density = energy ÷ volume (J m−3)
Nuclear fuel wins on both counts by an enormous margin. The table shows how uranium’s specific energy dwarfs everyday fuels — which is exactly why a tiny amount of it goes so far.
Fuel
Specific energy (MJ kg−1)
Wood
15.5
Coal
35
Petrol (gasoline)
45
Hydrogen
130
Uranium-235 (fission)
7.5 × 107
Quick recap: fission products are more tightly bound than the parent, so there’s a mass defect and energy is released; find it from total binding energies (BE per nucleon × A), products minus reactant; and remember specific energy is per kg while energy density is per m3.
WE 1
A uranium-235 nucleus undergoes fission: 23592U + n → 14156Ba + 9236Kr + 3n. Using binding energies per nucleon of 7.59 MeV (U-235), 8.33 MeV (Ba-141) and 8.55 MeV (Kr-92), calculate the energy released per fission.
Step 1 — total binding energy of each nucleus (BE/nucleon × A)
U-235: 7.59 × 235 = 1783.65 MeV
Ba-141: 8.33 × 141 = 1174.53 MeV
Kr-92: 8.55 × 92 = 786.6 MeV
Step 2 — energy released = products − reactant= (1174.53 + 786.6) − 1783.65= 1961.13 − 1783.65energy released ≈ 177 MeVThe products are more tightly bound than U-235, so the difference comes out positive — energy is released.
WE 2
The specific energy of uranium-235 is 7.5 × 107 MJ kg−1 and that of coal is 35 MJ kg−1. For the same total energy output, estimate how many times more coal (by mass) is needed than uranium.
Step 1 — link mass to specific energy
for a fixed energy, mass needed ∝ 1 ÷ specific energy
so the mass ratio is the inverse ratio of specific energies
Step 2 — take the ratio
mass of coal ÷ mass of uranium = specific energy of uranium ÷ specific energy of coal
= (7.5 × 107) ÷ 35≈ 2.1 × 106 times more coalAbout 2 million times more coal by mass — a vivid illustration of nuclear fuel’s energy density.
💡 Top tips
Work with total binding energies (BE per nucleon × A), then take products minus reactant — a positive answer means energy is released
Read the curve carefully: the daughter products sit higher than the parent, closer to iron
Specific energy = per kg; energy density = per m3. Check the units the question gives you
1 MeV = 1.6 × 10−13 J for converting a per-fission energy into joules
⚠ Common mistakes
Doing reactant minus products — it’s products minus reactant, so the released energy is positive
Forgetting to multiply BE per nucleon by A — you need each nucleus’s total binding energy
Swapping specific energy (per kg) and energy density (per m3)
Thinking the daughter nuclei are less tightly bound — they’re more tightly bound, which is why energy is released
Up next: Chain Reactions from Fission. You’ve seen the energy from a single split — next we follow the neutrons it releases as they trigger more fissions, and meet critical mass and the runaway chain reaction.
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