Nuclear Fission Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Nuclear Fission.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Nuclear fission is the splitting of a heavy nucleus into smaller nuclei, releasing energy and often additional neutrons.

A large unstable nucleus can split apart and release a huge amount of energy.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Nuclear Fission asks whether the system is nuclear, quantum, or relativistic before using an everyday model.

Common stuck point: Students often know a formula related to nuclear fission but skip the recognition step: Does the situation involve particles, nuclei, photons, or relativistic speeds where everyday mechanics is not enough? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Does the situation involve particles, nuclei, photons, or relativistic speeds where everyday mechanics is not enough?

Worked Examples

Example 1

medium
A mass defect of 0.20 u0.20\text{ u} (1 u=1.66×10−27 kg1\text{ u} = 1.66\times 10^{-27}\text{ kg}) is converted to energy in fission. Find EE in joules. (c=3×108c = 3\times 10^8.)

Answer

E≈2.99×10−11 JE \approx 2.99\times 10^{-11}\text{ J}

First step

1
m=0.20×1.66×10−27=3.32×10−28 kgm = 0.20\times 1.66\times 10^{-27} = 3.32\times 10^{-28}\text{ kg}.

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Example 2

medium
Fission of 1 kg1\text{ kg} of U-235 releases roughly 8×1013 J8\times 10^{13}\text{ J}. Burning 1 kg1\text{ kg} of coal releases about 3×107 J3\times 10^7\text{ J}. By what factor is U-235 more energy-dense per kg?

Example 3

medium
A fission fuel pellet of mass 5 g5\text{ g} is 4%4\% U-235 by mass. If all U-235 fissions (releasing 200 MeV/200\text{ MeV}/atom; MU−235=235 g/molM_{U-235}=235\text{ g/mol}, NA=6×1023N_A = 6\times 10^{23}), find total energy.

Example 4

hard
A subcritical assembly has k=0.95k = 0.95 and starts with 101010^{10} fissions in the first generation. Roughly how many total fissions occur before the chain dies out? (Use ∑n=0∞kn=1/(1−k)\sum_{n=0}^{\infty} k^n = 1/(1-k).)

Example 5

hard
A reactor with k=1.01k = 1.01 doubles its fission rate every how many generations? (log⁡2(1.01)≈0.01435\log_2(1.01)\approx 0.01435.)

Example 6

challenge
A reactor's prompt-neutron generation time is τ≈10−4 s\tau \approx 10^{-4}\text{ s} and k=1.001k = 1.001. Estimate how long until the fission rate grows by a factor ee. (T=τ/(k−1)T = \tau/(k-1).)

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Nuclear fission is the splitting of what kind of nucleus?

Example 2

easy
Fission of a heavy nucleus typically releases what particles that can trigger further fission?

Example 3

easy
Is the energy released in fission far larger or far smaller than in a chemical reaction?

Example 4

easy
A chain reaction in fission is sustained by what released particles?

Example 5

easy
Using E=mc2E = mc^2 with c=3×108 m/sc = 3\times10^8 \text{ m/s}, find the energy from a mass defect of 1×10−27 kg1\times10^{-27} \text{ kg}.

Example 6

easy
In fission, is the total mass of products slightly more or slightly less than the original nucleus?

Example 7

easy
Which heavy element is most commonly used as fission fuel in reactors?

Example 8

easy
Does fission occur in light nuclei like hydrogen or in heavy nuclei like uranium?

Example 9

medium
A single U-235 fission releases about 3.2×10−11 J3.2\times10^{-11} \text{ J}. Find the energy from 1×10201\times10^{20} fissions.

Example 10

medium
A fission reaction has mass defect 3×10−28 kg3\times10^{-28} \text{ kg}. Find the energy released (c=3×108c = 3\times10^8).

Example 11

medium
If each fission yields 2.52.5 neutrons on average and all cause new fissions, how many fissions occur in the 3rd generation starting from 11?

Example 12

medium
A reactor produces 9×108 J9\times10^8 \text{ J} per second. Using E=mc2E = mc^2 (c=3×108c = 3\times10^8), find the mass converted per second.

Example 13

medium
Compare the energy per reaction: fission releases about 200 MeV200 \text{ MeV}, a chemical bond about 4 eV4 \text{ eV}. Find the ratio.

Example 14

medium
A fission fuel pellet converts 2×10−9 kg2\times10^{-9} \text{ kg} of mass to energy. Find the energy (c=3×108c = 3\times10^8).

Example 15

medium
In a controlled reactor, the neutron multiplication factor is kept at exactly 11. What does this mean for the reaction rate?

Example 16

medium
Each fission releases 3.2imes10−11extJ3.2 imes10^{-11} ext{ J}. How many fissions are needed to release 6.4imes108extJ6.4 imes10^{8} ext{ J}?

Example 17

medium
A fission converts 4imes10−28extkg4 imes10^{-28} ext{ kg} of mass. Find the energy released (c=3imes108c = 3 imes10^8).

Example 18

challenge
A reactor runs at 600 MW600 \text{ MW} for 11 day. Using E=mc2E = mc^2 (c=3×108c = 3\times10^8), find the total mass converted. (1 day=86400 s1 \text{ day} = 86400 \text{ s})

Example 19

challenge
Fission of U-235 yields about 200 MeV200 \text{ MeV} per atom. Find the energy from 1 mol1 \text{ mol} (6×10236\times10^{23} atoms) in joules. (1 MeV=1.6×10−13 J1 \text{ MeV} = 1.6\times10^{-13} \text{ J})

Example 20

challenge
A critical mass is needed for a chain reaction because below it too many neutrons escape. If a sphere's surface-to-volume ratio falls as radius grows, why does a larger sphere reach criticality?

Example 21

easy
Using E=mc2E = mc^2 with c=3×108 m/sc = 3\times 10^8\text{ m/s}, find the energy released when 2×10−27 kg2\times 10^{-27}\text{ kg} of mass disappears.

Example 22

easy
Each U-235 fission releases about 200 MeV200\text{ MeV}. How many MeV are released by 55 fissions?

Example 23

easy
Convert 200 MeV200\text{ MeV} to joules. (1 MeV=1.6×10−13 J1\text{ MeV} = 1.6\times 10^{-13}\text{ J}.)

Example 24

easy
A reactor releases 4×10194\times 10^{19} fissions per second. If each releases 3.2×10−11 J3.2\times 10^{-11}\text{ J}, find the power output.

Example 25

medium
A nuclear power plant outputs 1.0 GW1.0\text{ GW} thermal for 11 hour. Using E=mc2E = mc^2 with c=3×108c=3\times 10^8, find the mass converted.

Example 26

medium
If a fission generates 22 neutrons that each cause new fission (with no losses), how many fissions occur in the 55th generation, starting from 11 in the 11st generation?

Example 27

medium
A reactor needs to release 1.6×1014 J1.6\times 10^{14}\text{ J}. If each fission gives 3.2×10−11 J3.2\times 10^{-11}\text{ J}, how many fissions are required?

Example 28

medium
U-235 absorbs a neutron, becomes U-236, and splits into Ba-141 and Kr-92 plus some neutrons. How many free neutrons are emitted? (Conserve nucleon number; 235+1=141+92+n235+1 = 141 + 92 + n.)

Example 29

medium
A reactor with multiplication factor k=1.001k = 1.001 starts with 101610^{16} fissions in one generation. After 100100 generations, how many fissions per generation? (Use 1016(1.001)10010^{16}(1.001)^{100}.)

Example 30

medium
A reactor uses 11 g/day of U-235 (mass converted, not burned mass). Find the average power. (c=3×108c=3\times 10^8, 1 day=86400 s1\text{ day} = 86400\text{ s}.)

Example 31

medium
Fissioning all atoms in 1 mol1\text{ mol} of U-235 releases ∼1.92×1013 J\sim 1.92\times 10^{13}\text{ J}. A typical household uses 30 kWh/day=1.08×108 J/day30\text{ kWh/day} = 1.08\times 10^8\text{ J/day}. For how many days could one mole of U-235 power one household?

Example 32

hard
A nuclear plant runs 900 MW900\text{ MW} thermal continuously. Over 3030 days it converts mass mm to energy. Find mm. (c=3×108c = 3\times 10^8, 1 day=86400 s1\text{ day} = 86400\text{ s}.)

Example 33

hard
If 30%30\% of a reactor's released energy actually reaches the grid as electricity, how much electrical energy comes from 1 kg1\text{ kg} of U-235 fissioned, given 1 kg1\text{ kg} releases 8×1013 J8\times 10^{13}\text{ J} thermal?

Example 34

hard
Each U-235 fission releases roughly 0.21 u0.21\text{ u} of mass-equivalent energy (1 u≈931 MeV1\text{ u}\approx 931\text{ MeV}). Find the energy per fission in MeV.

Example 35

hard
A pile of fissile material has k=1k = 1. Doubling the radius (with density fixed) makes surface area grow as r2r^2 but volume as r3r^3. How does the surface-to-volume ratio change?

Example 36

hard
A reactor consumes 3.0 g3.0\text{ g} of U-235 to release 2.4×1011 J2.4\times 10^{11}\text{ J} over a run. Find the energy released per gram of U-235.

Example 37

challenge
A reactor at 1.2 GW1.2\text{ GW} thermal runs continuously for 11 year (3.15×107 s3.15\times 10^7\text{ s}). At a yield of 3.2×10−11 J/fission3.2\times 10^{-11}\text{ J/fission}, find the total U-235 mass fissioned (atomic mass 235 u235\text{ u}, 1 u=1.66×10−27 kg1\text{ u} = 1.66\times 10^{-27}\text{ kg}).

Example 38

challenge
A neutron with kinetic energy 2 MeV2\text{ MeV} (3.2×10−13 J3.2\times 10^{-13}\text{ J}) and mass 1.67×10−27 kg1.67\times 10^{-27}\text{ kg} has what speed? (Nonrelativistic OK since v≪cv\ll c.)
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Background Knowledge

These ideas may be useful before you work through the harder examples.

radioactive decayspeed of light