Practice Nuclear Fission in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

hard

Each U-235 fission releases roughly

0.21\text{ u}

of mass-equivalent energy (

1\text{ u}\approx 931\text{ MeV}

). Find the energy per fission in MeV.

Example 2

medium

A reactor with multiplication factor

k = 1.001

starts with

10^{16}

fissions in one generation. After

100

generations, how many fissions per generation? (Use

10^{16}(1.001)^{100}

Example 3

challenge

A reactor's prompt-neutron generation time is

\tau \approx 10^{-4}\text{ s}

and

k = 1.001

. Estimate how long until the fission rate grows by a factor

e

. (

T = \tau/(k-1)

Example 4

hard

A nuclear plant runs

900\text{ MW}

thermal continuously. Over

30

days it converts mass

m

to energy. Find

m

. (

c = 3\times 10^8

1\text{ day} = 86400\text{ s}

Example 5

hard

A reactor consumes

3.0\text{ g}

of U-235 to release

2.4\times 10^{11}\text{ J}

over a run. Find the energy released per gram of U-235.

Example 6

medium

A fission reaction has mass defect

3\times10^{-28} \text{ kg}

. Find the energy released (

c = 3\times10^8

Example 7

medium

A fission fuel pellet of mass

5\text{ g}

4\%

U-235 by mass. If all U-235 fissions (releasing

200\text{ MeV}/

atom;

M_{U-235}=235\text{ g/mol}

N_A = 6\times 10^{23}

), find total energy.

Example 8

medium

If each fission yields

2.5

neutrons on average and all cause new fissions, how many fissions occur in the 3rd generation starting from

1

Example 9

easy

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

Example 10

easy

In a fission chain reaction, what particle from one fission triggers the next?

Example 11

easy

Using

E = mc^2

with

c = 3\times10^8 \text{ m/s}

, find the energy from a mass defect of

1\times10^{-27} \text{ kg}

Example 12

challenge

A neutron with kinetic energy

2\text{ MeV}

(

3.2\times 10^{-13}\text{ J}

) and mass

1.67\times 10^{-27}\text{ kg}

has what speed? (Nonrelativistic OK since

v\ll c

Example 13

easy

A reactor releases

4\times 10^{19}

fissions per second. If each releases

3.2\times 10^{-11}\text{ J}

, find the power output.

Example 14

hard

30\%

of a reactor's released energy actually reaches the grid as electricity, how much electrical energy comes from

1\text{ kg}

of U-235 fissioned, given

1\text{ kg}

releases

8\times 10^{13}\text{ J}

thermal?

Example 15

medium

A single U-235 fission releases about

3.2\times10^{-11} \text{ J}

. Find the energy from

1\times10^{20}

fissions.

Example 16

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 + n

Example 17

hard

A subcritical assembly has

k = 0.95

and starts with

10^{10}

fissions in the first generation. Roughly how many total fissions occur before the chain dies out? (Use

\sum_{n=0}^{\infty} k^n = 1/(1-k)

Example 18

medium

Fissioning all atoms in

1\text{ mol}

of U-235 releases

\sim 1.92\times 10^{13}\text{ J}

. A typical household uses

30\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 19

easy

What controls the rate of fission in a working reactor by absorbing excess neutrons?

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?

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