Nuclear Fusion Examples: 43 Problems with Answers

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

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 fusion is the joining of light nuclei to form a heavier nucleus, releasing energy if the final nucleus is more tightly bound.

Small nuclei can combine and release energy, especially inside stars.

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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 Fusion 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 fusion 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 D-T reaction releases

17.6\text{ MeV}

. If

80\%

of this is carried by the neutron, find the neutron's kinetic energy in joules. (

1\text{ MeV}=1.6\times10^{-13}\text{ J}

)

Answer

K E_{n} \approx 2.25 \times 10^{- 12} J

First step

Neutron share:

0.80 \times 17.6 = 14.08\text{ MeV}

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Example 2

medium

Compare

1\text{ kg}

of fusion fuel (

\sim 0.4\%

mass-to-energy) with

1\text{ kg}

of gasoline (

\sim 4.7\times10^7\text{ J}

). How many times more energy does fusion give? (

c=3\times10^8

)

Example 3

medium

A neutron of kinetic energy

14\text{ MeV}

comes from a D-T fusion. Find its speed (non-relativistic approximation,

m_n = 1.675\times10^{-27}\text{ kg}

1\text{ MeV}=1.6\times10^{-13}\text{ J}

Example 4

hard

The Sun has

\sim 1.4\times10^{30}\text{ kg}

of hydrogen-rich core fuel and converts about

0.7\%

to energy. Estimate the total fusion energy reserve. (

c=3\times10^8

)

Example 5

hard

A fusion reactor runs for

1

hour at

500\text{ MW}

. Find the mass-energy converted. (

c=3\times10^8

)

Example 6

challenge

A D-T fusion releases

17.6\text{ MeV}

into an alpha (

3.5\text{ MeV}

) and a neutron (

14.1\text{ MeV}

). Verify momentum conservation by comparing the magnitudes of

\sqrt{2 m KE}

for each. (

m_\alpha = 6.64\times10^{-27}\text{ kg}

m_n = 1.675\times10^{-27}\text{ kg}

1\text{ MeV}=1.6\times10^{-13}\text{ J}

)

Practice Problems

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

Example 1

easy

Nuclear fusion is the joining of what kind of nuclei?

Example 2

easy

Where in nature does nuclear fusion occur most prominently?

Example 3

easy

Does fusion release energy when the final nucleus is more or less tightly bound than the originals?

Example 4

easy

Why is fusion hard to achieve on Earth?

Example 5

easy

Using

E = mc^2

(

c = 3\times10^8

), find the energy from a fusion mass defect of

4\times10^{-29} \text{ kg}

Example 6

easy

In fusion, is the product nucleus's mass slightly more or less than the sum of the original nuclei?

Example 7

easy

Which reaction joins nuclei: fusion or fission?

Example 8

easy

The Sun fuses hydrogen into what element?

Example 9

medium

A fusion reaction has mass defect

5\times10^{-29} \text{ kg}

. Find the energy released (

c = 3\times10^8

Example 10

medium

Each fusion releases

4\times10^{-12} \text{ J}

. Find the energy from

1\times10^{18}

fusions.

Example 11

medium

Fusion releases about

17.6 \text{ MeV}

per D-T reaction. Convert this to joules (

1 \text{ MeV} = 1.6\times10^{-13} \text{ J}

Example 12

medium

The Sun converts about

4\times10^9 \text{ kg}

of mass to energy per second. Find the power output (

c = 3\times10^8

Example 13

medium

Compare energy per nucleon: fusion of light nuclei can release more per nucleon than fission. Why does fusion appeal as an energy source?

Example 14

medium

A fusion mass defect is

0.7\%

of the reactant mass

1\times10^{-26} \text{ kg}

. Find the energy released (

c = 3\times10^8

Example 15

medium

Why do two positively charged nuclei need high speed (temperature) to fuse?

Example 16

medium

Each fusion releases

2.8 imes10^{-12} ext{ J}

. Find the energy from

5 imes10^{17}

fusions.

Example 17

medium

A fusion reaction has mass defect

6 imes10^{-29} ext{ kg}

. Find the energy released (

c = 3 imes10^8

Example 18

challenge

The Sun's luminosity is

3.8\times10^{26} \text{ W}

. Using

E = mc^2

(

c = 3\times10^8

), find the mass lost per second.

Example 19

challenge

Four hydrogen nuclei (each

1.6726\times10^{-27} \text{ kg}

) fuse to helium (

6.6447\times10^{-27} \text{ kg}

). Find the energy released (

c = 3\times10^8

Example 20

challenge

Fusion of

1 \text{ kg}

of hydrogen converts about

0.7\%

of its mass to energy. Find that energy (

c = 3\times10^8

Example 21

easy

Which fundamental force must two protons overcome before they can fuse?

Example 22

easy

A D-T fusion reaction has mass defect

\Delta m = 3.1\times10^{-29}\text{ kg}

. Find the energy released. (

c=3\times10^8

)

Example 23

easy

4.5\times10^{-12}\text{ J}

is released per fusion, how many joules come from

2\times10^{15}

fusions?

Example 24

easy

True or false: in fusion, the total mass of the products is greater than the total mass of the reactants.

Example 25

easy

What worked example: a tokamak heats hydrogen isotopes to about

10^8\text{ K}

. Why does it need to be that hot, in one sentence?

Example 26

medium

A fusion reactor sustains

5\times10^{19}

D-T reactions per second, each releasing

2.82\times10^{-12}\text{ J}

. Find the thermal power.

Example 27

medium

The Sun loses about

4.3\times10^9\text{ kg/s}

to fusion. Over

1

year (

3.15\times10^7\text{ s}

), find the mass converted.

Example 28

medium

The proton-proton chain in the Sun converts

4

protons into a helium-4 nucleus plus

2

positrons and

2

neutrinos. Net energy released is about

26.7\text{ MeV}

. Convert to joules. (

1\text{ MeV}=1.6\times10^{-13}\text{ J}

)

Example 29

medium

A reactor uses

0.5\text{ g}

of D-T fuel and converts

0.4\%

of it to energy. Find energy released. (

c=3\times10^8

)

Example 30

medium

The deuteron has mass

3.34358\times10^{-27}\text{ kg}

; two protons have combined mass

3.34754\times10^{-27}\text{ kg}

(ignoring positron/neutrino subtleties). Estimate the mass defect for forming a deuteron.

Example 31

medium

A fusion reaction has mass defect

4.4\times10^{-29}\text{ kg}

. Express the released energy in MeV. (

c=3\times10^8

1\text{ MeV}=1.6\times10^{-13}\text{ J}

)

Example 32

medium

5\text{ g}

of D-T fuel completes fusion with

0.38\%

mass-energy conversion, find the released energy. (

c=3\times10^8

)

Example 33

hard

The Sun's energy reaches Earth as a solar constant of

1360\text{ W/m}^2

. With Earth-Sun distance

1.5\times10^{11}\text{ m}

, find the Sun's total luminosity.

Example 34

hard

Each pp-chain cycle releases

4.27\times10^{-12}\text{ J}

. If the Sun's luminosity is

3.85\times10^{26}\text{ W}

, find the number of cycles per second.

Example 35

hard

A fusion product has

KE = 3.5\text{ MeV}

(the alpha particle from D-T). Find its speed non-relativistically (

m_\alpha = 6.64\times10^{-27}\text{ kg}

1\text{ MeV}=1.6\times10^{-13}\text{ J}

Example 36

hard

A fusion plant outputs

1.0\text{ GW}

of thermal power. If each reaction releases

2.82\times10^{-12}\text{ J}

, find reactions per second.

Example 37

challenge

1\text{ kg}

fusion fuel sample releases

3.4\times10^{14}\text{ J}

. Assuming

40\%

of this becomes electrical energy, find how long it can supply a

500\text{ MW}

city.

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Related Concepts

Speed of Light

Background Knowledge

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

speed of light