5.3.4 Nuclear Fission and Fusion

(a) select and use Einstein’s mass–energy equation ΔE = Δmc2

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sics Introduction and background

All nuclei want to be (more) stable

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sics Introduction and background

Elements with a proton (atomic) number greater than 83 are unstable in the sense that they decay naturally.

They do so through radioactive emission. There is a way of causing some of the larger

nuclei, 238U and 239Pu each with 92 and 94 protons respectively, to split apart into two more stable fragments, forming new nuclei.

This is known as Nuclear Fission.

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sics Nuclear fission

We induce fission through neutron collision. The neutron is initially absorbed by the nucleus it

collides with. This makes it more unstable and it therefore

breaks apart often releasing several neutrons which can go on to cause further nuclei to split.

Note – Charge is conserved

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sics Fission clip

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sics Nuclear fission

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sics Nuclear fission

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sics Nuclear fission

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sics Fusion

All nuclei want to be (more) stable

Nuclei of very low mass can also become more stable by joining together to make more massive nuclei.

H + H He

H + H H + H

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sics Where does the energy come from?

Nucleons are held together by the strong, nuclear force.

To remove a nucleon from a nucleus, work has to be done against this attractive force. As work is done, the potential energy of the nucleon increases. This is similar to doing work against gravity.

The total energy required or work done is said to be the binding energy of the nucleon. In other words, the energy by which it was originally bound to the nucleus.

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sics Where does the energy come from?

The lower the potential energy of a nucleus, the greater its binding energy. Similarly the lower a rocket is in the Earth’s gravitational field, the greater the energy needed in order for it to escape.

Nuclear interactions do not obey ‘normal’, (classical mechanics), laws of conservation of energy and mass as it is possible for energy to be converted into mass and vice-versa.

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sics Einstein’s mass-energy equation

E = mc2

where

E = Energy (J)

m = Mass (kg)

c = Speed of light (ms-1)

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sics Example 1

Particles A and B interact to make particles C and D.

A + B C + D

If the measured mass of A added to that of B is greater than the measured mass of C added to that of D;

mA + mB > mC + mD

then the missing mass on the right hand side turned into energy in the interaction and was released.

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sics Example 1

The energy released also represents the overall increase in the binding energy of the two new particles.

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sics Example 2

Particles A and B interact to make particles C and D.

A + B C + D

If the measured mass of A added to that of B is less than the measured mass of C added to that of D;

mA + mB < mC + mD

then the missing mass on the left hand side is the energy required to make the interaction take place.

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sics Example 2

This ‘missing mass’ or ‘mass deficit’ in nuclear interactions allows us to determine either the energy released or required by an interaction

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sics How is this calculated?

E = mc2

Where;

E = Energy (J)

m = ‘deficit’ or ‘missing’ Mass (kg)

c = Speed of light (ms-1)

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sics Units

Use (kg) and (J) in E = mc2

However, as the energy released during nuclear reactions or processes is so small, it is often quoted in eV.

1eV ≡ 1.6×10-19J

It is similar with the masses involved. They are often quoted in unified atomic mass units. Carbon 12 has a mass of 12u

1u ≡ 1.661×10-27kg

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sics Units

As mass and energy are interchangeable on this level we can say that;

1u ≡ 1.66×10-27kg ≡ 931MeV ≡ 1.49×10-10J

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sics Worked Example

H + H He + n + energy

Measured mass of H = 2.015u

Measured mass of LHS = 2 x 2.015u = 4.030u

Measured mass of He = 3.017u and n = 1.009u

Measured mass of RHS = 4.026u

RHS mass deficit of 0.004u, therefore 3.7MeV of energy produced in this interaction.

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sics Question

DATA; all masses are measured.

He = 4.001506u, p = 1.007276u, n = 1.008665u

a.) Calculate the energy (in eV and J) released when an alpha particle is constructed.

b.) Does this represent the binding energy of an alpha particle?

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sics Answers

a.) 28.3MeV and 4.53x10-12J

b.) Yes

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sics Mass deficit

The Binding energy of any nucleus can be calculated in the same way. The ‘missing mass’, the difference between the mass of the nucleus and that of the ‘free’ nucleons is called the mass deficit.

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sics Binding energy per nucleon

If we divide the binding energy of a nucleus by the number of nucleons it contains, we have calculated the average binding energy per nucleon B.

A graph of B against nucleon number is one of the most important in nuclear physics.

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sics Binding energy graph

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sics Fusion clip