Fission & Fusion

Nuclear Physics Lesson 14

Learning Objectives To describe the process of nuclear To describe the process of nuclear

fission.fission.

To describe the process of nuclear fusionTo describe the process of nuclear fusion

To calculate the energy released in To calculate the energy released in nuclear fusion & fission reactions.nuclear fusion & fission reactions.

To describe how a nuclear reactor To describe how a nuclear reactor works.works.

VideoVideo

Einstein’s Equation of Life and Einstein’s Equation of Life and Death Part 3 & 4.Death Part 3 & 4.

Spontaneous Fission

Large nuclei (> 92 protons) are unstable and usually results in radioactive decay.

Very rarely a large nucleus will split up spontaneously into two smaller nuclei.

This splitting of the nucleus is called fission and when it happens by itself we call it spontaneous fission.

Liquid Drop Model

We can imagine large unstable nuclei as drops of liquid.

Nuclei are not tidy and neatly arranged rows of neutrons and protons. 

The strong nuclear force acts between neighbouring nucleons. 

More About Fission

The nucleons are not linked with the same neighbours all the time.  Instead they are constantly swapping about. 

However enough of the nucleons are linked to stop the repulsive electromagnetic force tearing the nucleus apart.

Spontaneous Fission

If the drop is too large, the strong If the drop is too large, the strong force is too weak to hold the drop force is too weak to hold the drop together, so it can split into two together, so it can split into two drops all by itself.drops all by itself.

The limits the number of nucleons The limits the number of nucleons that a nucleus can contain (limits that a nucleus can contain (limits number of elements).number of elements).

Induced Fission

If you fire neutrons at the drop it will make it oscillate.

The drop can split in two if the induced oscillations are large enough.

Important Note Nuclear fission has

NOTHING whatever to do with radioactive decay.  However the parent nucleus may decay by normal radioactive decay processes, and the daughter nuclei may well be radioactive.  This is a common bear trap.

Induced Fission

We can induce fission in large nuclei such as uranium-235.  The most common isotope of uranium, U-238, does not split easily, but the 235 isotope does. 

We induce fission by encouraging the nucleus to split with a “thermal” neutron.  The neutron has to have the right kinetic energy…

Thermal because close to kinetic energies of moderator molecules.

Thermal Neutrons Too little kinetic energy means that the

neutron will bounce off the nucleus. Too much kinetic energy means that the

neutron will go right through the nucleus.

Just right means that the neutron will be captured by the strong force, which is attractive between nucleons.  The neutron gives the nucleus enough energy to resonate, and this will make the nucleus neck as shown above

Chain Reaction The nucleus flies apart

into a number of fragments, leaving on average three neutrons left over. 

These too are able to induce other nuclei to split.  Each neutron spawns three more neutrons in each fission, so we get a chain reaction.  

Fission ProductsFission Products

The fission products vary from fission to The fission products vary from fission to fission, a wide range of isotopes are fission, a wide range of isotopes are produced.produced.

For example the nucleus could split this For example the nucleus could split this way:-way:-

Or it could split this way:-Or it could split this way:-

nSrXenU 10

10038

13454

10

23592 2

nBaKrnU 10

14156

9236

10

23592 3

Calculating the Energy Calculating the Energy ReleasedReleased

We can calculate the energy released by We can calculate the energy released by finding the mass defect.finding the mass defect.

Let’s take the top example, the original Let’s take the top example, the original mass:-mass:-

And the mass after fission is:-And the mass after fission is:-

Show that the energy released per fission is Show that the energy released per fission is about 180 MeV (huge compared to chemical about 180 MeV (huge compared to chemical reactions).reactions).

unuUu 053.236)(009.1)(044.235 10

23592

unuSruXeu 859.235)2(009.12)(9354.99)(9054.133

Different Fission Different Fission ProductsProducts

The graph (red line) The graph (red line) shows the relative shows the relative number of fission number of fission products versus products versus nucleon number.nucleon number.

The most common The most common products are products are around A=90 and around A=90 and A=140.A=140.

E=Δmc2

There is a mass defect in the products of the fission so energy is given out.  

In an uncontrolled chain reaction, the energy is given out in the form of a violent explosion, which is many times more powerful than the explosive decomposition of TNT. 

In an atomic bomb, the mass that is converted to energy is about 20 grams. 

Radioactive Waste

The daughter fragments often have too many neutrons and are therefore highly unstable and decay by radioactivity. 

These form the dangerous fall-out of an atomic bomb detonation, or the waste from a nuclear power station.

May be used for things like tracers but often needs to be disposed of carefully.

The Sun – An Example of The Sun – An Example of FusionFusion

In fusion, light nuclei are joined together, increasing the binding energy per nucleon. An example is the p-p chain in the Sun:-

This will result in lots of energy being given out About 25 MeV for a helium nucleus so 6 MeV

per nucleon, but it is easier said than done…

MeV 0.4201

21

11

11 eHpp

MeV 5.49 32

11

21 HepH

MeV 12.86211

42

32

32 pHeHeHe

Question 6 Data to use: Mass of deuterium nucleus = 3.3425 × 10-

27 kg Mass of tritium nucleus = 6.6425 × 10-27

kg Mass of helium nucleus = 6.6465 ×10-27 kg Mass of a neutron = 1.675 × 10-27 kg

What is the energy in J and eV released in this reaction above?

Answer

Mass on the left hand side = 3.3425 × 10-27 kg + 6.6425 × 10-27 kg = 9.985 × 10-27 kg (P)  

Mass on right hand side = 6.6465 ×10-27 kg + 1.675 × 10-27 kg = 8.3215 × 10-27 kg (P)  

Mass deficit = 9.985 × 10-27 kg - 8.3215 × 10-

27 kg = 1.6635 × 10-27 kg (P)   Energy = 1.6635 × 10-27 kg × (3.00 × 108

m/s)2 = 1.50 × 10-11 J (P)   Energy in eV = 1.50 × 10-11 J / 1.6 × 10-19 =

9.4 × 108 eV = 940 MeV (P)

Difficulties of Fusion

It is not simply a case of sticking some protons together and shaking it up.  Each nucleus has to have sufficient energy to:

Overcome electrostatic repulsion from the protons.

Get close enough so that the attractive force of the strong force holds them together.

Difficulties of Fusion

This means that the gases have to be heated to a very high temperature, about 8 × 109 K. 

As all matter at this temperature exists as an ionised gas (plasma), it has to be confined in a very small space by powerful magnetic fields. 

Fusion has occurred, but the energy put in to cook the gases enough to make them fuse is far greater than the energy got out by a fusion reaction.

Comon Mistaiks Compared to the speed of many particles in

nuclear and particle physics, this speed is pretty sluggish.

A common bear trap is to say that nuclei are smashed to pieces by neutrons.  The neutrons tickle the nucleus; they do not hammer it.

Some students confuse fission and fusion and use the “fussion”.  It will be marked wrong in the exam, so don’t.

H-Bomb

The only use that fusion has been put to is in a thermonuclear device.  The third bomb from the left is a genuine thermonuclear device, now on display (with the nasty bits taken out).  The amount of hydrogen required in the bomb below (430 kilo-tonnes) would fill a small party balloon. 

Cold Fusion? Some scientists claim to have found fusion at

low temperatures.  They had a strange chemical reaction, but it was not fusion.

Fusion, if it could be made to work, has a number of advantages over fission:

Greater power per kilogram of fuel used; Raw materials are cheap and readily available No radioactive elements are made by the

reaction.   The downside is that materials that make up

the reactor will be irradiated with neutrons which will make them radioactive.

Summary Atomic Mass Unit: 1/12th the mass of a carbon

atom Mass defect: Difference between the mass of

nucleons separately and together within a nucleus. Difference between the two sides of a nuclear interaction equation. Energy worked out by E = mc2.                                                    

Binding Energy: Energy equivalent of the mass defect in a nucleus.  Binding energy per nucleon increases in more stable nuclei.

Fission Splitting of a nucleus.  Rarely spontaneous.  Occurs after the nucleus has been tickled with a neutron

Fusion  Joining together of two light nuclei to make a heavier nucleus.