3 nuclear reactions, fission, fusion - presentation.ppt

1 Mass Energy Equivalence, Unified Mass Units and Atomic

Units

2 of 39 © Boardworks Ltd 2010

Mass and energy

Albert Einstein’s famous equation E = mc2 gives the universal relationship between energy and mass.

If a piece of material of mass 5.0 kg could be completely converted into energy, how much energy would be released?

energy (J) = mass (kg) × [speed of light (m s–1)]2

energy (J) = 5.0 × (3.0 × 108)2

energy released (J) = 4.5 × 1017 J

This is a colossal amount of energy – three times the amount that arrives at the Earth from the Sun every second.

Unified mass unit (u)

• Defined as 1/12 of the mass of an atom of Carbon-12

u = 1.6605402 x 10-27 kg


Atomic mass unit

1 u = 1.66 × 10–27 kg

The mass of an atom is often expressed in atomic mass units (u), to avoid using very tiny fractions of the kilogram. One atomic mass unit is equal to one-twelfth of the mass of a carbon-12 atom:

The mass and relative charge of each of the constituent particles of the atom is shown in the table below:

1.0073

1.0087

5.49 × 10–4

proton

neutron

electron

particle mass / u relative charge

+1

0

–1

Energy mass equivalence

• E = mc2

• E = 1.6605402 x 10-27 x (2.9979 x 108)2

• E = 1.4923946316 x 10-10 J

• Remembering 1 eV = 1.602177 x 10-19 J

• 1 u = 931.5 MeV


Mass and energy calculations


Mass and energy: true or false?

2 Mass Defect and Binding Energy


Mass defect

The mass of a nucleus is always less than the total mass of the nucleons from which it is made.

The difference between the mass of a nucleus and the total mass of its nucleons is called the mass defect of the nucleus.

mass defect = (mass of nucleons) – (mass of nucleus)

From the definition of an atomic mass unit, one carbon atom has a mass of 12 u. But what is the combined mass of the six protons and six neutrons that make up a carbon-12 nucleus?

total mass = (6 × 1.0073) + (6 × 1.0087) = 12.096 u

(mass defect can be given in kg or atomic mass units)

Mass defect

For helium, the mass of the nucleus = 4.00156 u

But, the mass of two protons and two neutrons = 4.0320 u!!!!

Where is the missing mass?

Mass defect

For helium, the mass of the nucleus = 4.00156 u

But, the mass of two protons and two nuetrons = 4.0320 u!!!!

Where is the missing mass?

Mass defect

The missing mass (mass defect) has been stored as energy in the nucleus. It is called the binding energy of the nucleus.

It can be found from E = mc2

Mass defect calculation

• Find the mass defect of the nucleus of gold, 196.97 - Au


• The mass of this isotope is 196.97u

• Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u


• The mass of this isotope is 196.97u

• Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u

• This nucleus has 79 protons and 118 neutrons, individually these have a mass of 79x1.0007276u + 118x1.008665u = 198.080u


• The mass of this isotope is 196.97u• Since it has 79 electrons its nuclear mass

is 196.97u – 79x0.000549u = 196.924u• This nucleus has 79 protons and 118

neutrons, individually these have a mass of 79x1.0007276u + 118x1.008665u = 198.080u

• The difference in mass (mass defect) is therefore 1.156u


• The difference in mass (mass defect) is therefore 1.156u

• This “missing mass” is stored as energy in the nucleus (binding energy).

• 1u is equivalent to 931.5 MeV


Binding energy

The binding energy of a nucleus is defined as the energy required to separate all of the nucleons in a nucleus. This is the energy needed to provide the extra mass required for all the nucleons to exist separately – it is the energy equivalent of the mass defect.

binding energy (J) = mass defect (kg) × c2

It can also be useful to calculate the binding energy in MeV from the mass defect in atomic mass units:

binding energy (MeV) = mass defect (u) × 931.3

(1 u = 931.3 MeV)

Binding energy

This is the work required to completely separate the nucleons of the nucleus.

Binding energy per nucleon

This is the work required to completely separate the nucleons of the nucleus divided by the number of nucleons.

It is a measure of how stable the nucleus is.

The binding energy per nucleon curve


Binding energy per nucleon example

1. Find the mass difference.

mass difference = (26 × 1.00728) + (30 × 1.00867) – 55.92067 = 0.52871 u

2. Find the binding energy.

binding energy = 0.52871 × 931.3 = 492.39 MeV

3. Find the binding energy per nucleon.

binding energy per nucleon = 492.39 / 56 = 8.7927 MeV

[proton mass = 1.00728 u; neutron mass = 1.00867 u]

Q. What is the binding energy per nucleon of a Fe nucleus, which has a mass of 55.92067 u? 26

56


Binding energy – questions

Mass Defect and Binding Energy Summary

• The mass of a nucleus is found to be less than the sum of the masses of the constituent protons and neutrons.

• This is explained as being due to the binding of the nucleons together into a nucleus.

• The mass defect represents the energy which would be released in forming the nucleus from its component particles.

• binding energy per nucleon = binding energy ∕number of nucleons(mass number).

E = mc2 - Einstein mass–energy equivalence

relationship.

Binding energy

This is the work required to completely separate the nucleons of the nucleus.


This is the work required to completely separate the nucleons of the nucleus divided by the number of nucleons.

It is a measure of how stable the nucleus is.

The binding energy curve

3 Nuclear Stability, Decay Series

Radioactive decay processes

decay

2 fewer protons2 fewer neutronsproton number Z

ZN

Z–2N–2

– decay

1 more proton1 less neutronproton number Z

+ decay

1 less proton1 more neutronproton number Z

decay

same protonsand neutronsproton number Z

ZN

–

+

Z+1N–1

ZN

Z–1N+1

ZN

4 Fission and Fusion

Fusion

• is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus.

Fission

• either a nuclear reaction or a radioactive decay process in which the nucleus of an atom splits into smaller parts (lighter nuclei).

Nuclear Fission

Uranium

Uranium 235 has a large unstable nucleus.

Capture

A lone neutron hitting the nucleus can be captured by the nucleus, forming Uranium 236.

Fission

The Uranium 236 is very unstable and splits into two smaller nuclei (this is called nuclear fission)

Free neutrons

As well as the two smaller nuclei (called daughter nuclei), three neutrons are released (with lots of kinetic energy)

Fission

These free neutrons can strike more uranium nuclei, causing them to split.

Chain Reaction

If there is enough uranium (critical mass) a chain reaction occurs. Huge amounts of energy are released very quickly.

Bang!

This can result in a nuclear explosion!YouTube -

nuclear bomb 4

Nuclear fusion – Star power!

Controlled fission

The chain reaction can be controlled using control rods and a moderator. The energy can then be used (normally to generate electricity).

Moderator

This slows the free neutrons down, making them easier to absorb by the uranium 235 nuclei. Graphite or water is normally used.

Control rods

These absorb excess neutrons,making sure that the reaction does not get out of control. Boron is normally used.

Heat

The moderator gets hot from the energy it absorbs from the neutrons.

Heat

This heat is used to heat water, to make steam, which turns a turbine, which turns a generator, which makes electricity.

Fission

These free neutrons can strike more uranium nuclei, causing them to split.

Chain Reaction

If there is enough uranium (critical mass) a chain reaction occurs. Huge amounts of energy are released very quickly.

The binding energy curve

Example

Bang!

This can result in a nuclear explosion!YouTube -

nuclear bomb 4


Nuclear chain reactions

When a uranium-235 nucleus undergoes induced fission after collision with a neutron, it breaks up into two smaller nuclei and two neutrons. These are called fission neutrons.

These fission neutrons can go on to cause further fission events, which will produce further neutrons, and so on, causing a chain reaction.

The smallest amount of mass needed to sustain a chain reaction is called a critical mass.

fission neutron

chain reaction


Energy from induced fission

A nuclear reactor uses a controlled chain reaction to produce heat to produce steam for a generator. Apart from the source of heat, it works in the same way as a coal-fired power station.

1. Reactor produces heat.

2. Hot coolant from core heats water to

produce steam.

3. Steam powers turbine generator.

4. Steam cooled and condensed by

cooling tower.


The thermal nuclear reactor


Controlling the reactor output


Parts of a thermal nuclear reactor


Low Level Waste


High Level Waste

Fuel rods are highly radioactive at the end of their useful life. They are an example of High Level Waste (HLW).

HLW storage at Sellafield Nuclear Reprocessing Plant in West Cumbria.

They are very hot when they leave the reactor, and continue to produce heat for years afterwards. They are kept underwater until they have cooled down considerably.

The fuel rods can then be reprocessed to extract useful fuel, before the waste goes into interim storage.


Deep underground storage

Most of the heat produced by spent nuclear fuel comes from the decay of fission products such as caesium-137 and strontium-90, which each have a half-life of about 30 years.

Both HLW and ILW also contain elements with much longer half-lives, which will remain radioactive for thousands of years. They therefore require long-term storage in deep underground facilities.

Reactor fuel cladding, and any other materials contaminated by contact with reactor fuel, are also very highly radioactive. These are termed Intermediate Level Waste (ILW).

300 m


Nuclear safety: true or false?

Nuclear fusion – Star power!


Fission and fusion

Fission and fusion are the two processes that release energy from atomic nuclei. What are they?

Fission is the splitting of large, unstable nuclei to form smaller ones. This can happen spontaneously, or it can

be encouraged to happen, as in a nuclear reactor. In the latter case, it is called induced fission.

Fusion is the combining of two smaller nuclei to create a larger one. This can only happen if the nuclei have

enough energy to overcome the electrostatic repulsion between their protons, so that they can get close enough

to be attracted by the strong nuclear force.


Nuclear fission

The energy released in nuclear power plants comes from nuclear fission.

Large, unstable nuclei such as uranium-235 or plutonium-239 break into smaller fragments, releasing energy as they do so.

The energy is then used to heat water to form steam, which powers a turbine generator, much like any other power station.

235U + neutron fission fragments + neutrons + energy


Nuclear fusion

The energy emitted by a star, such as the Sun, comes from nuclear fusion. In order for this to happen, the core temperature has to be extremely high – in excess of 10 million degrees Kelvin.

Typically, nuclear fusion in a star like the Sun involves the combination of lighter isotopes of hydrogen to form helium, and the release of energy:

Once these reactions have begun, the energy released maintains the temperature in the star, and fusion continues until all the reactants have been used.

H + H He + energy211

2 1 3


Fission and fusion – processes


m (deuterium) = 2.01355 u; m (tritium) = 3.01550 u;m (helium) = 4.00151 u; m (neutron) = 1.00867 u

Energy released by fusion

A hydrogen atom that consists of a single proton and an electron has no binding energy. Adding nucleons and binding them into the nucleus therefore releases energy.

Q: Find the energy released when deuterium and tritium fuse to form helium, according to the equation:

mass difference = (2.01355 + 3.01550) – (4.00151 + 1.00867) = 0.01887 u

energy released = 0.01887 u × 931.3 = 17.574 MeV

H + H He + n + energy211

2 3 4 1

0


Energy released by fission

Very large atoms are unstable because their nuclei are too large to be held together by short-range nuclear forces very effectively. Taking away nucleons therefore increases their stability, binds them more tightly and releases energy.

Q: Find the energy released when uranium-238 undergoes spontaneous fission into thorium according to the equation:

mass difference = (238.05078) – (234.04360 + 4.00150) = 0.0568 u

m (U-238) = 238.05078 u; m (Th-234) = 234.04360 u;m (α) = 4.00150 u

energy released = 0.0568 u × 931.3 = 52.898 MeV

U Th + α + energy238

292

234 4

90



The binding energy of a uranium nucleus is 1801 MeV. The binding energy of a helium nucleus is only 28 MeV.

Why is the helium nucleus stable, whereas the uranium nucleus is unstable?

The stability of a nucleus is based not on the binding energy but on the binding energy per nucleon. This is equal to the binding energy divided by the number of nucleons and indicates how tightly bound each nucleon is on average.

uranium helium


Binding energy per nucleon graph

mass number

bin

din

g e

ner

gy

per

n

ucl

eon

/ M

eVHow does the binding energy per nucleon vary for atoms of different sizes?

2

4

6

8

0 50 100 150 200

fusion fission

most tightly bound nuclei

Fe

U-235

energy yield from fusion

energy yield from fission


Fission and fusion – calculations

5 Nuclear Reactions

Nuclear reactions

N7

14

+ O8

17

+ p1

1

He2

4 2+

Changes in Mass and Proton NumberAlpha decay:

Am241

95Np

237

93α

4

2+

11

5

0

+1C

11

6B β+ν+

90

39Sr

90

38Y β+ν

0

-1+

Beta - decay:

Beta + decay:

“positron”

Nuclear reactions - Artificial transmutation

One atomic mass unit (u) is defined as one twelfth of the mass of one atom of the carbon 12 isotope.1 u = 1.661x10-27 kg = 931.5 MeV c −2 = 931.5GeV c −2

• The change of one element to another through the bombardment of a nucleus is known as artificial transmutation.

Fission means splitting up. Bombarding Uraniumwith neutrons can trigger a fission reaction.

• Fusion means joining together. • Fusion gives out more energy per kilogram of fuel than fission.• The stars (e.g. our SUN) are powered by fusion reactions.

The antineutrino

The antineutrino in beta decay was not detected until 1953, although its presence had been predicted theoretically.

n p + e + ve 10

11

0-1

00

The antineutrino

The mass of the neutron is bigger than that of the proton and electron together.

n p + e + ve

1.008665u – (1.007276 + 0.0005486)u = 0.00084u

10

11

0-1

00

1.008665 u 1.007276 u 0.0005486 u

The antineutrino

This corresponds (using E = mc2) to an energy of 0.783 MeV.

n p + e + ve 10

11

0-1

00

The antineutrino

This extra energy should show up as kinetic energy of the products (proton and electron). Since the electron should carry most of the kinetic energy away, so we should observe electrons with an energy of about 0.783 MeV.

n p + e + ve

In fact we observe electrons with a range of energies from zero up to 0.783 MeV.

10

11

0-1

00

The antineutrino

Where is the missing energy? In 1933 Wolfgang Pauli and Enrico Fermi hypothesized the existence of a third very light particle produced during the decay. Enrico Fermi coined the term neutrino for the ”little neutral one”

n p + e + ve 10

11

0-1

00

Ahhhhh! The little neutral one!

Transmutation

• changing a nucleus by adding nucleons.


Energy–mass conversion

The conversion of small masses into large quantities of energy is the basis of nuclear power and the nuclear bomb. It is also the source of the Sun’s energy.

Energy can also be converted into mass. For example, a gamma photon can be converted into an electron and a positron.

γ

e–

e+

This is called pair production.


Binding energy

Fission is a splitting of nuclei, while fusion is a combining of nuclei. How can both of these processes release energy?

Energy is released in a nuclear reaction when the binding energy of the products is greater

than the binding energy of the reactants.

This is the equivalent of saying that the mass of the products is less than the mass of the reactants. The difference in mass is released as energy.

Very small nuclei release energy by increasing in size.

Very large nuclei release energy by decreasing in size.

Why is this, and what happens to the elements in between?


Understanding binding energy


Multiple-choice quiz


What’s the keyword?


Glossary

Not Used or Need Transferring

Nuclear energy levelsThere are 2 distinct length of tracks in this Alpha decayTherefore, the energy levels in the nucleus are discrete.Gamma-ray spectra are also discrete.So the nucleus, like the atom, is a quantum system.

11

5

0

+1C11

6 B β+

“positron”Beta + decay:

Beta energy spectra are continuous, the neutrino was postulated to account for these spectra.

Nuclear energy levels

We have seen previously that electrons exist in specific energy levels around the atom.

There is evidence that energy levels exist inside the nucleus too.

Wow!


When a nucleus decays by emitting an alpha particle or a gamma ray, the particles or photons emitted are only at specific energies (there is not a complete range of energies emitted, only certain specific levels).


An alpha particle or photon thus has an energy equal to the difference between energy levels of the nucleus.

energy levels in 235U (MeV)

51.57

0.051

0.013

0.000


In the alpha decay of 239Pu to 235U, the plutonium nucleus with an energy of 51.57 MeV can decay into Uranium at 3 different energy levels.


51.57

0.051

0.013

0.000

Plutonium-239


If the 239Pu (51.57 MeV) decays to the ground state of 235U (0 MeV), an alpha particle of energy 51.57 MeV is emitted.


51.57

0.051

0.013

0.000

Plutonium-239

Alpha emission (51.57 MeV)


If the 239Pu (51.57 MeV) decays to the 2nd excited state of 235U (0.051 MeV), an alpha particle of energy 51.57-0.051 = 51.52 MeV is emitted. The uranium nucleus is now in an excited state so can decay further by gamma emission to the ground state.


51.57

0.051

0.013

0.000

Plutonium-239


Gamma emission (0.051 MeV)


In fact the nucleus could decay first to the 0.013 level, and then the ground state, thus emitting two gamma photons.


51.57

0.051

0.013

0.000

Plutonium-239


Gamma emission (0.038 MeV)

Gamma emission (0.013MeV)

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Nuclear safety

Nuclear reactors produce huge amounts of energy, much of which is in the form of gamma rays.

Gamma rays are highly energetic photons of electromagnetic radiation. If they come into contact with the body they can cause cellular mutations, which can lead to cancer.

Thick concrete shielding is used to absorb as many as possible of the stray gamma ray photons that try to escape from the reactor.

γ

damaged DNA

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Radiation exposure

When handling radioactive material, the user should:

The ALARA principle defines acceptable levels of exposure: the risk should be As Low As Reasonably Achievable.

use tongs, a glove box or robots

be as far from the source as possible

minimize exposure time.

A radiation badge can be worn by a radiation worker to monitor his or her cumulative exposure to radiation.

film badge dosimeter

photographic film

aluminium

lead

3 nuclear reactions, fission, fusion - presentation.ppt

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mass defectthe mass

atomic mass unitthe

nuclear mass

total mass

mass of 79x1

combined mass

mass energy equivalence

energy mass equivalencee