Atomic and Nuclear Physics

Topic 7.1 The Atom

Objectives

7.1.1 Describe a model of the atom that features a small nucleus surrounded by electrons.

7.1.2 Outline the evidence that supports a nuclear model of the atom.

7.1.3 Outline one limitation of the simple model of the nuclear atom.

7.1.4 Outline evidence for the existence of atomic energy levels.

Atomic Structure John Dalton said that atoms were tiny indivisible spheres,

but in 1897 J. J. Thomson discovered that all matter contains tiny negatively charged particles.‑

He showed that these particles are smaller than an atom.

He had found the first subatomic particle the electron.‑

Scientists then set out to find the structure of the atom.

Thomson thought that the atom was a positive sphere of matter and the negative electrons were embedded in it as shown here

This `model' was called the `plum pudding' model ‑of the atom.

Discovering the atom

Rutherford's alpha scattering experiment

Ernst Rutherford decided to probe the atom using fast moving alpha (α) particles.

He got his students Geiger and Marsden to fire the positively charged ‑ α particles at very thin gold foil and ‑observe how they were scattered.

In 1911 Rutherford described his nuclear model of the atom. He said that:

All of an atom's positive charge and most of its mass is concentrated in a tiny core.

Rutherford called this the nucleus.

The electrons surround the nucleus, but they are at relatively large distances from it.

The atom is mostly empty space!

The Nuclear Model of the atom

Using this model Rutherford calculated that the diameter of the gold nucleus could not be larger than 10-14 m.

The previous diagram is not to scale. With a 1 mm diameter nucleus the diameter of the atom would have to be 10 000 mm or 10 m!

The nucleus is like a pea at the centre of a football pitch.

Limitations to the Nuclear Atom

This model was unable to account for the fact that many elements exhibited a range of atomic weights.

Energy Levels Thomas Melville was the first to study the light

emitted by various gases.

He used a flame as a heat source, and passed the light emitted through a prism.

Melvill discovered that the pattern produced by light from heated gases is very different from the continuous rainbow pattern produced when sunlight passes through a prism.

The new type of spectrum consisted of a series of bright lines separated by dark gaps.

This spectrum became known as a line spectrum.

Melvill also noted the line spectrum produced by a particular gas was always the same.

In other words, the spectrum was characteristic of the type of gas, a kind of "fingerprint" of the element or compound.

This was a very important finding as it opened the door to further studies, and ultimately led scientists to a greater understanding of the atom.

Spectra can be categorized as either emission or absorption spectra.

An emission spectrum is, as the name suggests, a spectrum of light emitted by an element.

It appears as a series of bright lines, with dark gaps between the lines where no light is emitted.

An absorption spectrum is just the opposite, consisting of a bright, continuous spectrum covering the full range of visible colors, with dark lines where the element literally absorbs light.

The dark lines on an absorption spectrum will fall in exactly the same position as the bright lines on an emission spectrum for a given element, such as neon or sodium.

Emission Spectra

Absorption Spectra

For example, the emission spectrum of sodium shows a pair of characteristic bright lines in the yellow region of the visible spectrum.

An absorption spectrum will show 2 dark lines in the same position.

Evidence

What causes line spectra?

You always get line spectra from atoms that have been excited in some way, either by heating or by an electrical discharge.

In the atoms, the energy has been given to the electrons, which then release it as light.

Line spectra are caused by changes in the energy of the electrons.

Large, complicated atoms like neon give very complex line spectra, so physicists first investigated the line spectrum of the simplest possible atom, hydrogen, which has only one electron.

Planck and Einstein's quantum theory of light gives us the key to understanding the regular patterns in line spectra.

The photons in these line spectra have certain energy values only, so the electrons in those atoms can only have certain energy values.

The electron, shown by the blue dot, has the most potential energy when it is on the upper level, or excited state.

When the electron is on the lower level, or ground state, it has the least potential energy.

This energy jump, or transition, has to be done as one jump.

It cannot be done in stages.

This transition is the smallest amount of energy that this atom can lose, and is called a quantum (plural = quanta).

The potential energy that the electron has lost is given out as a photon.

This energy jump corresponds to a specific frequency (or wavelength) giving a specific line in the line spectrum.

Nuclear Structure

Objectives

7.1.5 Explain the terms nuclide, isotope and nucleon.

7.1.6 Define nucleon number A, proton number Z and neutron number N.

7.1.7 Describe the interactions in a nucleus.

Mass Number

The total number of protons and neutrons in the nucleus is called the mass number (or nucleon number).

Protons and neutrons are called nucleons.

Each is about 1800 times more massive than an electron, so virtually all of an atom's mass is in its nucleus.

Atomic Number

All materials are made from about 100 basic substances called elements.

An atom is the smallest `piece' of an element you can have.

Each element has a different number of protons in its atoms:

It has a different atomic number (sometimes called the proton number).

The atomic number also tells you the number of electrons in the atom.

Isotopes

Isotopes are atoms with the same proton number, but different nucleon numbers.

Every atom of oxygen has a proton number of 8. That is, it has 8 protons (and so 8 electrons to make it a neutral atom).

Most oxygen (168O) atoms have a nucleon number of 16.

This means that these atoms also have 8 neutrons.

There is an isotope of oxygen 188O.

How many neutrons are there in the nucleus of an 188O

atom?

Evidence for Neutrons

The existence of isotopes is evidence for the existence of neutrons because there is no other way to explain the mass difference of two isotopes of the same element.

By definition, two isotopes of the same element must have the same number of protons, which means the mass attributed to those protons must be the same.

Therefore, there must be some other particle that accounts for the difference in mass, and that particle is the neutron.

Interactions in the Nucleus Electrons are held in orbit by the force of

attraction between opposite charges.

Protons and neutrons (nucleons) are bound tightly together in the nucleus by a different kind of force, called the strong, short-range nuclear force.

There are also Coulomb interaction between protons due to the fact that they are charged particles.

Atomic and Nuclear Physics

Topic 7.2 Radioactive Decay

Objectives

7.2.1 Describe the phenomenon of natural radioactive decay.

7.2.2 Describe the properties of alpha (α) and beta (β) particles and gamma (γ) radiation.

7.2.3 Describe the ionizing properties of alpha (α) and beta (β) particles and gamma (γ) radiation.

7.2.4 Outline the biological effects of ionizing radiation.

Radioactivity

In 1896, Henri Becquerel discovered, almost by accident, that uranium can blacken a photographic plate, even in the dark.

Uranium emits very energetic radiation it is radioactive.‑

Then Marie and Pierre Curie discovered more radioactive elements including polonium and radium.

Scientists soon realized that there were three different types of radiation.

These were called alpha (α), beta (β), and gamma (γ) rays.

INVESTIGATE ALPHA, BETA-, BETA+, GAMMA RAYS & BIOLOGICAL EFFECTS OF RADIATION

Alpha, Beta and Gamma

Properties

Properties

The diagram on the right shows how the different types are affected by a magnetic field.The alpha beam is a flow of positively (+) charged particles, so it is equivalent to an electric current.It is deflected in a direction given by Fleming's left hand rule.‑

The beta particles are much lighter than the alpha particles and have a negative ( ) charge, so they are deflected more, ‑and in the opposite direction.

Being uncharged, the gamma rays are not deflected by the field.

Alpha and beta particles are also affected by an electric field in other words, there is a force on them if they pass ‑between oppositely charged plates.

Ionising Properties

α particles, ‑ β particles and ‑ γ ray photons are all ‑very energetic particles.

Typically the kinetic energy of an α particle is ‑about 6 million eV (6 MeV).

We know that radiation ionizes molecules by `knocking' electrons off them.

As it does so, energy is transferred from the radiation to the material.

Why do the 3 types of radiation have different penetrations?

Since the α-particle is a heavy, relatively slow moving particle with a charge of +2e, it ‑interacts strongly with matter.

It produces about 1 x 105 ion pairs per cm of its path in air.

After passing through just a few cm of air it has lost its energy.

the β particle ‑ is a much lighter particle than the α particle and it travels much faster.‑

Since it spends just a short time in the vicinity of each air molecule and has a charge of only e, it causes less ‑intense ionization than the α particle.‑

The β particle produces about 1 x 10‑ 3 ion pairs per cm in air, and so it travels about 1 m before it is absorbed.

A γ ray photon ‑ interacts weakly with matter because it is uncharged and therefore it is difficult to stop.

A γ ray photon often loses all its energy in ‑one event.

However, the chance of such an event is small and on average a γ photon travels a ‑long way before it is absorbed.

Detection of Radiation

Geiger M‑ uller (GM) tube

This can be used to detect alpha, beta, and gamma radiation.

The `window' at the end is thin enough for alpha particles to pass through.

If an alpha particle enters the tube, it ionizes the gas inside.

This sets off a high voltage spark across the gas and a pulse of ‑current in the circuit.

A beta particle or burst of gamma radiation has the same effect.

The ionisation chamber is another detector which uses the ionising power of radiation.

The chamber contains fixed electrodes, which attract electrons and ions produced by the passage through the chamber of high speed ‑particles or rays.

When the electrodes detect ions or electrons, a circuit is activated and a pulse is sent to a recording device such as a light.

If you plot the neutron number N against the proton number Z for all the known nuclides, you get the diagram shown here

As Z increases the `stability line' curves upwards.

Heavier nuclei need more and more neutrons to be stable.

It is the strong nuclear force that holds the nucleons together, but this is a very short range force.

The repulsive electric force between the protons is a longer range force.

So in a large nucleus all the protons repel each other, but each nucleon attracts only its nearest neighbours.

More neutrons are needed to hold the nucleus together (although adding too many neutrons can also cause instability).

There is an upper limit to the size of a stable nucleus, because all the nuclides with Z higher than 83 are unstable.

Transformations Examples

Alpha Decay

An alpha particle is a helium nucleus and is ‑written 4

2He or 42α.

It consists of 2 protons and 2 neutrons.

When an unstable nucleus decays by emitting an α particle it loses 4 nucleons ‑and so its nucleon number decreases by 4.

Also, since it loses 2 protons, its proton number decreases by 2

The nuclear equation is

AZ X → A-4

Z-2 Y + 42α.

Note that the top numbers balance on each side of the equation. So do the bottom numbers.

Beta Decay

Beta decay

Many radioactive nuclides (radio nuclides) decay by ‑β emission.‑

This is the emission of an electron from the nucleus.

But there are no electrons in the nucleus!

What happens is one of the neutrons changes into a proton (which stays in the nucleus) and an electron (which is emitted as a β particle).‑

This means that the proton number increases by 1, while the total nucleon number remains the same.

The nuclear equation is

AZ X → A

Z+I Y + 0-1e

Notice again, the top numbers balance, as do the bottom ones.

A radio nuclide ‑ above the stability line decays by β emission.‑

Because it loses a neutron and gains a proton, it moves diagonally towards the stability line, as shown on this graph

Gamma Decay

Gamma emission does not change the structure of ‑the nucleus, but it does make the nucleus more stable because it reduces the energy of the nucleus.

Decay chains

A radio nuclide often produces an unstable daughter ‑nuclide.

The daughter will also decay, and the process will continue until finally a stable nuclide is formed.

This is called a decay chain or a decay series.

Part of one decay chain is shown below

When determining the products of decay series, the same rules apply as in determining the products of alpha and beta, or artificial transmutation.

The only difference is several steps are involved instead of just one.

Objectives

7.2.6 State that radioactive decay is a random and spontaneous process and that the rate of decay decreases exponentially with time.

7.2.7 Define the term radioactive half life‑ .

7.2.8 Determine the half-life of a nuclide from a decay curve.

7.2.9 Solve radioactive decay problems involving integral numbers of halflives.

Half Life Suppose you have a sample of 100 identical nuclei.

All the nuclei are equally likely to decay, but you can never predict which individual nucleus will be the next to decay.

The decay process is completely random.

Also, there is nothing you can do to `persuade' one nucleus to decay at a certain time.

The decay process is spontaneous.

Does this mean that we can never know the rate of decay?

No, because for any particular radio nuclide ‑there is a certain probability that an individual nucleus will decay.

This means that if we start with a large number of identical nuclei we can predict how many will decay in a certain time interval.

Iodine 131 is a radioactive isotope of iodine.‑On average, 1 nucleus disintegrates every second for every 1000 000 nuclei present.

To begin with, there are 40 million undecayed nuclei.

8 days later, half of these have disintegrated.

With the number of undecayed nuclei now halved, the number of disintegrations over the next 8 days is also halved.

It halves again over the next 8 days... and so on.

Iodine 131 has a ‑ half life ‑ of 8 days.

Definition

The half life of a radioactive isotope is the time ‑taken for half the nuclei present in any given sample to decay.

Activity and half‑life

In a radioactive sample, the average number of disintegrations per second is called the activity.

The SI unit of activity is the becquerel (Bq).

An activity of, say, 100 Bq means that 100 nuclei are disintegrating per second.

Definition 2

The half life of a radioactive isotope is the time ‑taken for the activity of any given sample to fall to half its original value.

Exponential Decay

Any quantity that reduces by the same fraction in the same period of time is called an exponential decay curve.

The half life can be calculated from decay curves

Take several values and then take an average

Example

A freshly prepared sample of the isotope iodine-131 has a n initial activity of 2.0 * 105 Bq. After 40 days, the activity of the sample is 6.3 * 103 Bq.

Estimate the half-life of iodine-131.

By plotting a suitable graph, estimate the activity of the sample after 12 days.

Atomic and Nuclear Physics

Topic 7.3 Nuclear Reactions, Fission and Fusion

Objectives

7.3.1 Describe and give an example of an artificial (induced) transmutation.

7.3.2 Construct and complete nuclear Equations.

7.3.3 Define the term unified atomic mass unit..

7.3.4 Apply the Einstein mass–energy equivalence relationship

7.3.5 Define the concepts of mass defect, binding energy and binding energy per Nucleon.

7.3.6 Draw and annotate a graph showing the variation with nucleon number of the binding energy per nucleon.

7.3.7 Solve problems involving mass defect and binding energy.

Nuclear reactions Rutherford conducted experiments bombarding

nitrogen gas with alpha particles from bismuth 214.‑

He discovered that fast moving particles were ‑produced that could travel further in the gas than did the alpha particles.

Furthermore, the "new" particles were deflected by a magnetic field in the way one would expect positively charged particles to be deflected.

Rutherford concluded that the particles released in the collision were protons.

Since the number of protons in a nucleus defines an element, a change in this number literally changes the element.

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

Rutherford used the cloud chamber to test his two theories of artificial transmutation.

He realized that if a proton was simply being chipped off the nitrogen nucleus, then the cloud chamber should show four distinct tracks,

one for the alpha particle before the collision and one each for the alpha particle, proton, and recoiling transmuted nucleus after the collision.

However, if the alpha particle was absorbed by the nitrogen nucleus, then the alpha particle track should disappear, leaving only three tracks, that of the alpha particle before the collision, and the tracks of the proton and recoiling nucleus after the collision.

In 1925, P M. S. Blackett, an associate of Rutherford's, settled the issue when he discovered only three tracks, proving the alpha particle is indeed absorbed upon colliding with the nitrogen nucleus.

The collision between an alpha particle and nitrogen can be represented by the following equation:

42α + 14

7N → 178O + 1

1H

The equation shows that when nitrogen is bombarded by an alpha particle, it is transmuted into oxygen, releasing a proton in the process.

The proton is represented as a hydrogen nucleus, that is, a hydrogen atom with no electron.

It carries a positive charge equal in magnitude to the charge on an electron.

Artificial transmutation does not happen only with alpha particle bombardment.

In fact, neutrons, protons, and deuterons ( 21H )

can also be used to produce artificial nuclear reactions.

The key to understanding these reactions, and making predictions about the products of such reactions is being able to balance nuclear equations.

Example Let X represent the unknown nucleus.

168O +1

0n → AZX + 2

1H

Einstein’s Mass-Energy Equivalence Relationship

In 1905, while developing his special theory of relativity, Einstein made the startling suggestion that energy and mass are equivalent.

He predicted that if the energy of a body changes by an amount E, its mass changes by an amount m given by the equation

E = mc2

where c is the speed of light.

Radioactive decay, which is a spontaneous nuclear reaction, is useful for producing a large enough energy change to measure the change in mass.

Thus for a radium atom, the combined mass of the alpha particle it emits and the radon atom to which it decays is, by atomic standards, appreciably less than the mass of the original radium atom.

Mass appears as energy and the two can be regarded as equivalent.

In nuclear physics mass is measured in unified atomic mass units (u)

1 u being one twelfth of the mass of the carbon 12 atom which equals 1.66 x 10‑ -27 kg.

It can readily be shown using E = mc2 that 931 MeV has mass 1 u

A unit of energy may therefore be considered to be a unit of mass, and in tables of physical constants the masses of various atomic particles are often given in MeV as well as in kg and u.

For example, the electron has a rest mass of about 0.5 MeV

If the principle of conservation of energy is to hold for nuclear reactions it is clear that mass and energy must be regarded as equivalent.

The implication of E = mc2 is that any reaction producing an appreciable mass decrease is a possible source of energy.

Mass Defect and Binding Energy

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

The energy equivalent is called the binding energy of the nucleus

Binding energy is the energy required to separate the nucleus into its individual nucleons

OR the energy that would be released in assembling a nucleus from its individual nucleons

The binding energy, derived in a similar manner for other nuclides, is found to increase as the mass (nucleon) number increases.

For neon, 2010Ne, it is 160 MeV

If the binding energy of a nucleus is divided by its mass number, the binding energy per nucleon is obtained.

The next graph shows how this quantity varies with mass number; in most cases it is about 8 MeV

AL

Objectives

7.3.8 Describe the processes of nuclear fission and nuclear fusion.

7.3.9 Apply the graph in 7.3.6 to account for the energy release in the processes of fission and fusion.

7.3.10 State that nuclear fusion is the main source of the Sun’s energy.

7.3.11 Solve problems involving fission and fusion reactions.

Fission

Fission means splitting up.

In a fission reaction a large nucleus (A > 200) splits in two.

Look again at the binding energy per nucleon curve

If a nucleus with A > 200 splits in half, the two fragments have a higher binding energy per nucleon than the parent.

This means that the fragments are more stable than the parent.

The excess energy is released by the reaction.

Spontaneous fission is very rare. Uranium is the largest nucleus found on Earth.

Its isotopes will sometimes fission naturally.

Bombarding the nucleus with neutrons can trigger a fission reaction.

The strong forces that hold the nucleus together only act over a very short distance.

When a uranium nucleus absorbs a neutron it knocks the nucleus out of shape.

If the nucleus deforms enough, the electrostatic repulsion between the protons in each half becomes greater than the strong force.

It then splits in two.

Fission of a uranium nucleus gives out about 200 MeV of energy.

Chain Reactions When the uranium nucleus splits, a number of neutrons

are also ejected.

If each ejected neutron causes another uranium nucleus to undergo fission, we get a chain reaction.

The number of fissions increases rapidly and a huge amount of energy is released.

Uncontrolled chain reactions are used in nuclear bombs

The energy they unleash is devastating.

Nuclear power stations use the heat released in carefully controlled fission reactions to generate electricity.

They use control rods to absorb some of the neutrons.

Fusion

Fusion means joining together.

In a fusion reaction two light nuclei join together to make a heavier nucleus.

Fusion gives out more energy per kilogram of fuel than fission.

The increases in binding energy per nucleon are much larger for fusion than for fission reactions, because the graph increases more steeply for light nuclei.

So fusion gives out more energy per nucleon involved in the reaction than fission.

Stars are powered by fusion reactions.

Each second, in our Sun, more than 560 million tonnes of hydrogen fuse together to make helium.

One series of reactions for this is shown here:

The energy released is radiated by the Sun at a rate of 3.90 x 1020 MW.

This is the power output of a million million million large power stations!

One possible reaction that is usable as a source of power is the fusion of deuterium and tritium.

Fusion has a number of advantages over fission: greater power output per kilogram, the raw materials are cheap and readily available, no radioactive elements are produced directly, irradiation by the neutrons leads to radioactivity

in the reactor materials but these have relatively short half lives and only need to be stored safely for a short time.

The JET (Joint European Torus) project was set up to carry out research into fusion power.

It has yet to generate a self sustaining fusion ‑reaction.

The main problem is getting two nuclei close enough for long enough for them to fuse.

The enormous temperatures and pressures in the Sun's core provide the right conditions.

On Earth temperatures of over 100 million kelvin are needed.

At this temperature all matter exists as an ionised gas or plasma.

Another problem is containment.

What can you use to hold something this hot?

JET uses magnetic fields in a doughnut shaped chamber called a torus to keep the plasma away from the container walls.

Unfortunately generating high temperatures and strong magnetic fields uses up more energy than the fusion reaction produces!

We are still some years off a fusion power station.