Tutorial 2 - Stable and Unstable nuclei

 Contents

What holds the Nucleus together?

The nucleus is a very small space, so the repulsion force is very strong.  Protons repel each other, because they are like charges - the electrostatic force.  This means that the nucleus should fly apart, but we know it doesn't. There has to be a force that counteracts the repulsion:

• It is called the strong force.

• Neutrons and protons provide the strong force.

 What element is this the nucleus of?  Write it out in isotope notation.

The protons and neutrons are called nucleons.  Both feel the strong force.  The strong force has these features:

• Electrostatic repulsion between 2 protons has a value of about 200 N;

• This means that the protons would move apart with an acceleration of 1.2 ื 1029 m s-2;

• Therefore the strong force must pull nucleons with at least that kind of force;

• It has a very short range, about 3 femtometres (3 fm = 3 ื 10-15 m).

This is shown on the graph showing the force between two protons:

From this graph we can see that:

• The repulsive electrostatic force is equal in value, but has the opposite direction to the attractive strong force.

• This happens at about 1 fm.

• The strong force is zero at 3 fm.

• Therefore, if the distance from the centre is more than 3 fm, there is an overall repulsive force and the two protons will fly apart.

Neutrons help to bind the nucleus together by the strong force, but the numbers of neutrons and protons have to be right.  Otherwise the nucleus is unstable.  The more protons there are, the more neutrons are needed to keep the nucleus stable.  There is a limit, which is reached when the proton number is 82, i.e. lead:

Lead is the largest stable nucleus.  To hold the 82 protons of the lead nucleus together, 126 neutrons are needed.

Unstable Nuclei

Most isotopes have the right numbers of protons and neutrons to be stable.  However some isotopes are unstable.  This results from the nucleus:

• being too big;

• having too many neutrons;

• having too many protons (rare).

This activity will show you how the neutrons hold together the nucleus to keep it stable:  https://phet.colorado.edu/en/simulation/build-an-atom

Radiation is the process by which an unstable parent nucleus becomes more stable by decay into a daughter nucleus by emitting particles and/or energy.  The basic form of radioactive decay can be summed up in this diagram:

The decay can consist of several steps.  The unstable nucleus decays to another nucleus of a different atom by a process called transmutation.  If the new nucleus is unstable it will decay again.  This is known as a decay chain.  There may be several steps, some of which last a very long time indeed, or can be very short.  Some elements have a decay time of thousands of millions of years.  In others the decay time can be microseconds.  Whichever, the process is entirely random.  If you watch an individual nucleus, the decay may occur in 10 seconds, or several million years.  There is nothing whatever you can do to speed up the process.

Elements have different isotopes.  An element and its isotope have:

• The same number of protons (and electrons)

• Different numbers of neutrons.

If the isotope is unstable, it is radioactive and is called a radioisotope

The radioactive decay is measured by the number of counts per second or disintegration per second.  A computer can act as a rate-meter and store the results.  It will also plot a graph.  The unit for counts per second is the Becquerel (Bq):

1 Bq = 1 count per second

There are three kinds of radiation:

• Alpha  a helium nucleus;

• Beta  a high speed electron;

These kinds of radiation can be emitted individually or in any combination, depending on the type of isotope that is emitting the radiation.  Often when an alpha particle is emitted the nucleus is excited and releases the excess energy in the form of a gamma ray or gamma photon.

When specimens of radioactive isotopes decay they do so entirely randomly.  There is no pattern whatsoever, and the rate of decay is not affected by temperature or other physical factors, or chemical reactions.  This means you cannot speed it up by hitting the material, heating it strongly, or reacting it with strong acids.

The table helps us to compare the properties of radiation

 Radiation Description Penetration Ionisation Effect of E or B field Alpha (a) Helium nucleus 2p + 2n Q = + 2 e Few cm air Thin paper Intense, about 104 ion pairs per mm. Slight deflection as a positive charge Beta (b) High speed electron Q = -1 e Few mm of aluminium Less intense than a, about 102 ion pairs per mm. Strong deflection in opposite direction to a. Gamma (g) Very short wavelength em radiation Several cm lead, couple of m of concrete Weak interaction about 1 ion pair per mm. No effect.

We will look at the mechanisms of production of alpha and beta radiations later.

We need to be aware that elements with unstable nuclei can be harmful to living organisms.

• Alpha particles are intensely ionising.  The good news is that they are stopped by a few cm of air or by the skin.  The bad news is that if you ingest an alpha emitter, the radiation quickly will macerate the DNA of living cells, such as the lining of the intestines or lungs.

• Beta particles can penetrate the body, but are stopped by a few mm of Aluminium.  They are less damaging than gamma rays or alpha particles.  They are weakly ionising.  Some medical tracers are radioisotopes that are beta emitters

• Gamma rays are considered the most dangerous form of radiation, as they are very penetrating.  They are attenuated by several centimetres of lead, but not stopped completely.  So they can pass easily through our bodies.  Surprisingly, they cause very little ionisation, which causes genetic damage, and are not absorbed very efficiently by DNA, so quite a long exposure to gamma rays is needed to destroy DNA completely.  However random damage can be done by smaller doses.  It can be repaired by the cells repair mechanisms, but misrepair can cause mutations, which can lead to cancer.  Intense radiation can mess up DNA sufficiently to cause radiation sickness.  This can of course apply to other radiations as well.

People working with radioactive materials must take precautions to ensure their safety, such as:

• Not touching the material directly, but handling it with tongs;

• Washing their hands after each job handling radioactive materials;

Work with highly radioactive materials is carried out remotely behind walls that are 2 metres thick.

In a school physics lab, the sources are VERY weak, but you must always follow the rules in their handling.  Students under 16 are not allowed to handle radioactive materials.

Possible modes of decay for unstable nuclei

Alpha radiation (a) mostly comes from heavy nuclides with proton numbers greater than 82, but smaller nuclides with too few neutrons can also be alpha emitters.  The term Q stands for the energy.  The animation shows the idea:

The general decay equation is summarised below.

We should note the following:

• The alpha particle is a helium nucleus (NOT atom).

• Energy is released in the decay. The energy is kinetic, with the majority going to the alpha particle and a little going to the decayed nucleus.

• The velocity of the alpha particle is much greater than that of the nucleus.

• The nucleon number goes down by 4, the proton number by 2.

• A typical alpha decay is:

Alpha particles are intensely ionising.  They smash through air molecules, knocking off electrons as they go.  However this reduces the kinetic energy, so that in the end they stop.  Then they pick up a couple of free electrons to become helium atoms.  To collect an appreciable sample of helium from an alpha emitter would take a very long time.

Neutron rich nuclei tend to decay by beta minus (b-) emission.  The beta particle is a high-speed electron ejected from the nucleus, NOT the electron clouds.  It is formed by the decay of neutrons, which are slightly more energetic than a proton.  Isolated protons are stable; isolated neutrons last about 10 minutes.

Watch how the neutron suddenly emits an electron (blue) and the electron anti-neutrino (black), turning into a proton.

The neutron, having emitted an electron, is converted to a proton, and this results in the proton number of the nuclide going up by 1.  A new element is formed.  The reaction at the nucleon level is:

Notice that as well as the neutron (n) and the proton (p), the beta particle is represented as an electron (e).  The strange symbol ne (noo-bar e) is a strange little particle called an electron antineutrino.  (Note: The sign for an antiparticle is usually the particle symbol with a bar over it.  It is not possible to do this satisfactorily in this web-editor, so in the text, I will show it as white font highlighted in black.  Therefore X-bar will be shown as X.  The equations are pictures produced by a graphics equation editor.)

Observations of beta minus decay led to the concept of the neutrino.  Enrico Fermi (1901 - 1954) noticed that when a nucleus ejected a high speed electron, it did not recoil in the opposite direction to the path of the electron.  It recoiled at a slight angle.  Conservation of momentum rules suggested that there must have been a third very tiny particle, which he called the neutrino (neutral little thing).

Later it was called the electron neutrino (as it was associated with an electron).  However the use of quantum numbers showed that it must be an electron anti-neutrino.

The general equation for b- decay is:

A typical decay is:

Notice that:

• The nucleon number remains the same ;

• The proton number goes up by 1.

• The beta particle is created at the instant of the decay.

• The antineutrino is very highly penetrating and has a tiny mass.  It is very hard to detect.

• A precise amount of energy is released, according to the nuclide.

• That energy is shared among the nucleus, the electron and the antineutrino.

Beta Plus decay

There is another kind of decay, beta plus decay.  In this case, the nucleus has too many protons, and gets rid of the excess charge by turning a proton into a neutron.  This is rare in nature, but proton-rich unstable nuclei are found in reactors.

The beta plus decay spits out a positively charged particle called a positron.  The positron is an anti-particle to the electron.  It has the same mass, but the opposite charge to the electron.  The other particle emitted is an electron neutrino.

 What is the balanced nuclear equation for the following decays? (a)    emission of a beta- particle from oxygen 19 (b)   emission of an alpha particle from polonium 212 (c)    emission of a beta + particle from cobalt 56   Proton numbers O  8, F  9, Fe  26, Co  27, Pb  82, Po  84

Radioactive nuclides often decay to other unstable nuclides.  There may be several of these that happen until a stable nuclide is formed.  The term used for one of these multiple-step decays is a radioactive decay series.

 The particles emitted by radioactive nuclei are NOT in themselves radioactive.   The helium nuclei of alpha particles are very stable.  Once they pick up electrons, they become helium nuclei which are unreactive.   The electrons in beta minus radiation are normal electrons.

Each time a particle is ejected from the nucleus, energy is transferred.  Most of this is in the kinetic energy of the ejected particle.  We will assume that all the energy in the particle is kinetic. Some is left as energy in the nucleus, which is lost as a gamma ray.  We will study this more in Nuclear Physics.

Consider a particle that has been ejected from a nucleus.  It has energy Ek.  We know that the kinetic energy is given by:

The particle will hit any atoms in the way, ionising them.

This means that an electron is knocked off.  This electron will have picked up a certain amount of energy, which we will call E1.  The idea is shown in the picture:

The particle continues on its journey, having lost a certain amount of energy.  Its new kinetic energy, E' ("E-prime") is given by:

We assume that:

• the space between atoms is empty, so no energy is lost;

• it loses the same amount of energy, E1 in every collision, we can work out the number of collisions, N, by:

 Alpha and beta particles lose about 5 ื 10-18 J of kinetic energy in each collision they make with an air molecule. An alpha particle makes about 105 collisions per cm with air molecules, while a beta particle makes about 103 collisions. What is the range of an alpha particle and a beta particle if both start off with an energy of 4.8 ื 10-13 J?

We use the term model to describe a miniature train or aeroplane.  We can also use it to describe a model girl or boy in the fashion industry.  In the context of a model farm, it means a technique or method.

A model in physics is a way of making something complicated simpler to understand, or using a mathematical technique to show the concept.

A simple way of modelling radioactive decay is using dice.  We take 100 dice in a container, and throw them onto a tray.  We pick out those that show a 6 and put those to one side.  These represent the decayed nuclei.  We count these and take them away from 100  to give us the undecayed nuclei.  We then put the dice that don't show a 6 back into the container, and repeat the process.  You then plot a graph for your results.  It shows a rough exponential decay shape, but not very good.  If we use the whole class data, the graph looks a lot better:

The half life is about 3.75 throws.  Yes, I know you can't have 0.75 of a throw, but radioactive decay is a statistical phenomenon.  To get a perfect exponential decay, we need many thousands of throws.  In a small sample of atoms, we might have 1020 nuclei.

We can model radioactive decay using a computer program at http://www.walter-fendt.de/ph14e/lawdecay.htm .   It needs Java .

You can identify a radioactive decay series and analyse the types of decay taking place that lead to the series.

You will find the following website useful: