# Nuclear Physics Tutorial 1 - a, b, and g Decay

Revision

You will remember the simple model of the nuclear atom as proposed by Nils Bohr:

This is a neutral lithium atom.  The number of protons is the same as the number of electrons.  The electrons are in shells.  The first shell can contain 2 electrons only.  The next shell can contain up to 8 electrons.

Different atoms are distinguished by their numbers of protons and neutrons.  We write the symbols using the following notation:

• A is called the nucleon number, or the mass number.  It is the total number of nucleons.

• Z is the proton number or the atomic number, which is the number of protons.  The number of protons determines the element.

Therefore lithium is written like this:

Be careful not to confuse atomic number with the symbol A.  We will refer to A as the nucleon number in these notes and Z as the proton number.

We can determine the number of neutrons simply by subtracting the proton number from the nucleon number.  ( No of neutrons = A – Z)  Atomic particles are always in whole numbers.

• Isotopes have the same numbers of protons, but different numbers of neutrons.

• Isotopes have the same chemical properties.  Some physical properties are different, e.g. density.

• If the proton number is altered, the element changes.

Some isotopes are radioactive, as the nuclei are unstable.

Chemical reactions involve the electrons of the outer shells.  Nuclei are not involved in any way, and remain totally unaltered even in the fiercest chemical reactions.

Unstable Nuclei

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 can be summed up as:

The decay can consist of several steps.  The unstable nucleus can decay 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.

 Question 1 What is meant by the term transmutation?

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.  We must be aware that radioactive decay is NOT the same as nuclear fission.

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 constraints, or chemical reactions.

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.

Question 2

 Complete the table that describes the properties of the three common radiations Radiation Particle Range in air Stopped by Alpha Beta Gamma

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.  Then you are in serious trouble.  The main fear from the fall-out of a nuclear catastrophe is from alpha emitters (although you wouldn’t want to take a gamma source to bed with you).

• 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.  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 (reduced) 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.

In the early days of radiation research, people had little clue as to how dangerous the stuff was. In those days lumps of uranium were used as ice-breakers at parties (“Darling, do come and feel my magic metal.”); the metal felt warm, and gave the person feeling it a massive dose of radiation!  Today the nuclear industry takes safety very seriously indeed, and workers are rigorously monitored.  If it appears that personnel are being exposed to higher levels of radiation than they should be, they are withdrawn from that work.  Safety must the primary consideration in every function of the nuclear industry.  However, things can go wrong as in any human activity, e.g. falsification of records, or unauthorised experiments, such as those that led to the Chernobyl disaster, when 7 tonnes of caesium-137 was scattered over Europe.

 Explain the dangers associated with radioactive sources. 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 particles start off with an energy of 4.8 × 10-13 J?

Those who work with radiation are issued with a film badge, as shown in the picture below:

The film is exposed to all kinds of radiation.  There are strips of metal that stop alpha, beta, and lead that attenuates gamma.  Every month the film is taken in and processed, and a new film is issued.  If the workers are found to be exposed to a higher than safe level of radiation, they have to be removed from that line of work for a period of time.  This is a rare event, because in reality most workers are exposed to little above background radiation anyway.

Those who handle radioactive materials are highly trained and aware of the risks.  They will take elementary precautions such as:

• carrying sources in lead-lined containers;

• handling sources with tongs and gloves;

• keeping the sources well away from themselves;

• not pointing sources at others;

• monitoring radiation levels with a portable Geiger counter.

Fixed sources of radiation are contained in cells or bunkers with thick concrete walls.  The cells have interlocking to prevent access when the source is exposed.  The interlocks will not unlock unless the source has been retracted.

Whenever radiation experiments are carried out, it is important to realise that there is always a certain amount of background radiation.  Many elements have radioactive isotopes as well as stable isotopes.  These will give off radiation.

While it's not important to know the sources of the background radiation, we must correct the count by subtracting the background radiation.  Because the emission of backgrounds counts  is a random process, it is not appropriate to take a momentary sample.  To reduce uncertainty, we need to take a count of at least 60 seconds and divide it by 60 to get an average background count.

Corrected count (Bq) = Total count (Bq) - background count (Bq)

Background radiation is entirely normal, and we are adapted to cope with it.

Production of Alpha Particles

Alpha particles come from heavy elements of mass greater than 106 atomic mass units.  In classical physics, the strong force balances the electro-magnetic force, so the alpha does not have the energy to get out.

In quantum physics, there is a small chance that the alpha can get out by a process of quantum tunnelling.

At this level we assume that all the energy is kinetic. Alpha particle energy is between 3 and 7 MeV.

Particles in Magnetic Fields

You may want to revise the motion of charged particles in magnetic fields (Magnetic Fields Tutorial 3).  If the particles are deflected by a magnetic field going into the screen, the result is this:

The deflections tell us not only the charge on the particle, but the mass and the speed of the particles.  The equation derived in Magnetic Fields Tutorial 3 is applicable:

If we know the kinetic energy of a particle, we can then work out the velocity.  Alpha particles have kinetic energy between 3 and 7 MeV.

 An alpha particle has a kinetic energy of 5.45 MeV.  It is travelling horizontally across the screen from left to right. It is deflected by a magnetic field of 0.86 T which is perpendicular to the screen and going into the screen. (a)  Calculate the speed of the particle. (b)  Calculate the radius of curvature.  Give your answer to an appropriate number of significant figures. (c)  In which direction, upwards or downwards, is it deflected?   Mass of an alpha particle = 6.64 × 10-27 kg Electronic charge = 1.60 × 10-19 C