Radioactivity & Quantum Phenomena

RADIOACTIVITY (return to CONTENTS)


INTRODUCTION (return to start of page)

Atoms, elements and molecules

The lightest element is hydrogen (chemical symbol H) – its atoms have just one proton in a central nucleus and one electron in orbit around the nucleus. A small percentage of its atoms have one or two neutrons in their nucleus in addition to the proton.

The next heaviest element is helium (He) with 2 protons in the nucleus of each its atoms, and 2 electrons in orbit. All its atoms have one or two neutrons in their nucleus in addition to the protons. The following represents a helium atom:

Increasing the number of protons by one at a time takes us though all the elements, from hydrogen, helium, lithium, … … etc. to the heaviest naturally occurring element, uranium, which has 92 protons in its nucleus, and 92 electrons in orbit. Some elements with even more protons have been artificially created.

Most materials around us, and inside us for that matter, are not pure elements, but molecules. A molecule is made up of atoms which have joined together. For example, two atoms of the element hydrogen can combine with one atom of the element oxygen to form one molecule of water (symbol H2O).

Main sub-atomic particles

Some terminology

A neutral atom has equal numbers of protons in its nucleus and electrons in orbit about the nucleus.

Hydrogen has 3 isotopes:

Helium has 2 protons and its most common isotope has 2 neutrons (as in the above diagram), and is represented by:

We also represent this as Helium-4 or He-4.

Note: Chemical reactions only involve the outer electrons of atoms, so isotopes of a given element act the same chemically. For example, the most common form of water is made up of molecules of H2O. But there also exist water molecules, about 1 part in 5000,  in the form of D2O (‘heavy water’).


DISCOVERY OF RADIOACTIVITY (return to start of page)

Henri Becquerel in 1896 discovered that uranium compounds emitted invisible radiation, which could:

Ionisation occurs when neutral atoms have electrons knocked off them, producing positive ions and free electrons.

Observation:

A strip of polythene or a strip of Perspex rubbed with wool become charged by friction, negatively and positively respectively. If one of them is held close to the cap of the electroscope, and the cap is momentarily touched with a finger, the cap acquires a charge opposite to that of the charged strip. When the strip is removed, the charge spreads itself around the cap, the rod and the gold leaf. The leaf is seen to diverge, since it and the metal rod have the same charge.

When a radium source (held in tongs, and well away from the face) is held close to the cap, without touching it, the leaf is seen to collapse. This is due to the ionisation of the air produced by the radiation emitted by the radium, which produces positive ions and negative electrons. If the cap is negative it attracts the ions, and if it is positive it attracts the electrons. In either case the electroscope is neutralised.


TYPES OF RADIATION (return to start of page)

Experiments have shown that there are three types of radiation emitted by radioactive substances, named as:

They can be separated by a magnetic field, since those that are charged will be deviated:

A dark spot is produced on the photographic plate, where impacted by radiation.

From the directions of the deflections produced by the magnetic field (using Fleming's left hand rule - covered in other notes) we can infer that:

Note: The above diagram is something of a ‘composite’ - it indicates the relative directions of the deflections but not the true relative sizes of deflections. Since alpha particles are helium nuclei, they are 1000s of times more massive than beta particles (electrons) - if the magnetic field were strong enough to move the alphas by the amount indicated, the betas would be deviated so much as to not reach the plate.

Absorption by matter

1. Alpha particles. These have a range of only a few cm in air and are stopped completely by a thin piece of paper. This is because they produce intense ionisation (i.e. many ions are produced for each mm they travel) and so they lose their energy quickly. Radium-226 (‘Ra-226’) is an alpha source.

2. Beta particles. These can pass though paper, but are stopped by thin sheets of aluminium. They are much lighter than alpha particles and so produce much less ionisation per mm of travel, and so they lose their energy less quickly. Strontium-90 (‘Sr-90’) is a beta source.

3. Gamma rays. These are very penetrating. Several cm of lead or several metres of concrete are required to absorb them significantly. Cobalt-60 (‘Co-60’) is a gamma source.

Radiation detectors

The ionising effect of radiation can be used to detect it:

1. A Geiger-Müller tube (‘GM tube’) - a pulse of current is produced when it detects radiation. It can be connected to a scaler or a ratemeter. A scaler counts the number of pulses. A ratemeter gives the average number of pulses per second or per minute, and may give a click for each pulse (a ‘Geiger counter’).

2. A cloud chamber or bubble chamber. Though we cannot see radiation directly, we can see where it has been using these devices. A cloud chamber contains vapour and as an alpha particle, for example, passes though, it collides with atoms, producing a path of ions. Vapour condenses along the path of ions, making it visible. A bubble chamber contains liquid, and vapour bubbles are formed along the ion path, again making it visible.

Safety
We cannot avoid exposure to background radiation (due primarily to naturally occurring radioactivity in the Earth and cosmic rays from space). However, we should avoid unnecessary exposure to radiation. Radioactive materials used in schools and colleges are relatively weak, but should be treated with caution:
NUCLEAR CHANGES (return to start of page)

Radioactivity occurs because some atoms have unstable nuclei. Nuclear 'decay' occurs when a nucleus rearranges itself internally to become more stable, at the same time giving out ‘radiation’. Isotopes of elements which are radioactive are called ‘radioisotopes’ (= radioactive isotopes).

An alpha particle is a helium nucleus consisting of 2 protons and 2 neutrons, so when a nucleus undergoes alpha decay its nucleon number decreases by 4 and its proton number decreases by 2.

So, A è A - 4 and Z è Z - 2

In the following, radium decays by alpha emission to radon:

Notice that the top and bottom balance independently. The radon is also unstable, and a sequence of decays occur until a stable isotope of lead is reached.

When beta decay occurs, a neutron changes into a proton and an electron. The proton stays in the nucleus (so the proton number goes up by one) and the electron (=a beta particle) is emitted.

In the case of gamma emission it is inferred that nuclei have ‘energy levels’, and that if an alpha or beta is emitted, the nucleus is left in an 'excited state', and a gamma ray is emitted when the nucleus returns to its 'ground state'.


ACTIVITY AND THE RADIOACTIVE DECAY LAW (return to start of page)

The SI unit of activity is the becquerel (Bq) - it equals an activity of one disintegration per second.

Activity, A, can be expressed as:


In a given set of unstable nuclei we could not predict which particular ones were about to decay. In this sense, the process is said to be ‘random’.

However, the rate of decay, i.e. the activity, is proportional to the number of undecayed nuclei present (E.g. doubling the number present, doubles the rate of decay).


Why the minus sign?

We can obtain a verbal definition of the decay constant:

Thus:

Note: In the above equation, the number e = 2.718....., and is the base of  'natural' logarithms.
(Enter '1' on a calculator and press ex to get the value of 'e'. Then press ln - this shows that the natural log of e equals 1).

The second of these indicates that the decay is ‘exponential’, as represented in the previous graph.


HALF-LIFE, T1/2 (return to start of page)

As nuclei in a radioactive sample decay, the activity gets less, till eventually there are no more nuclei left to decay.

Or, since the activity of a source is directly proportional to the number of undecayed nuclei, then:

Note for the next example - talking in terms of the mass of undecayed atoms or nuclei is equivalent to talking in terms of the number of undecayed, since these quantities are proportional to each other.

Example

A radioactive sample has a mass of 16 kg and a half-life of 1 hour. What mass remains undecayed after 3 hours?

Answer: 2 kg

Example

The half-life of radium is 1600 years. How long will it take for 3/4 of a given sample to decay?

Now, if 3/4 has decayed then 1/4 remains undecayed.

Answer: 3200 years.

Relationship between the decay constant and half-life

To follow the derivation below you may have to read up about 'logarithms' - your syllabus may not require you to know the derivation - but the final relationship, between the decay constant and T1/2, is important:

Example
A radioactive source contains 5.1*1015 atoms and 5000 nuclei decay per second. What is its half-life?


DEFINITIONS OF UNIFIED ATOMIC MASS UNIT ETC. (return to start of page)

It is convenient to collect together here some useful definitions:

1. Unified atomic mass unit (symbol 'u')

The above is a useful unit of mass at an atomic level (the kg is a very large unit of mass at this level):

Carbon-12 has 6 protons and 6 neutrons in its nucleus.

2. Avogadro’s constant, NA

3. The mole ('mol')

Avogadro’s constant is usually stated as 6.023*1023mol-1 since it is the number of particles per mole of a substance.

4. Relative molecular (or atomic) mass, Mr


E.g. Mr = 12 for C-12.

5. Molar mass, Mm

E.g. Mm = 12 grams for C-12.

6. Number of moles, n

7. The electron-volt ('eV')

The above is a useful unit of energy at an atomic level (the joule is a very large unit of energy at this level):

The definition of potential difference (which will be found in electric field notes) implies that if a charge Q (coulombs) passes through a p.d. V (volts), the kinetic energy that it gains equals Q*V (joules).

So, 1 eV = charge on 1 electron * 1 volt = 1.6 * 10-19 * 1

Example

A sample of U-235 decays at a rate of 300 000 atoms per second. Find the:

  1. radioactive decay constant
  2. initial number of atoms
  3. number of moles
  4. mass of uranium
(half life of U-235 = 4.5*109years; NA = 6.023*1023 mol-1)




USES OF RADIOACTIVITY (return to start of page)

Carbon dating

A radioactive form of carbon (carbon-14) is produced in the upper atmosphere by the bombardment of nitrogen-14 with neutrons.

The carbon-14 forms radioactive carbon dioxide (CO2) and is taken in by plants (along with ordinary CO2). The proportion of radioactive CO2 in the atmosphere determines the proportion of radioactive carbon in a plant, and therefore determines its activity. When a plant dies, no more CO2 is absorbed, and the radioactive carbon which is present decays with a half-life of 5700 years. Living plants have an activity of about 15 disintegrations per minute per gram of carbon. So, for example, if a dead plant has an activity of 7½ disintegrations per minute per gram of carbon, then one half-life has passed since it died, i.e. 5700 years. This assumes that when the plant died it had an activity of 15 disintegrations per minute per gram of carbon, which is equivalent to assuming that the fraction of radioactive CO2 in the atmosphere has not changed over the centuries.

Radioactive tracers

Detectors can detect very small concentrations of a radioisotope.

If a small amount of a radioisotope (the ‘tracer’) is added to the liquid carried by an underground pipe, the location of the pipe can be determined, or a leak from the pipe found, since liquid containing the isotope will accumulate around the leak. There is no prolonged danger in this process, if a radioisotope with a short half-life is used.

In medicine, radioactive iodine can be given to a patient and monitored externally, and reveals the rate at which iodine passes through the thyroid gland.

Radioactive phosphorous is used to assess how well a plant takes up phosphorous from various phosphate fertilisers.

Tracers are also used to measure wear. If the object that is wearing (such as the insides of a machine) is radioactive, the wear can be detected in the lubricating oil.

Cancer treatment

Gamma rays are very penetrating, and most would pass straight though flesh without stopping. However, those that are absorbed can damage cells. Gamma radiation can be an effective treatment of cancer since, if exposed to a dose of gamma rays, a greater proportion of the cancer cells are destroyed than of the healthy cells.

Sterilizing

Gamma rays can kill bacteria, which makes them useful for sterilizing medical instruments after they have been sealed. A disposable syringe, for example, would be sealed in a plastic container and the container then exposed to gamma rays, killing the bacteria inside.

Controlling thickness

The amount of beta particles absorbed by the paper depends on its thickness. The gap between the rollers can be automatically adjusted, keeping the beta count rate, and therefore the thickness of the paper, constant.

Alpha particles are not used since they are completely absorbed by even thin paper. Gamma rays are not used because they would not be absorbed at all by the paper.

A similar process to the above can be used to automatically control the thickness of steel sheet, but in this case a gamma source would be used.


NUCLEAR STABILITY (return to start of page)

This can be seen if a graph of neutron number against proton number is plotted for known stable isotopes.

The solid line is approximate - there is actually a spread of points about the line.

Two protons + two neutrons (= an alpha particle, a helium nucleus) is a very stable combination. The following are very abundant elements, and each is a multiple of He-4:


MASS AND ENERGY (return to start of page)

In 1905 Einstein made the suggestion that mass and energy are related by his famous equation:

When a nucleus decays, it is always found that the original mass of the nucleus is greater than the total mass of the decay products.


The alpha particle takes about 4.8MeV as kinetic energy, some KE is acquired by the recoiling nucleus, and the rest of the energy is emitted as a gamma ray.

Mass defect and binding energy

A nucleus is formed when nucleons (protons and neutrons) bind together. Measurements show that:

The mass difference is called the mass defect of the nucleus. This can be expressed in terms of mass (kg) or energy (J or MeV).

Definitions

Though the above is calculated for the helium atom, the final figure is also the binding energy of the helium-4 nucleus, since the binding energy of the electrons is negligible compared to that of the nucleus.

Binding energy per nucleon

This is a useful quantity for comparing the stability of different nuclei:

The following represents the variation of binding energy per nucleon with nucleon number (mass number):

The greater the binding energy per nucleon, the more stable a nucleus is, since the more energy it would require per nucleon to separate the constituent nucleons in the nucleus.

We see that both light and heavy nuclides have less binding energy per nucleon that intermediate nuclides. This means that energy is released if:

Nuclear fission

It was found (in 1939) that if uranium was bombarded with neutrons (these have no charge and are not repelled by the nuclei), that a uranium nucleus could be split into two nuclei. This is nuclear fission (it is not the same as spontaneous radioactivity).

One such splitting is:

In this event, the uranium nucleus absorbs the neutron, and then splits into barium and krypton nuclei, with also the emission of two neutrons.

Since one initial neutron produces two neutrons, there is the potential for a ‘chain reaction’:

About 200MeV of energy is released per fission. This is millions of times more than the energy released per atom of fuel in a chemical reaction, such as burning coal. Chemical reactions involve interactions between the outer electrons of atoms, which are low energy events compared to nuclear events.

In a nuclear reactor the chain reaction is controlled (usually!), in order to liberate energy in a steady manner. The chain reaction is uncontrolled in an atom bomb (also referred to as an atomic bomb, an A-bomb or a fission bomb).

Nuclear fusion

This is the union of light nuclei into heavier nuclei. Again, each event produces a mass decrease, and a consequent liberation of energy.

A reaction with heavy hydrogen (deuterium) which liberates 3.3MeV per fusion is:

For fusion to occur, deuterium nuclei need to overcome their electrostatic repulsion (due to both being positive). This can occur at very high temperatures (E.g. ~ 107 K), when the nuclei can collide at very high speed.

Fusion occurs in hydrogen bombs, the high temperatures required being produced by exploding an atom bomb.

Nuclear fusion is the source of the energy of stars, which includes our own Sun. In the Sun, fusion converts 564 million tonnes of hydrogen to 560 million tonnes of helium each second ( a 'tonne', also called a 'metric ton', equals 1000kg). Thus, 4 million tonnes of mass is converted (recall E = mc2) to about 1026 joules of energy per second! Even at this rate, the Sun will last for much more than a further 1000 million years.

The main difficulties in using controlled fusion on the Earth as an energy source are of achieving the very high temperatures required, and of containing the fuel at such temperatures. However, if controlled fusion is achieved, not only is it much 'cleaner' than nuclear fission, but there is enough deuterium in sea water to potentially provide energy by fusion for many years.

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A Level Physics - Copyright © A C Haynes 1999 & 2004