Additional Physics Topic 13 - Atoms and Radiation


Some isotopes have an unstable nucleus.  This means that at some point the nucleus will decay into a more stable nucleus.  When it does so, it will emit some kind of radiation:

For example, carbon-12 is the most common isotope of carbon.  Carbon-13 is less common.  It has an extra neutron, but has a stable nucleus.  Carbon-14 has two extra neutrons, and has an unstable nucleus that decays by beta decay.  Like all radioactive isotopes, it decays randomly and no chemical or physical process can change the way in which it decays.  Radioactive decay involves the nucleus only.  The electrons are not involved in any way.


Alpha and beta decays result in the emission of a particle.  Gamma radiation is an electromagnetic wave of very short wavelength (see Topic 5).


Let us look at how each of these radiations occur:


Alpha Decay



An alpha particle is a helium nucleus.  It consists of 2 neutrons and 2 protons (i.e. 4 nucleons).



In the animation look at how the alpha particle is given off.  The nucleus is excited and gives off a gamma ray.


  An alpha particle is a helium nucleus, NOT a helium atom.





Question 1

How can you tell that an alpha particle is not a helium atom?



When there is alpha decay the nucleon number goes down by 4 and the proton number by 2.



Question 2

Polonium has a proton number of 84 and a nucleon number of 210.  It decays by alpha decay to lead.  What is the proton number and nucleon number of lead?



If we send alpha particles through the poles of a magnet (a magnetic field), we find that they are deflected.  This means that they are charged.  If we pass them between a positively charged plate and a negatively charged plate (an electric field), we find that they are attracted to the negatively charged plate.  This means they are positively charged.



Beta Decay



A beta particle is a high speed electron which is ejected from the nucleus.  A neutron turns into a proton and the electron is ejected.  It has nothing to do with the electrons surrounding the atom.  In the animation, look at how the neutron turns into a proton, giving out an electron and an electron antineutrino.


In beta decay the nucleon number stays the same, but the proton number goes up by 1.  Because the proton number changes, the element changes.



Question 3

Carbon-14 decays by beta decay.  What does it decay to?



If we send beta particles through the poles of a magnet (a magnetic field), we find that they are deflected in the opposite direction to alpha particles.  This means that they are charged.  If we pass them between a positively charged plate and a negatively charged plate (an electric field), we find that they are attracted to the positively charged plate.  This means they are negatively charged.  We will see this later.


A beta particle is an electron that comes from the nucleus, NOT the electron shells.


Gamma Radiation



Gamma rays are very short wavelength and highly energetic electromagnetic radiation. They are given off by very energetic or excited nuclei when some other decay has occurred. Cobalt-60 is a common source of gamma rays.


Gamma radiation does not in itself alter the nucleon and proton numbers.


Gamma rays are not affected by electric or magnetic fields.


Alpha particles, beta particles, and gamma rays are NOT radioactive themselves.




Properties of Radiation

The table shows some properties:





Ionising Power

Effect of Electric or Magnetic field

Alpha (a)

Helium nucleus

2p + 2n

Q = + 2 e

Few cm air

Thin paper

Intensely ionising

Deflection as a positive charge

Beta (b)

High speed electron

Q = -1 e

Few mm of aluminium

Less than alpha

Deflection in opposite direction to alpha.

Gamma (g)

Very short wavelength em radiation

Several cm lead, couple of m of concrete

Weakly ionising

No effect.


Alpha particles are stopped by a few cm of air, while beta particles have a range of several metres in air.  This means that an alpha source can be used safely with minimal shielding.  Your skin will stop alpha particles.


Alpha particles are intensely ionising.  Being quite big and moving fast, they collide frequently with other atoms, knocking off electrons, causing ionisation.  They rapidly lose their energy.  Eventually they stop and then pick up two stray electrons to become helium atoms.  All the Earth's helium atoms are thought to come from alpha decay.



Interaction with Fields

The charged radiations (a and b) interact with magnetic fields and electric fields. Gamma rays do not. This can be summed up in the pictures below:


In an electric field:


The alpha particles, being positively charged, are attracted towards the negative plate. Beta particles are negative and are attracted to the positive plate.


For a magnetic field:

The charged particles are deflected by the magnetic field.


Gamma rays, not being charged, are not affected by either an electric or a magnetic field.



Uses and Hazards of Radiation

Uses of Radiation

Radiation can be used to treat cancer. Gamma rays from several sources are focused onto the cancer. The combined dose is fatal for the cancer cells, but cells in each beam don't get too high a dose.  Hospital equipment can be sterilised by exposure to gamma rays which kill bacteria and moulds. This can be preferable to heating with high pressure steam.


Tracers that emit gamma rays are used to detect leaks in pipes. The gamma emitter gives of gamma rays that can pass through the ground. Where there is a leak, the gamma emitter will pool.

Other uses of radiation are:



Dangers of radiation

The waste material from nuclear fission is some of the nastiest muck known to man. There is a whole range of radioactive isotopes that give off alpha, beta, and gamma.

The high energy of these radiations can kill cells. The injuries are rather like burns. A lower dose can do damage to the DNA and cause cancer. 


High doses of radiation are dangerous. The radiations ionise molecules in cells which do immense damage. In high doses, cells and tissues are killed leading to radiation sickness, a condition in which undamaged cells cannot replace the dead cells quickly enough. Your hair falls out, your skin gets blistered (just like a bad burn), and your organs then fail. It is an unpleasant death. 70 000 people died of radiation sickness after the Hiroshima bomb in 1945.








Alpha (a)

Used in smoke detectors

If taken in to the body (ingested), alpha emitters can do immense damage to living tissues

Beta (b)

Checking the thickness of paper sheet in manufacture.

Radioactive tracers in medical research and diagnosis

Some risk of tissue damage, although nowhere near as dangerous as alpha.

Gamma (g)

Medical research.

Non-destructive testing of castings.

Can cause genetic damage and cancer.



Question 4

Match the radiations to what they are stopped by.



Question 5

Now try the interactive crossword




The Effect of Alpha and Beta Decay on Nuclei (HT only)

Radioactive decay occurs in unstable nuclei.  The parent nucleus ejects a particle to form a new daughter nucleus.  The new nucleus is excited and loses energy by giving off a gamma ray.


Alpha Decay

When a nucleus decays by alpha decay, it ejects a helium nucleus (NOT atom).  The nucleus recoils, just like a canon firing a canon ball.



Question 6

What does the helium nucleus consist of?



The atomic number goes down by 2, because 2 protons are lost from the nucleus.  The mass number goes down by 4 because 4 nucleons are lost.


A typical alpha decay is that of radium to form radon, a radioactive gas.


Note that:

 The alpha particle is NOT a helium atom.


Question 7

Polonium has a proton number of 84 and a nucleon number of 210.  It decays by alpha decay to lead.  What is the proton number and nucleon number of lead?



Beta Decay

When a nucleus decays by beta decay, a neutron turns into a proton.  A high speed electron is ejected from the nucleus along with a second tiny particle called an electron antineutrino.


The atomic number goes up by 1, so a new element is formed, but the mass number stays the same.  The electron comes out of the nucleus, NOT the electron shells.

Polonium decays by beta decay to form Astatine, one of the halogens.


Note that:

Question 8

Carbon-14 decays by beta decay.  What does it decay to?


 The beta particle (electron) comes from the nucleus, NOT the electron shells.




Measuring Radiation

In the old days, radiation was detected by exposing a sheet of photographic film to the radioactive source.  Each decay caused the deposit of a grain of silver, and it was possible measure the density of the deposits when the film was developed.  This method is still used today with film badges that people wear if they are working with radioactive materials.




To get a real-time measurement, we measure the radiation from a radioactive sample using a radiation detector called a Geiger-Müller tube.  This is connected to a ratemeter.




The diagram shows the structure of the Geiger-Müller tube:



The Geiger-Müller tube is a metal tube that has a thin mica window on one end.  The apparatus is filled with gas at low pressure.  There is a metal rod charged to a high positive voltage (about 500 V).  The decay particle passes through the mica window.  It collides with a molecule of the low pressure gas.  The gas molecule is ionised, by having an electron knocked off to make a positive ion. The positive ion is attracted to the metal body, while the electron passes to the high voltage rod. This causes a pulse of current to flow through the central rod.


The radioactive decay is measured by the number of counts 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


It also possible to get solid state radiation detectors.



Background Radiation

When we take readings it is important that we measure the background count.  There is radioactivity all around us; it's a natural part of the environment.  So we find out what the background count is, then we take that away from the count we get with the source.  Background radiation stems from a variety of sources, as shown in the pie-chart:


Graphic by Resourceful Physics


You will see that much of the radiation is entirely natural. We even have radioactive carbon-14 in our bodies; the total amount of radiation is tiny and does us no harm. High-flying pilots wear film badges, as they are exposed more to cosmic rays, so that if they are over-exposed, they are grounded for a time.


The background radiation is different in different parts of the country. This is due to the different types of rock.


When we measure the decay of a radioactive material, we need to take a background count. This involves leaving the Geiger counter running for a period of time, say 10 minutes (600 s). Radioactive decay is random, so we could get no counts at all over a 10 s period, then 4 or 5 counts coming in at once.


When we are doing counts, we time the count for a period of time, then doing an average, to give an average count per second.


average count per second = total count in the time period ÷ time period


If we measure over 60 seconds, we would divide by 60.


Each count occurs when a nucleus disintegrates and radioactive decay is an entirely random event. Sometimes there are a lot of counts a second, then only a few. So again we need to time over a period and do an average.



average activity count per second = total average count per second - average background per second


The activity of a source is measured in becquerels (Bq) where 1 Bq = 1 count per second.



Question 9

A radiation detector detects a background rate of 2 counts per second.  When a source is exposed, it gives a reading of 50 counts per second.  What is the true rate of decay?





Radioactive decay is a random process.  If you look at a nucleus, it might decay within ten seconds, or twenty two million years.  Since there are many billions of nuclei, a random decay pattern is seen.


Radioactive decay is NOT influenced by any chemical or physical process, however violent.  You could dissolve the element in the most powerful acid, or vaporise it at extreme temperatures, but the decay would NOT be affected.


Each radioactive isotope decays in its own way and has its own half-life which is defined as:


the time taken for half the original number of atoms to decay.


The table below shows the way 10 000 atoms decay, when the half life is 10 hours.


Time (h)

Number of atoms

Fraction left



10 000

100 %

0 (start)



50 %




25 %




12.5 %




6.25 %




3.125 %




1.5625 %


In other words, you start off with 1, then 1/2, then 1/4, 1/8, 1/16, and so on. In theory you never get to zero activity, but in practice, after about 6 - 7 half-lives, the activity is very low indeed.


This is called exponential decay


Exponential decay can be modelled with dice.  You start with 100 dice and remove every die that has a 6.  With 100 dice, the graph is a bit wonky, but the more throws there are, the smoother the graph becomes.  The data from 1900 throws are shown on the graph:


After every 3.8 throws, half the dice have been removed.  After 7.9 throws, 75 % have been removed; 25 % are left.  We say that the half life in this model is 3.8 throws.


For a radioactive isotope, if it takes 4 days for half the atoms to decay:

  A common bear trap is to say that after two half-lives, all the atoms have decayed.  This is wrong.


Question 10

What fraction of the original number of atoms is left over after 4 half-lives?



Some half lives are extremely short, much less than 1 second.  Some are very long, about 4500 million years.




The average activity of a radioactive material is defined as:


the number of disintegrations every second.


Over a short period of time, this statement can be summed up using the simple equation:


Question 11

A sample of radioactive material measured to have an activity of 1200 counts per minute.  If the background radiation is 120 counts per minute, calculate:

(a) the activity of the material in Bq;

(b) the number of disintegrations over a 15 hour period.



The beta and gamma radiation will penetrate the body (alpha is stopped by skin).  Even if the chance of an interaction was quite low, your answer to Question 11 will show you that over a period of time, there would be a significant number of interactions, each of which could cause damage.  So we need to have a way of measuring the absorbed dose of radiation.


The absorbed dose is defined as:

energy absorbed per unit mass


 In physics code, this is written:

1 Gy is the equivalent of 1 J kg-1.


Question 12

What is the absorbed dose if a cancerous tissue of mass 150 g is exposed to 12 J of energy?



That is not the whole story, though.  The risk of damage depends not only on the absorbed dose, but also on:

So we give a weighting factor for each kind of radiation:



Weighting Factor Wr







Slow neutrons



A slow neutron is also known as a thermal neutron.  It travels at about 14 km s-1 which may sound fast, but is quite slow as far as particles are concerned.  The table shows that alpha particles are very damaging if they manage to penetrate the body.


The Weighting Factor is combined with the absorbed dose to give the equivalent dose, which is defined as:


the product between the weighting factor and the absorbed dose


It has the physics code, H, and the units are Sieverts (Sv).  The equation is:

Question 13

What is the equivalent dose on the tissue in Question 11, assuming that neutrons are used for the treatment?



The time of exposure needs to be taken into account as well.  A dose of, say, 15 millisieverts (mSv) will have more impact on the body if it is received in 1 day than if it is received in a year.  This is because the body has very good repair mechanisms.  So we need another quantity called the equivalent dose rate, which is the rate at which the equivalent dose is received.  As an equation, this is written as:


You don't have to use seconds for time.  You can use hours, or minutes, as long as you are consistent.  Use the time units given in the question.


Question 14

A technician works with radiation in the form of beta radiation and thermal (slow) neutrons.  His monthly dose from the beta radiation is 20 mGy and the thermal neutrons is 50 mGy.

(a)  Calculate the total equivalent dose received;

(b)  Calculate the daily equivalent dose rate.





  • The nucleus consists of nucleons.

  • The nucleons are protons and neutrons.

  • If the number of neutrons is different, the nucleus is an isotope of the original element.

  • If the number of protons changes, the element changes.

  • The number of neutrons = mass number - atomic number.

  • Some isotopes are unstable; they are radioactive.

  • Radioactive decay leads to the emission of an alpha or beta particle.

  • Rate of decay is measured with a Geiger-Müller tube and a ratemeter.

  • The background count needs to be taken into account.

  • Alpha scattering led to the idea of the nuclear atom.