A-level Physics/Forces, Fields and Energy/Radioactivity

When atoms are unstable, they will try to make themselves stable again. One way that they do this is by giving off matter and energy known as radiation. A material with unstable atoms is said to be radioactive.

Types of radiation

There are 3 different types of ionising radiation, simply called α (alpha), β (beta) and γ (gamma), each with their own properties.

α-particles

An alpha particle is basically a helium nucleus. The table below shows its properties:

Nature:	2 protons & 2 neutrons (a helium nucleus)
Symbol:	α, $\ _{2}^{4}He$
Mass:	4 times the mass of a proton (~4u)
Charge:	+2e
Speed:	$10^{6}\ ms^{-1}$ (~5% speed of light)
Penetration:	Stopped by paper, skin or a few centimeters of air
Affected by electric and magnetic fields?:	yes

β-particles

A beta particle is an electron. The table below shows its properties:

Nature:	an electron
Symbol:	β, e
Mass:	1/1840 the mass of a proton (~0.00055 u)
Charge:	-e
Speed:	$10^{8}\ ms^{-1}$ (up to 98% the speed of light)
Penetration:	Stopped by 3mm of aluminium or about 1m of air
Affected by electric and magnetic fields?:	yes

γ-rays

A gamma ray is an electromagnetic wave with a wavelength of around $3\times 10^{-15}m$. The table below shows its properties:

Nature:	an electromagnetic wave of very short wavelength
Symbol:	γ
Mass:	0
Charge:	0
Speed:	$3\times 10^{8}\ ms^{-1}$ (speed of light)
Penetration:	Reduced greatly by several centimetres of lead. Rays are absorbed by several meters of concrete
Affected by electric and magnetic fields?:	no

Ionisation

α, β and γ radiation are all forms of ionising radiation and they affect the matter that they pass through. They can cause atoms to become ionised by colliding into, or passing closely to them. The atoms have their electrons pushed or pulled by the radiation and become ions, hence the name ionisation.

α particles

α particles are the most strongly ionising because they have the greatest mass and charge, and have the lowest velocity. This means that they affect the most amount of atoms and affect each atom stronger than the other types of radiation.

β particles

β particles are the second most strongly ionising because they are lighter, faster and have a smaller charge then α particles.

γ rays

γ rays are the least ionising of the 3, since they have no charge.

Penetration

Radiation can pass through different materials, though each type of radiation has its own penetration power.

α radiation

α radiation can be easily absorbed by a sheet of paper or by human skin. This is because it is highly ionising and easily gives its kinetic energy to surrounding atoms and therefore cannot penetrate far into matter.

β radiation

β radiation is less ionising, which makes it more penetrating than α radiation. It needs a denser material such as aluminium to completely absorb it.

γ radiation

γ radiation is the most pentrating and several metres of concrete or a few centimeters of lead are required to completely absorb it. Again, this is related to its strength of ionisation.

Nuclear equations

Just like other nuclear processes, radiation emissions can be represented by balanced nuclear equations. An alpha particle has a symbol of $\ _{2}^{4}$He and a beta particle has a symbol of $\ _{-1}^{0}$e. These can easily be used in equations where radiation is emitted. Gamma photons do not have any effect on the equations since they have no mass and no charge.

Electric and magnetic fields

Because of their different charges and masses, each type of radiation behaves differently in electric and magnetic fields. The behaviour of positive and negative particles moving in electric and magnetic fields have already been discussed earlier. Be especially careful using the left hand rule for β particles in a magnetic field because, as you may recall, the current is in the opposite direction to the movement of an electron. Gamma rays are not affected by either types of field and will continue in a straight line.

The hazards of ionising radiation

Radiation is dangerous and steps must be taken to ensure that we are exposed to as little radiation as possible. We will have a look at these dangers and see how we can minimize the damage to ourselves and the environment.

Effects on living organisms

Since radiation is ionising, it can alter the atoms that make up our own cells. There are two main ways that our cells can become damaged by radiation:

• Exposure to intense radiation can kill cells, causing tissue damage known as radiation burn. This same principle is used to kill microbes from food or on medical equipment.
• DNA can be altered by an ionisation, causing the cell to no longer function correctly. The radiation may affect the DNA directly, or break up a water molecule which will then react with the DNA. The cell may divide uncontrollably, forming a tumour. Also, if the radiation affects an egg or sperm cell, there will be mutations passed on to the next generation.

Alpha particles are the most dangerous to cells, but fortunately our skin is sufficient to prevent them from entering our bodies .

Handling radioactive materials safely

Since radiation is very hazardous, radioactive materials must be handled, stored and disposed of in a safe manner.

To handle radioactive materials, they must not come into contact with the skin, and must be handled in a glove box or with tongs. Care must be taken to not inhale radioactive gas.

To store radioactive materials you can use lead-lined containers, since lead absorbs all of the different types of radiation. This is also true for materials that emit α radiation, since most α emitting materials will also emit γ radiation.

Radioactive materials can be disposed of by diluting the radioactive substance with a large amount of non-radioactive material. They can also be disposed of by containment, which involves storing the radioactive material until it has dropped to a safe level of radioactivity.

Radioactive decay

As radioactive materials emit radiation, the number of stable nuclei increase, and the number of unstable nuclei decrease. The substance is said to decay because it decreases in mass as particles and energy is given off.

Spontaneous radiation emission

If we were to observe a single nucleus of an unstable atom, we would eventually see it decay. We won't be able to predict how long it would take for it to decay, and there is no way to tell if it is about to decay or not. It will be undecayed at one moment, and an instant later, it would have decayed. It is a spontaneous action. This is very strange to the way things are on the macroscopic level that we are used to, where we can see gradual changes or the build up to an event.

Also, each atoms nucleus decays independently of any neighbouring atoms, because if you recall the relative distances and sizes of subatomic particles, there is an enormous amount of empty space between the nucleus and its orbiting electrons, which means that one nucleus cannot affect another.

Since we cannot predict when a nucleus will decay, we have to find an average over a period of time.

The decay constant

The decay constant is the probability that a particular nucleus will decay per unit time, and is denoted by the symbol λ. It can be found for a particular sample by measuring how many nuclei decay for a given length of time. So, if in a sample with 10,000 nuclei, 1000 were to decay in an hour, the probability of one particular nucleus decaying within an hour is 0.1, because only 10% of the nuclei decayed.

The decay constant has the units $s^{-1}$ in the SI system, but $h^{-1}$, or even $day^{-1}$ may be used. In the example above, the decay constant, λ, is equal to 0.1$h^{-1}$.

Activity and count rate

The activity of a radioactive substance is the number of nuclei that decay in a unit of time, or the rate of decay. Activity is measured in decays per second, and one decay per second is called one becquerel.

If you know the decay constant of a particular substance, and the number of undecayed nuclei it has, you can find the activity for that material using the formula:

$A=\lambda N$

where A is the activity, λ is the decay constant, and N is the number of undecayed nuclei.

As you can see, this would take us back to how we originally found the decay constant, and so you can how the two are related.

When you are obtaining the activity of a sample with an experiment, you will hardly ever detect all of the radiation emitted. Some will be emitted where there are no detectors. The count rate, R, is the measurement from the experiment, which will be less than the activity of the sample. A can be calculated from R if you know the efficiency of the measuring device.

Exponential decay

As a radioactive substance decays, the number of undecayed nuclei will decrease. Since there are less radioactive particles in the substance, the rate of radioactive particles emitted will decrease. A graph of the amount of substance against time will show an exponential curve, where the curve continually gets less steep as the rate of decay decreases.

Calculating decay

The number of undecayed nuclei can be calculated with the following formula:

$N=N_{0}e^{-\lambda t}$

Where, $N_{0}$ is the number of undecayed at the start, $\lambda$ is the decay constant, $t$ is the time in seconds, and $e$, is the exponential function.

Similarly, the count rate and activity can be found from the following equations:

$R=R_{0}e^{-\lambda t}$

$A=A_{0}e^{-\lambda t}$

Half-life

The half life of a substance is the mean length of time it takes for half of its radioactive material to decay. If you look at the graph, you can see that the time on the horizontal axis for the number of undecayed nuclei to half is the same as the time for it to decrease from 50% to 25%, and from 25% to 12.5%.

Half life is written as $t_{\frac {1}{2}}$, and is usually measured in seconds, but for materials that are more stable, it is common to state the half life in hours, days, or even years.

If you consider that a substance with a short half life must decay quickly, and therefore must have a high decay constant, and that a substance with a long half life will have a low decay constant, you can relate the two using the equation:

$\lambda t_{\frac {1}{2}}=\ln 2\approx 0.693$

This is useful if you are only given either the half life or the decay constant and asked to find the other, as you can rearrange the equation to find the unknown value.