7. Radioactive decay and nuclear equations : Educating Physics

Objectives

To understand what radioactive decay is as well as the spontaneous and random nature of decay
To understand the three different types of nuclear radiation, α, β and γ as well as the nature, penetration and range of these radiations
To appreciate the techniques and procedures used to investigate the absorption of α-particles, β-particles, γ-rays by appropriate materials
To understand nuclear decay equations for alpha, beta-minus and beta-plus decays; balancing nuclear transformation equations

What is radioactive decay?

Radioactive decay is the process by which unstable nuclei loses energy by emitting a form radioactive radiation. There are three main types of nuclear radiation that will be discussed on this page; alpha ( $\alpha$ ), beta ( $\beta$ ) and gamma ( $\gamma$ ) radiation. Radioactive decay is a spontaneous process whereby a single unstable nuclei will emit either $\alpha$ , $\beta$ or $\gamma$ radiation to become more stable. The instability of the parent nuclei (parent nuclei is the term used to describe a nucleus before it has undergone a decay process), is dependent on several factors which will be discussed over the next couple of pages but include;

whether the parent nuclei is in an excited state
whether the proton to neutron ratio is too large
whether the proton to neutron ratio is too small

It is impossible to predict when any individual nucleus will undergo radioactive decay due to its spontaneous (random) nature. However, the rate of decay of a nucleus in a particular sample can be predicted and therefore statistics can be used to estimate how many will decay in a period of time – this will be reviewed on a later page (Activity of a Radioactive Substance and Simulating the Decay).

The Three Main Types of Nuclear Radiation

Before continuing ensure you understand the following terms:

Deflection – the action or process of something changing direction
Penetration – the ability an object has to pierce or enter a medium.
Ionisation – an action which can convert an atom into an ion, typically by removing one or more electrons. Ionisation and penetration in terms of radiation can be pictured as opposites of one another (in the sense that if an object ionises a medium it cannot penetrate any further, if the object has not yet ionised a medium it can continue to penetrate further).

As discussed above, the three main types of nuclear radiation are $\alpha$ , $\beta$ or $\gamma$ , but what are they and how do they differ from one another?

Alpha:
An alpha particle is a helium nuclei, consisting of two protons and two neutrons. It is not to be confused with a helium atom which has two electron orbiting the nucleus. An alpha particle can be donated by $^{4}_{2}\alpha$ or $^{4}_{2}He$ , either is acceptable. This type of radiation has an atomic mass of 4 units and an atomic number of 2, as a result it is highly ionising. This is because it is influenced by the electrostatic force and due to its large mass it cannot travel very fast and so collide with other atoms easily. Alpha particles are absorbed by very thin materials including skin and paper, they also gets absorbed in air after approximately 5cm.

Beta:
A beta particle is a highly energetic (fast moving) electron that is ejected from a nucleus when a proton transforms into a neutron (this is discussed more on β- and β+ Decay with Quark Equations page). There are two types of beta particle, beta-minus $\beta^{-}$ and beta-plus $\beta^{+}$ , the difference is one ejects an electron whilst the other ejects an anti-electron known as a positron. A beta-minus particle can be donated by $^{0}_{-1}e$ or $^{0}_{-1}\beta$ and a beta plus particle by $^{0}_{+1}e$ or $^{0}_{+1}\beta$ .
This type of radiation has almost zero mass (hence the atomic mass is zero) an an atomic number of one unit, this makes it ionising but less so than alpha. This is because it has half the charge of an alpha particle and therefore is influenced by the electrostatic force by half the amount, in addition to this, it has a tiny mass in comparison to an alpha particle, therefore it can travel very fast and becomes less likely to collide with other atoms. Beta particles can penetrate thin materials like air and skin but get absorbed and therefore ionise thin pieces of aluminium foil (a few mm’s). Beta can also get absorbed in air but can penetrate further, approximately 15cm.

Gamma:
A gamma ray is a high frequency electromagnetic wave – s you are familiar with. They are generate when an unstable nuclei releases energy rather than mass (alpha and beta) to become more stable.
Gamma rays are photons and as such do not have an atomic number nor do they have an atomic mass, therefore they are not influenced by the electrostatic force. In addition to this they have no mass and can travel at the speed of light, therefore they are can travel much further than alpha or beta particles before ionising a medium – they have a very high penetration ability and as such are lowly ionising.

Summary table:

Techniques and procedures used to determine the different types of radiation

The ionisation and penetration abilities of alpha, beta and gamma can be used to determine what type of radiation is being emitted from an unstable radioactive nuclei.

A piece of equipment used to detect nuclear radiation is known as a Geiger-Müller tube (imaged to the left), this is normally connected up to to a Geiger counter (imaged above). A Geiger-tube works by allowing alpha, beta or gamma to ionise a gas inside the tube. Since ionisation converts an ion into an electron, the electron that is knocked free can then be detected.

The electron can be detected using an anode connected across a high potential difference. Due to the anode being positively charge it will accelerate the electrons towards it, with an increasing speed, these electrons will likely ionise more atoms, releasing more electrons. With a collection of electrons incident upon the anode, it will be discharged, this discharge can then be detected. Click on this link or the image below and watch the animation for more information;

Interesting fact: Since the gas inside the Geiger-Müller tube is needed to be ionised for it to detect radiation, over time the gas will transform into a different element and will eventually not work due to not being able to be ionised effectively, a Geiger-Müller tube has a finite useful life-span.

By placing a unstable radioactive source near to a Geiger-Müller tube that is connected to a counter, will enable alpha beta and gamma to be detected. A radioactive rock sample will, over a short period of time, emit a relatively constant amount of radiation ( $\alpha \ \ \beta$ and/or $\gamma$ ). Measuring the the number of counts in a specific amount of time (say 30 seconds) and then dividing by this time interval will give the number of counts per second, also known as Becquerels, Bq. Doing this with the rock sample at a short distance away from the Geiger-Müller tube (>3cm) will enable materials to be placed between the rock sample and the piece of apparatus. Detecting alpha is displayed in red below, detecting beta is in blue and gamma is in green:

Since paper absorbs alpha radiation, by placing a single piece of paper between the rock sample and apparatus will enable a new number of counts per second to be obtained. If this count rate is similar to before, then it is likely no alpha is emitted (because nothing is being absorbed). If the amount has decreased then it is likely alpha is being emitted.

Removing the paper and replacing it with a thin sheet of aluminium foil (approximately 3mm in thickness) will enable a new set of data to be obtained. Again, if the rate has not changed from the initial result (with no absorbing material), then it is likely no beta radiation is being emitted from the sample, but if the rate decreases then it is likely that beta is being emitted because it is being absorbed by the aluminium.

Finally, removing the aluminium foil and replacing it with a piece of lead (approximately 3cm in thickness) will enable a final set of data to be obtained. If the rate does not differ from the initial result (with no absorbing material), then it is likely that no gamma radiation is being emitted from the sample, but if the rate decreases then it is likely that gamma is being emitted because it is being absorbed by aluminium.

In the above statements the word likely was continuously used, this is because radiation is a spontaneous process. The longer that each individual result (from the above procedures) is taken over the more probable it is going to be that a specific type of radiation can be determined. It is important to note however that the longer the experiment takes place the more exposure the scientist carrying out the experiment will have to the radiation, it is important to keep this to a minimal

There are other methods for determining the type of radiation that is emitted exist. One uses the charge of each type of nuclear radiation. Since gamma has no charge it would not be deflected in a electric field, beta has a small charge and moves very quickly so will will be deflected in a electric field but less so than an alpha particle which has twice the charge and moves much more slowly due to its atomic mass.

The direction in which the alpha and beta particles deflect can be determined using Fleming’s left hand rule. It is quite clear from the above image the different radii beta particles take in comparison to alpha particles. Since positrons are also know to exist, this same method can be used to determine their presence; Since they would have the same charge as an alpha particle they would deflect in the same direction as them, but the mass would be much lower and so the radii of deflection would be much smaller. The charge to mass ratio would have to be taken into account – refer back to the charge to mass ratio detailed in the electric fields topic.

Nuclear Decay Equations

Alpha Decay

When a radioactive atom emits an alpha particle (Helium nuclei – $^{4}_{2}He$ , it is converted into another element of atomic number two fewer than before and an atomic mass of four fewer than before. Because the atomic number is decreased by two units the new atom, known as the daughter nuclei, can be found using a periodic table and shifting the previous element two places to the left. Uranium-238 is an example of an unstable nuclei undergoing alpha emission:

$^{238}_{92}U \ \ \rightarrow \ \ ^{234}_{90}Th + \ ^{4}_{2}He$ \

Beta Decay

When a radioactive element emits a beta particle (highly energy electron – $^{0}_{-1}e$ , it is converted into another element that has an atomic number one greater than previously (because a negative charge is thrown out, the charge of the nucleus needs to increase by one for charge to be conserved) and an atomic mass that is equal to the previous nuclei. The reason the atomic mass does not change is because the mass of an electron is negligible in comparison to the mass of a nucleon (the atomic mass is approximately zero). Thorium-234 is an example of an unstable nuclei undergoing beta emission:

$^{234}_{90}Th \ \ \rightarrow \ \ ^{234}_{91}Pa + \ ^{0}_{-1}e$
(Not yet a complete equation)

Gamma Radiation

If an atomic nuclei has a good balance of protons to neutrons but has excess energy due to it being in an excited state, it may emit a photon with a frequency in the gamma part of the electromagnetic spectrum. A gamma ray put in atomic notation is $^{0}_{0}\gamma$ , you can therefore see that after gamma emission, the new nuclei will have the same atomic number and atomic mass number – the new nuclei will be the same as the initial nuclei however it will no longer be in its excited state. An excited nuclei of Iodine will undergo gamma emission:

$^{125}_{53}I^{*} \ \ \rightarrow \ \ ^{125}_{53}I^{'} + \ ^{0}_{0}\gamma$

where
$^{125}_{53}I^{*}$ is the excited state of the Iodine nuclei
$^{125}_{53}I^{'}$ is the de-excited state if the Iodine nuclei

The general rules for nuclear equations are:

The sum of the electrical charges before decay must equal to the sum of the charges after the decay.
The sum of the atomic mass numbers before the decay must equal the sum of atomic mass number after the decay.

For more information regarding radioactive decay watch this video by Khan Academy :

Further reading:

Read about the work carried out by Marie Curie.

\

(Not yet a complete equation)

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Like this:

$^{238}_{92}U \ \ \rightarrow \ \ ^{234}_{90}Th + \ ^{4}_{2}He$ \

$^{234}_{90}Th \ \ \rightarrow \ \ ^{234}_{91}Pa + \ ^{0}_{-1}e$
(Not yet a complete equation)