Introduction:
Radioactivity is a cool but complex topic - it’s not difficult per se, but unless you do the work beforehand, it can be confusing beyond belief. That’s why I like to lay out the main aspects before going into the details; without having a clear grasp of the basics, everything muddles together into a radioactive mess, and that is never ever a good thing.
Arguably, the two topics I will discuss today are the most complicated in the radioactivity topic of the A Level Physics AQA specification: I’m going to look at radioactive decay and nuclear instability (3.1.8.3 and 3.1.8.4 in the specification respectively for reference).
So, with that in mind, this is how I’ll lay this article out:
Key terms
Key equations and derivations
Graphs/Diagrams
Miscellaneous Notes
Exam Questions
Let’s get into it!
Key Terms:
This list assumes some prior knowledge from the previous blog and from GCSE Physics.
Half Life: the time taken of a radioactive isotope to decrease to half the initial mass.
Activity: the number of nuclei of the isotope that disintegrate each second.
Becquerel (Bq): unit of radioactivity - 1Bq = 1 disintegration per second
Decay Constant: probability of decay each second (per unit time)
Carbon Dating: measuring the activity of carbon in plants/trees and comparing it to the half life to calculate age.
Argon Dating: using the proportion of potassium-40 to daughter argon-40 to establish the age of a rock (gripping stuff, I know).
Stability: the nature of unstable isotopes to “want” to become stable by emitting particle radiation.
Corrected Count Rate: the measured count rate of a radioactive source, corrected for background radiation.
Equations:
Activity = Rate of disintegration A = ΔN/ΔT
Where N = number of nuclei at time t, and T = change in time, and λ = decay
constant
A = λN
Where N = number of nuclei at time t, and λ = decay constant
Rate of disintegration
ΔN/ΔT = -λN
Note that the introduced negative sign is to denote a decay, whereas activity above
is a positive measurement.
Power of source = Energy transfer of a radioactive source per second = AE
Where A = activity and E = emitted particle/photon energy
Solving ΔN/ΔT = -λN gives
Because N ∝ A,
Because N ∝ C,
Decay Constant
λ = (ΔN/N) / Δt
Relation between half life and λ:
Graphs/Diagrams:
Radioactive decay curve
This is the graph shape that any unstable isotope will exhibit throughout its lifetime - the example of tritium is used, courtesy of Mazor (2004).
Additionally, from this graph, you can work out the half life - referencing the definition, we look at 50% on the y-axis (if this were mass or activity etc., it would be half the mass/activity at 0 years or seconds (whatever time frame is used)). We then read across to the line, and read down to the respective time, which is the half-life for the isotope in question. In this case, tritium has roughly a 13 year half-life - try for yourself!
N-Z graph
This diagram takes a moment to get your head around, but once you grasp it, it's very clear what is going on, and can help massively in visualising why and how unstable isotopes emit radiation.
The blue line represents stable isotopes - this isn't an exact representation as there is a little bit of a leeway in the x-axis each side, but it's very close. Light isotopes up to 20 protons maintain a rough proportionality between N and Z, shown by how close the blue line follows N=Z until Z = 20. For 20 < Z < 60, there are more neutrons than protons, to help bind nucleons together without introducing complicated repulsive electrostatic forces. Beyond Z = 60, you begin to find alpha emitters (especially around Z=80), as the nuclei are too large to be stable. At this size, the strong nuclear force has lost its edge over electrostatic forces. See below to see how an alpha emission affects the isotope on the N-Z graph.
Beta-minus emissions (green) occur on the left of the blue line, where isotopes are neutron rich, and "want" to shed some of them to make themselves stable. They convert a neutron to a proton, emitting a beta-minus particle and an electron-antineutrino. The exact opposite is true for beta-plus emissions (red), with a proton becoming a neutron and a beta-plus particle and electron-neutrino being released.
N-Z series
When you consider the nature of particle radiation, it becomes apparent how radiation affects the stabilisation of an isotope - an alpha particle contains two protons and two neutrons, which means that emitting that must causes the isotope to lose that much - remember that mass is always conserved. Conversely, with beta emission, a proton and a neutron are exchanged - for B- a neutron is "converted" into a proton, and in B+ the opposite occurs. This is all indicated on the above image.
Use this image to work out for yourself what emissions are occurring. For a challenge, try to work out what the final isotope is, and refer to a N-Z graph to see if it would be stable. Feel free to use Subject Help if you are struggling with this and would like some assistance.
Miscellaneous Notes:
When a nucleus of a radioactive isotope emits an a or B particle, it becomes a nucleus of a different element because its proton number changes. The number of nuclei of the initial radioactive isotope therefore decreases, gradually reducing its mass. A decay curve describes this phenomenon graphically, relating it to time.
Uses of radioactivity:
Carbon Dating - carbon-14 is used for carbon dating to work out the age of dead trees and plants - it has a half-life of 5570 years so the life of the plant is relatively insignificant, and the carbon isn't going anywhere soon. Measuring the activity enables age to be calculated, because activity and atoms yet to decay are directly proportional - see the equations. The reason the carbon is in the organism after death is of course that plants and trees take up carbon dioxide from the atmosphere for photosynthesis.
Argon Dating - this uses the fact that rocks contain the isotope potassium-40, which decays by electron capture into argon-40, and by B- radiation into calcium-40, the latter of which is 8 times more likely that the former. Potassium-40 has an effective half life of 1250 million years, which means it is suitable for the average age of rocks, as well as the average age of teachers. Because the proportion of argon-40 atoms to calcium-40 atoms is 1:8, for every n argon-40 atoms, there must have been n+9 potassium-40 atoms at the time of formation. Which equation above would you use to solve for the lifetime of the rock? Write your answer in the comments.
Tracers - used in places where it is too difficult to use standard processes. This ranges from tracking iodine uptake by the thyroid gland to detecting underground oil leaks. The crucial thing here is the half-life being long enough for use but short enough to decay soon after so as not to pose a risk to subjects or nearby organisms. Additionally, radiation should be either beta or gamma to (A) reduce risk due to high ionising potential in alpha radiation and (B) to allow measurements to be made outside of the flow path.
Thickness Monitoring - metal foil is made through squeezing a metal plate through rollers. A B- emitter (with a long half life) above the foil combined with a detector below can act as a feedback source to indicate to the roller whether the foil is too thick or thin. Why do you think B- is used as opposed to alpha or gamma radiation?
Remote Device Power - refer to the equation regarding the energy transferred by a radioactive source. Can you see how this could be used to generate a small amount of power over a long period for a remote device such as a satellite or weather sensor? One point of note is that the half-life should be middling so as to not run out too quickly but alternatively provide a constant source of energy.
Gamma Radiation: gamma radiation (γ) is often overlooked as a source given its extremed attributes - non-ionising with the longest range, it's pretty much invisible. Why does it occur? The answer lies in energy levels. When a nucleus emits radiation to stabilise and becomes a new isotope, the daughter nucleus can form in an excited state, at a higher energy state than normal. This is inherently unstable - generally, excited atoms will seek ground state (you can think energy of being like a ball on a hill - if it's pushed up the hill by an external event, it's going to want to drop back down to the bottom, unless it goes all the way over the top and flies into space, which is ionisation, but that's a story for another day). To reach its ground state, the nucleus will emit a photon in the form of gamma radiation.
Exam Questions:
Try the questions below, and then refer to the mark schemes attached at the bottom. If you have any problems, ask in the comments or on the subject help forum. Try to do this within 15 minutes.
Questions:
Mark Schemes:
I hope you enjoyed this article, and learnt a lot! Let me know if you have any further questions in the comments. Don't forget to read the next blog in this 4 part series, which is on Nuclear Radius, Mass and Energy. Thanks for reading - see you soon!
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