1. A level Physics 2nd edition Pages 438-471
Radioactivity
A level Physics 2nd edition
Pages

2. 3 types of radiation
Radioactivity identified by Marie and Pierre Curie
3 types identified by Rutherford
α,β,γ

3. The discovery of the nucleus
John Joseph Thomson – electrons in atom
Rutherford, Geiger and Marsden – evidence for the nucleus
Gold foil experiment

5. In 1909, an undergraduate, Ernest Marsden, was being trained by Geiger
In 1909, an undergraduate, Ernest Marsden, was being trained by Geiger. To quote Rutherford (a lecture he gave much later):
"I had observed the scattering of alpha-particles, and Dr. Geiger in my laboratory had examined it in detail. He found, in thin pieces of heavy metal, that the scattering was usually small, of the order of one degree. One day Geiger came to me and said, "Don't you think that young Marsden, whom I am training in radioactive methods, ought to begin a small research?" Now I had thought that, too, so I said, " Why not let him see if any alpha-particles can be scattered through a large angle?" I may tell you in confidence that I did not believe that they would be, since we knew the alpha-particle was a very fast, massive particle with a great deal of energy, and you could show that if the scattering was due to the accumulated effect of a number of small scatterings, the chance of an alpha-particle's being scattered backward was very small. Then I remember two or three days later Geiger coming to me in great excitement and saying "We have been able to get some of the alpha-particles coming backward …" It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

6. Estimate the nuclear size
About 1/10000 α particles are scattered by more than 90o
Foil must be thin otherwise multiple scatters occur
For n layers the probability of scattering once is 1/(10000n) which depends upon the cross section area of the nucleus in the cross section of the atom
For a typical thin foil of n = 10000, d=D/10000
That is nucleus:atom = football:stadium

7. Marie Curie Maria Sklodowska
Born in Poland in 1867
1896 Henri Becquerel investigated materials that glowed with irradiated with X-rays -
1898 discovered 2 new elements with her husband Pierre Curie, Polonium and Radium
Awarded Nobel prizes in 1906 and 1911
Pierre was killed in 1906 by a horse drawn carriage
Marie died in 1934 of aplastic anaemia – a bone marrow damage probably caused by radiation.
Her note books are still stored in lead and readers have to sign a disclaimer to access them

8. Rutherford’s radioactivity experiments
Discovered α,β,γ radiation
α radiation is strongly ionising but only travels a few centimetres in air
β radiation is weakly ionising but more penetrating up to 1 metre in air
γ radiation even less ionising effects, carries no charge, much more penetrating. Found to be EM radiation – photons

9. The Geiger counter - history
Hans Geiger developed a device (that would later be called the "Geiger counter") in 1908 together with Ernest Rutherford. This counter was only capable of detecting alpha particles.
In 1928, Geiger and Walther Müller (a PhD student of Geiger) improved the counter so that it could detect all kinds of ionizing radiation.
The current version of the "Geiger counter" called the halogen counter was invented in 1947 by Sidney H. Liebson (Phys. Rev. 72, 602–608 (1947).
It has superseded the earlier Geiger counter because of its much longer life. This device also used a lower operating voltage.

10. The Geiger-Müller Tube
A "Geiger tube" contains a metal tube with a thin metal wire along its middle, the space in between them sealed off and filled with a suitable gas (usually Helium, Neon or Argon with halogens added), and with the wire at about volts relative to the tube

11. The Geiger Counter
An ion or electron penetrating the tube (or an electron knocked out of the wall by X-rays or gamma rays) tears electrons off atoms in the gas, and because of the high positive voltage of the central wire, those electrons are then attracted to it. In doing so they gain energy, collide with atoms and release more electrons, until the process snowballs into an "avalanche" which produces an easily detectable pulse of current. With a suitable filling gas, the flow of electricity stops by itself, or else the electrical circuitry can help stop it.
The instrument was called a "counter" because every particle(α,β,γ) passing it produced an identical pulse, allowing particles to be counted (usually electronically) but not telling anything about their identity or energy (except that they must have sufficient energy to penetrate the walls of the counter).

12. Modern Geiger Counters
The Geiger-Müller tube is one form of a class of radiation detectors called gaseous detectors or simply gas detectors. Although useful, cheap and robust, a counter using a GM tube can only detect the presence and intensity of radiation.
Gas detectors with the ability to both detect radiation and determine particle energy levels (due to their construction, test gas, and associated electronics) are called proportional counters. Some proportional counters can detect the position and or angle of the incident radiation as well.
Other devices detecting radiation include: ionization chamber, dosimeters, photomultiplier, semiconductor detectors and variants including CCDs, microchannel plates, scintillation counters, solid-state track detectors, cloud chambers, bubble chambers, spark chambers, neutron detectors and microcalorimeters.

13. Properties of α,β,γ radiation
Range in air… α – up to 100mm β – up to about 1 m γ – follows the inverse square law ie ∝ 1 𝑟 2

14. Penetrating power of nuclear radiation

15. Deflecting nuclear radiation

16. Properties of nuclear radiation

17. Properties of nuclear radiation

18. Inverse square law Intensity = energy per second per unit area
𝐼= 𝐸 𝑡𝐴 = 𝑃 𝐴 𝑢𝑛𝑖𝑡=𝐽 𝑠 −1 𝑚 −2 =𝑊 𝑚 −2
For a point source that emits 𝑛 photons per second each of energy, ℎ𝑓
The power (rate of energy transfer = 𝑛ℎ𝑓
The area over which it is spread = 4𝜋 𝑟 2
Intensity = 𝑛ℎ𝑓 4𝜋 𝑟 2
∴𝐼 ∝ 1 𝑟 2 , 𝐼= 𝑘 𝑟 2 𝑤ℎ𝑒𝑟𝑒 𝑘= 𝑛ℎ𝑓 4𝜋

19. Equations for radioactive decay
α emission
𝑍 𝐴 𝑋 → 2 4 𝛼 + 𝑍−2 𝐴−4 𝑌
𝛽 − emission
𝑍 𝐴 𝑋 → −1 0 𝛽 + 𝑍+1 𝐴 𝑌 + 𝜗 𝑒
𝛽 + emission
𝑍 𝐴 𝑋 → 1 0 𝛽 + 𝑍−1 𝐴 𝑌 + 𝜗 𝑒 −
Electron capture
𝑍 𝐴 𝑋 𝛽 → 𝑍−1 𝐴 𝑌 + 𝜗 𝑒 −
𝛾 emission
does not change A or Z but is emission of excess energy following 𝛼 or 𝛽 emission

20. Dangers of radioactivity
Ionising radiation
Causes damage to cell membranes which kills cells
Damages vital molecules such as DNA or ionises other molecules which react with vital molecules
Damaged DNA can cause uncontrolled growth – causing a tumour which may be cancerous.
Damaged sex cells can cause mutations in offspring.

21. Radiation monitoring
The badge has six filters: • An open window which allows all incident radiation that can penetrate the film wrapping to interact with the film. A thin plastic film which attenuates beta radiation but passes all other radiations  •A thick plastic filter which passes all but the lowest energy photon radiation and absorbs all but the highest beta radiation.  •A dural filter which progressively absorbs photon radiation at energies below 65 keV as well as beta radiation.  •A tin/lead filter of a thickness which allows an energy independent dose response of the film over the photon energy range 75 keV to 2 MeV.  •A cadmium lead filter where the capture of neutrons by cadmium produces gamma rays which blacken the film thus enabling assessment of exposure to neutrons. 

22. Radiation doses ALARA – as low as reasonably acheiveable
Dose equivalent measured in Sieverts, is the dose which causes the same damage as a dose of 250 kV X-rays.
The sievert (symbol: Sv) is a derived unit of ionizing radiation dose in the International System of Units (SI). It is a measure of the health effect of low levels of ionizing radiation on the human body and is measured in 𝐽 𝑘𝑔 −1 .

23. Background radiation

24. Safe use

25. Radioactive decay
Half life – the time taken for half of the material to decay. T1/2
After 1 half life ½ is left
After 2 half lives ¼ is left
After n half lives 𝑛

26. Activity
The activity A of an isotope is the number of decays that occur of that isotope per second.
The unit of A is the Becquerel (Bq) , named after Henri Bequerel.
1 Bq = 1 disintegration per second
If each decay releases E Joules of energy
Power = AE

27. Theory of radioactive decay
The activity, A = Δ𝑁 Δ𝑡 ∝𝑁
We can write Δ𝑁 Δ𝑡 =𝜆𝑁 where 𝜆 = decay constant
𝑠𝑜 𝐴=𝜆𝑁
Solution to equation is 𝑁= 𝑁 0 𝑒 −𝜆𝑡
So A= 𝐴 0 𝑒 −𝜆𝑡 too
T½ = ln(2)/λ

28. Proof of T½ = ln(2)/λ
𝑁= 𝑁 0 𝑒 −𝜆𝑡 at t= T½ N=N0/2 So 𝑁 0 2 = 𝑁 0 𝑒 −𝜆𝑡 ln 1 2 =− ln 2 =−𝜆T½ T½ = ln⁡(2) 𝜆

29. Uses of radioactivity Carbon-14 dating (5570 yr half life)
Uranium-238 (768 Million yr half life)
Potassium-40 (1250 Million yr half life)
Radioactive tracers (gamma)
Engine wear (gamma)
Foil thickness monitoring (beta)
Smoke alarm (alpha)
RTG – radioactive thermal generator
Radioactive decay heats source
thermocouple generates pd

30. More about nuclear decay
There are a number of nuclei which are stable and other isotopes which are less stable and liable to decay. These are often plotted on an N-Z plot or graph of Nuclides.

31. Graph of nuclides (isotopes) by type of decay
Graph of nuclides (isotopes) by type of decay. Orange and blue nuclides are unstable, with the black squares between these regions representing stable nuclides. The unbroken line passing below many of the nuclides represents the theoretical position on the graph of nuclides for which proton number is the same as neutron number. The graph shows that elements with more than 20 protons must have more neutrons than protons in order to be stable.

32. Most naturally occurring nuclides are stable (about 254 see wikioedia); and about 32 more (total of 286) are known radioactives with sufficiently long half-lives (also known) to occur primordially. If the half-life of a nuclide is comparable to, or greater than, the Earth's age (4.5 billion years), a significant amount will have survived since the formation of the Solar System, and then is said to be primordial. It will then contribute in that way to the natural isotopic composition of a chemical element. Primordially present radioisotopes are easily detected with half-lives as short as 700 million years (e.g., 235U). This is the present limit of detection, as shorter-lived nuclides have not yet been detected undisputedly in nature.
Many naturally-occurring radioisotopes (another 51 or so, for a total of about 339) exhibit still shorter half-lives than 68 million years, but they are made freshly, as daughter products of decay processes of primordial nuclides (for example, radium from uranium) or from ongoing energetic reactions, such as cosmogenic nuclides produced by present bombardment of Earth by cosmic rays (for example, 14C made from nitrogen).
Some isotopes that are classed as stable (i.e. no radioactivity has been observed for them) are predicted to have extremely long half-lives (sometimes as high as 1018years or more). If the predicted half-life falls into an experimentally accessible range, such isotopes have a chance to move from the list of stable nuclides to the radioactive category, once their activity is observed. E.g. 209Bi and 180W were formerly classed as stable, but have been recently (2003) found to be alpha-active. However, such nuclides do not change their status as primordial when they are found to be radioactive.
Most stable isotopes in the earth are believed to have been formed in processes of nucleosynthesis, either in the Big Bang, or in generations of stars that preceded the formation of the solar system. However, some stable isotopes also show abundance variations in the earth as a result of decay from long-lived radioactive nuclides. These decay-products are termed radiogenic isotopes, in order to distinguish them from the much larger group of 'non-radiogenic' isotopes.
The so-called island of stability may reveal a number of long-lived or even stable atoms that are heavier (and with more protons) than lead.

33. Nuclear decay on the NZ plot
Transition diagram for decay modes of a radionuclide, with neutron number N and atomic number Z (shown are α, β±, p+, and n0 emissions, EC denotes electron capture).
By MarsRover - Own work, GFDL,

34. Uranium decay chain

40. Nuclear energy levels (background)

41. Nuclear energy levels
Daughter nucleus formed in excited state. Just like atoms in excited state – electrons drop to lower energy level emitting photon Similarly excited nuclei can return to ground state by emitting gamma (much bigger energy because strong force)
A 𝑀𝑔 nucleus decays by 𝛽 − decay to form an 𝐴𝑙 nucleus in an excited state 1.02MeV above its ground state at zero energy.
The aluminium nucleus de-excites by emitting either a 1.02 MeV photon (3) or a 0.19 MeV (1)photon, followed by a 0.83 MeV photon (2).

42. The technetium generator
The technetium generator is used in hospitals to produce a gamma only emitting source 𝑇𝑐 (Tc 99m) can be generated by 𝑀𝑜 decay in a semi-stable or metastable state which lasts long enough to be useful with a half life of 6 hours it lasts long enough to be separated from the parent and deployed in the body to emit gamma rays at a site of interest, which can be detected outside the body. Tc99m decays to Tc99 which has a half life of years – therefore not causing concern. The sample of Tc99m with Mo removed is effectively a gamma only emitter.

43. Diagnostic uses of Tc99m
Monitoring blood flow through the brain using external detectors after a small quantity of sodium pertechnate is administered intravenously
The gamma camera is designed to ‘image’ internal organs by detecting gamma radiation from sites in the body where a gamma emitting isotope is located. For example bone deposits can be located using a phosphate tracer labelled with Tc99m. The gamma camera uses photomultipliers to detect the gamma rays.

44. The gamma camera

45. Nuclear radius
Using high energy electron diffraction, we can measure the nuclear radius. High energy electrons of de Broglie wavelength, are diffracted by the target nuclei in the foil. λ = 10-15m, roughly the diameter of the nuclei.
Scattering of electrons like α, except they are attracted.
Diffraction pattern (as for diffraction grating)
λ = h/mv and E = mc2 so λ = hc/E
Θmin can be used to calculate the nuclear diameter
R sin Θmin =0.61 λ
Derived from wave diffraction through circular gap (cf Rayleigh Criterion)

46. Nuclear radius and nucleon number
Plotting ln A (or log A) vs ln R (or log R)
Gradient = 1\3
R ∝ 𝐴 1/3
Plot R vs A1/3
Gradient = ro= radius of proton
𝑅= 𝑟 0 𝐴 1/3
𝑟 0 =1.25±0.2 𝑓𝑚
By Marekich - Own work (vector version of PNG image), CC BY-SA 3.0,

47. Nuclear density Volume, 𝑉= 4 3 𝜋 𝑅 3 and 𝑅= 𝑟 0 𝐴 1/3
∴𝑉= 𝜋 𝑟 𝑜 3 𝐴
So V is directly proportional to A
So the density of the nucleus is constant
𝑚=𝐴𝑢 where 𝑢=1.661 𝑥 10 −27 𝑘𝑔
So the density of a nucleus is 3.4 x 1017 kg m-3
Interesting to note the density of a nucleus is about the density of a neutron star so a neutron star of 25 km diameter has a mass of about 2 solar masses.

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