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Chapter 30: The Atom, the Nucleus and Radioactivity Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier. In the early 1900’s the most popular model of the atom was ‘the plum pudding’ model; which assumed that the atom is composed of electrons surrounded by a soup of positive charge to balance the electron's negative charge, like negatively-charged ‘plums’ surrounded by positively-charged ‘pudding’.
Ernest Rutherford’s gold foil experiment In 1909 the New Zealand physicist Ernest Rutherford carried out the following experiment; He fired alpha particles at a very thin sheet of gold foil. The alpha particles could be detected by small flashes of light that they produced on a fluorescent screen (see diagram).
He found that*:
- Most alpha particles were undeflected and passed straight through the gold foil.
- Some were deflected through small angles.
- A very small number were turned back through angles greater than 90^0!
Obviously this couldn’t be explained using the ‘plum pudding’ interpretation. Instead Rutherford interpreted his results as follows:
- The atom is mostly empty space, but there is a solid centre, which has a positive charge.
- The electrons orbit the nucleus.
Bohr Model of the atom* The Danish physicist Neils Bohr developed this theory to state that electrons could only inhabit certain discrete levels or orbits. They can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation of frequency f, corresponding to a packet of energy of size hf = E 2 – E 1 where E 2 and E 1 are the energies associated with the two electron levels.
Emission spectrums are lines of various colours visible when viewing a gas through a diffraction grating or spectrometer. The different colours correspond to the frequency of the electromagnetic radiation emitted.
We now know that the radius of a nucleus is about 10-15^ m, while the radius of an atom is about 10-10^ m*.
The atomic number (Z) of an atom tells us the number of protons present in the atom*.
The mass number (A) of an atom tells us the number of protons plus neutrons present in the atom.
Isotopes are atoms which have the same Atomic Number but different Mass Numbers.
Radioactivity Radioactivity is the breakup of unstable nuclei with the emission of one or more types of radiation*.
However, relatively stable (and therefore non-radioactive) atoms can be made radioactive by bombarding them with neutrons. These are known as artificial radioactive isotopes , and are often used in industry for the following;
Medical Imaging Food irradiation Radiocarbon dating Medical Therapy Agriculture Smoke Detectors
Ionisation occurs when an atom loses or gains an electron. An ion is a charged atom.
Alpha, beta and gamma radiation
The three different types of radiation emitted during radioactive decay are called Alpha, Beta and Gamma
radiation.
Alpha Radiation ( α ) An alpha particle is identical to a helium nucleus (2 protons and 2 neutrons). Since they have a relatively large charge they cause a lot of ionisation as they pass through a material. Consequently they lose their energy quickly and their penetrating ability is poor. Charge = +
Note that the Mass Number of the parent atom decreases by four and its Atomic Number decreases by two. Examples:
We say that the particles on the right are ‘daughter products’.
Beta Radiation ( β ) In this case a neutron splits up into a proton and an electron (and a neutrino)!!:* A beta particle is identical to a fast moving electron.
They are less ionising and therefore more penetrative than alpha particles. Charge = -
Examples:
Note: The –1 below the electron symbol obviously doesn’t represent an Atomic Number; it is merely a little accounting trick used to check if the (atomic) books are balancing.
Gamma Radiation (γ) Gamma radiation is radiation of very short wavelength (and therefore high frequency and therefore high energy (from E =hf)). It is uncharged and so its ionising ability is relativity poor but it is highly penetrating.
There is no change in Atomic Number or Mass Number, so there is no equation as such. Gamma radiation usually only accompanies alpha and beta decay.
Half-Life The half-life* (T1/2) of an element is the time taken for half of the nuclei in the sample to decay. Or The half-life (T1/2) of an element is the time taken for the activity of a sample to decrease to half of its original value. Obviously, the more atoms that are present, the greater will be the number of disintegrations. This is summed up by the Law of Radioactive Decay.
The law of radioactive decay states that the number of disintegrations per second is proportional to the number of nuclei present.
Mathematically: dN/dt ∝ N ⇒
Where N = number of nuclei present, and λ is called the Decay Constant.
There is also a relationship between Half-life (T½) and the Decay Constant (λ): T½ = ln 2/ λ or
Now see if you can follow the graph questions on Page 353.
dN/dt = λ N
T½ = 0.693 / λ
The effect of Ionising Radiation on humans depends on:
- The type of radiation (whether it’s alpha, beta or gamma)
- The activity of the source (in Bq)
- The time of exposure
- The type of tissue irradiated
Precautions when dealing with ionising radiation:
- Make sure sources are properly shielded.
- Keep sources as distant as possible from human contact, eg use a pair of tongs (and not, as one official safety brochure advised, a pair of thongs!).
- Use protective clothing. Leaving Cert Physics Syllabus
Content Depth of Treatment Activities STS
The Nucleus
- Structure of the atom
Principle of Rutherford’s experiment. Bohr model; descriptive treatment only. Energy levels
Emission line spectra. Hf = E 2 – E 1
Experiment may by simulated using a large-scale model or a computer or demonstrated on a video.
Demonstration of line spectra and continuous spectra.
Lasers. Spectroscopy as a tool in science.
- Structure of the nucleus
Atomic nucleus as protons plus neutrons. Mass number A, atomic numbers Z,
isotopes.
- Radioactivity Experimental evidence for three kinds of radiation; by deflection in electric or magnetic fields or ionisation or penetration. Nature and properties of alpha, beta and gamma emissions. Change in mass number and atomic number because of radioactive decay.
Demonstration of ionisation and penetration by the radiations using any suitable method, e.g. electroscope, G-M tube.
Uses of radioisotopes: medical imaging medical therapy food irradiation agriculture radiocarbon dating smoke detectors industrial applications.
Principle of operation of a detector of ionising radiation. Definition of Becquerel (Bq) as one disintegration per second.
Demonstration of G-M tube or solid state detector. Interpretations of nuclear reactions.
Law of radioactive decay. Concept of half-life T1/ Concept of decay constant Rate of decay = λN T½ = ln 2 / λ
Appropriate calculations Appropriate calculations
- Nuclear Energy Dealt with in next chapter
- Ionising radiation and health hazards
General health hazards in use of ionising radiations, e.g. X-rays, nuclear radiation; the effect of ionising radiation on humans depends on the type of radiation, the activity of the source (in Bq), the time of exposure, and the type of tissue irradiated.
Measurement of background radiation. Audiovisual resource material.
Health hazards of ionising radiation. Radon, significance of background radiation, granite. Medical and dental X-rays.
Disposal of nuclear waste. Radiation protection.
Extra Credit Some quotes: In science there is only physics; all the rest is stamp collecting. Lord Rutherford.
The energy produced by an atom is a very poor kind of thing. Anyone who expects a source of power from the transformation of these atoms is talking moonshine. Rutherford.
We must be wary of using this word ‘transmutation’ – lest people believe us to be alchemists****. When Rutherford split the atom he was quite literally changing one element into another – the goal of alchemists down through the years .Alchemists used all sorts of potions to try to turn lead into gold. They were also interested in creating something called the elixir of life – supposed to be responsible for eternal youth. They tended to use urine as a raw material rather a lot. All in all, rather a strange bunch – a bit like our modern day chemistry teacher.
I have observed many transformations in my work on radioactivity, but none so rapid as my own transformation from a physicist to a chemist ” Rutherford again, this time on receiving the Nobel Prize for Chemistry (hate that!).
Something most textbooks are uncomfortable with is the fact that the great Isaac Newton spent over 90% of his time as an alchemist. One noted historian claimed that Newton was not the first great scientist; he was the last of the great mystics.
_He found that..._* Now while Rutherford was indeed a brilliant physicist, do not think that these ideas came easily to him. For every one experiment that was productive, he had probably another 90 that were a waste of time. See for example the video ‘Rutherford’s Atom’, available in the physics lab. Indeed when he carried out this experiment he had no idea what the result would be. He described his astonishment at the results in very graphic terms: “It was quite the most incredible event that ever happened to me in my life. It was as incredible as if you fired a 15- inch shell at a piece of tissue paper and it came pack and hit you!” Rutherford puzzled over these results for some weeks and eventually realised that the alpha particles could only be scattered through such large angles if they had collided with a very dense and small core of matter within the atom – the atomic nucleus.
*Bohr model of the atom Shortly after 1900 the brothers Niels and Harald Bohr of Denmark became famous soccer players in Scandinavia. In 1908 Harald won a silver medal in the first Olympic soccer competition. Bohr was raised in a middle class Danish family and showed no particular talent as a child except for sports. He played soccer at almost a professional level and was an active skier until late in his life. Niels' son Aage was also a Nobel physicist. The American actress Olivia Newton-John (Remember Saturday Night Fever anyone?) is Niels Bohr's grand-daughter.
*We now know that the radius of a nucleus is about 10-15^ m, while the radius of an atom is about 10–10^ m. Therefore the radius of an atom is 100,000 times bigger than that of a nucleus. And volume of a sphere is proportional to the cube of the radius. This means that all matter is actually 99.99999999999 % empty space. So if we removed all the empty space in the body, we would we left with all the mass taking up a volume about the same as a grain of sand! Now, given that your fist is made up of atoms (which as we have seen are pretty much just empty space) why doesn’t your fist go straight through a table (which is just as empty) when you hit it? Also, if you and I are almost completely empty space, why do we give the appearance of being solid? AND WHY THE HELL DON’T WE DISCUSS THIS??
_The atomic number (Z) of an atom tells us the number of protons present in the atom._* Because the activity of an atom is determined by the number and arrangement of electrons, it is sometimes said that “protons give the atom its identity; electrons give it its personality”. Nice.
_Half-Life_* One of many analogies for half-life is the Gold Leaf Electroscope. They are very easily broken. In fact, after every 40-minute class using them, approximately half of them need to be repaired. It is (almost) impossible to predict in advance which electroscopes will break (although one could take a look at the students involved and make an educated guess from there).Assuming the broken ones do not get repaired, then the half which are still in working order get handed out in the next class. After 40 minutes, half of these come back broken. And so on. You could say that the half-life of a gold leaf electroscope is 40 minutes.
We can say the same about the decay of a large number of radioactive atoms (of the same element). If the element is Radon, then after a certain time approximately half of the atoms will have decayed. This time will be the same for Radon no matter how many atoms are present (assuming that there are a very large number). It’s a lot like saying that if I toss a coin it will come up heads half the time. This will only be accurate if we are talking about a very large number of coin tosses. The time it takes half of the radon atoms to decay is unique to radon and is called the half-like of radon. Each element has its own unique half-life. Protactinium-234, for instance, has a half-life of 1.2 minutes, while Uranium-238 has a half-life of 4.5 billion years! See the chain below for more examples.
Did you know? Each cubic metre of garden top soil contains typically: 0.5 grams of Uranium and the members of its decay chain. 1.5 grams of Thorium and the members of its decay chain.
Brazil nuts contain small amounts of radium, a radioactive material. Although the amount is very small, about 1– pCi/g (40–260 Bq/kg), and most of it is not retained by the body, this is 1,000 times higher than in other foods. According to Oak Ridge Associated Universities, this is not because of elevated levels of radium in the soil, but due to "the very extensive root system of the tree." Source: Wikipedia A 70 kg human has about 9 kBq of natural radioactivity; mostly K-40 and C-14.
Polonium Marie Curie discovered a new element while working on radioactivity. At the time (circa 1900) her country was in danger of being annexed by Germany. Fearing nobody would ever remember that her country had even existed, she called the new element Polonium so we would never forget. Her notebooks are still so radioactive that they are kept in lead cases!
Does any increase in exposure to radiation cause an increase in the risk of getting cancer? Short answer: We don’t know.
Long answer: There is no dispute that radiation can cause DNA damage and that such damage is an initiating event in cancer development. Single-strand breaks are easily repaired however while studies have shown that this is not the case with double-strand breaks.
The linear no-threshold (LNT) theory assumes that any exposure to radiation carries a risk of developing cancer. It is widely applied by radiological protection agencies and endorsed by the International Commission on Radiological Protection (ICRP).
On the other hand breaks in the genetic code inside the cell are commonplace and quickly repaired. On average there are up to 150,000 breaks per cell daily. We already have a background of DNA breaks and any contribution to this total by radiation may be minor or indeed negligible.
Radiation Experiments in the U.S. Radiation Experiments were carried out in the United States under the auspices of the American Department of Defense, Department of Energy and the Atomic Energy Commission between 1944 and 1974 on around 20, people. Many were subjected to the experiments without their consent. The experiments were carried out by both military officials and civilian doctors and scientists and were intended to study the short- and long-term effects of radiation exposure. They varied widely, according to the report in the British Medical Journal , from direct injections of uranium, polonium and plutonium into unsuspecting patients, to the irradiation of prisoners’ testicles to the deliberate release of radiation into the atmosphere. For example, isotope injections were given to 18 patients between 1945 and 1947 who had been admitted with various disorders including hepatitis, dermatitis, ulcers, heart attacks and Addison’s disease. The US federal government had now announced that it will pay £3.2 million in compensation to survivors of experiments which were part of one particular research programme, developed to gain an understanding of the biological consequences of biological warfare. These experiments violated the Nuremberg code because in most cases the patients were unaware of what was happening and they were not only unlikely to derive any therapeutic benefit but were subjected to potential harm. Irish Independent 02/12/
Decay Chains The daughter nuclide of a decay event may also be unstable (radioactive). In this case, it will also decay, producing radiation. The resulting second daughter nuclide may also be radioactive. This can lead to a sequence of several decay events. Eventually a stable nuclide is produced. This is called a decay chain.
An example is the natural decay chain of uranium-238 which is as follows: decays, through alpha-emission, with a half-life of 4.5 billion years to thorium- which decays, through beta-emission, with a half-life of 24 days to protactinium- which decays, through beta-emission, with a half-life of 1.2 minutes to uranium- which decays, through alpha-emission, with a half-life of 240 thousand years to thorium- which decays, through alpha-emission, with a half-life of 77 thousand years to radium- which decays, through alpha-emission, with a half-life of 1.6 thousand years to radon- which decays, through alpha-emission, with a half-life of 3.8 days to polonium- which decays, through alpha-emission, with a half-life of 3.1 minutes to lead- which decays, through beta-emission, with a half-life of 27 minutes to bismuth- which decays, through beta-emission, with a half-life of 20 minutes to polonium- which decays, through alpha-emission, with a half-life of 160 microseconds to lead- which decays, through beta-emission, with a half-life of 22 years to bismuth- which decays, through beta-emission, with a half-life of 5 days to polonium- which decays, through alpha-emission, with a half-life of 140 days to lead-206, which is a stable nuclide.
Some radionuclides may have several different paths of decay. For example, approximately 36% of bismuth-212, decays, through alpha-emission, to thallium-208 while approximately 64% of bismuth-212 decays, through beta- emission, to polonium-212. Both the thallium-208 and the polonium-212 are radioactive daughter products of bismuth-212, and both decay directly to stable lead-208. Source: Wikipedia
