University of Sydney Chemistry 1A (CHEM1101)

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1 University of Sydney Chemistry 1A (CHEM1101) Topic 1 Nuclear & Radiation Chemistry 1 Topic 2 Quantum Theory 10 Topic 3 Trends & Atomic Spectroscopy 16 Topic 4 Molecular Orbitals & Bonding 21 Topic 5 Structure and Shape 35 Topic 6 Gases and colligative properties 45 Topic 7 Topic 8 Topic 9 Topic 10 Thermochemistry Equilibrium Mining & Industrial Chemistry Electrochemistry Unless otherwise stated, all images in this file have been reproduced from: Blackman, Bottle, Schmid, Mocerino and Wille, Chemistry, 2012 (John Wiley) ISBN:

2 Topic 1: Nuclear and Radiation Chemistry Nucleons, nuclides and isotopes Nuclear fusion and stellar nucleogenesis Natural Radioactivity Which nuclides are stable and why Where decay mechanisms come from How fast does an unstable nucleus decay? Half-lives Radiocarbon Dating How does radiation interact with (biological) matter? How is radiation exposure measured? What are common sources of radioactivity? Medical Imaging Particle Symbol Charge Mass (a.m.u.) proton p neutron n electron e positron e The composition of any nucleus is defined by two numbers. The atomic number is the number of protons in the nucleus. This defines the chemical nature of the atom. It is equal to the total charge on the nucleus. The mass number is the total number of nucleons (protons and neutrons) in the nucleus. E.g C has an atomic number of 6 and a mass number of 12. A nuclide is an atom with a particular mass number and atomic number. Nuclei with the same atomic number but different mass numbers are called isotopes. The atomic mass of an element is the average of the atomic masses and abundances of each of the naturally-occurring isotopes. E.g. The atomic mass of carbon is That is ( x x 1.11)/100 1

3 Nucleogenesis The fundamental nuclear reaction is H + H H + e (Note H p ) This is rapidly followed by two other nuclear reactions H + H He + γ and He + He He + 2 p The overall hydrogen burning reaction 4 H He + 2 e γ releases energy into the surroundings as heat (exothermic) and radiation (also releases neutrinos ). As the star exhausts its hydrogen, it begins helium burning to fuse heavier nuclei to form increasingly larger atoms. E.g. He + He Be + and Be + H B + Nucleogenesis produces nuclides that can be stable or unstable. Unstable nuclei decay through a range of mechanisms involving the release of particles with high kinetic energy or of -radiation. These high-energy products are collectively known as radioactivity. Natural Radioactivity The four most important radioactive decay mechanisms are 1. decay e.g. Bi Tl + α 2. decay e.g. B C + e (Note e β 3. Positron (+) emission e.g. N C + e 4. Electron capture e.g.. Fe + e Mn Natural Radioactivity - worked example Balance the following nuclear decay reactions and identify the emitted particle where appropriate. 1. U Th + Ans: U Th + α 2. Ni + e Ans: Ni Cu + e 3. Cl + S Ans: Cl + e S ) 2

4 Nuclear reactions are balanced in the same way, but may involve more than one reactant. Balance the following nuclear reactions and identify the missing nuclide or particle. 1. N + He O + 2. Pu + He + n + 3. Si + H P Both x-rays and γ radiation are high energy (= high frequency or short wavelength) forms of light. Blackman Figure 4.4 Unstable heavy nuclei decay spontaneously by a series of steps through unstable intermediates. Over time, unstable nuclei give rise to a family of decay products in a decay series. E.g. 238 U decays into then then Th + α U Th Pa β Pa U β and so on Blackman Figure

5 A radioactive decay sequence (e.g. of 238 U) can be represented more concisely as a graph of atomic number versus neutron number. Nuclear Stability What factors determine whether a nucleus is stable or unstable? If we look at the range of stable nuclides that exist in nature, then there are two main observations 1. The size of the nucleus. 2. The composition of the nucleus (proton:neutron) All known stable nuclides fall inside the zone of stability. This zone has a N:Z ratio near to 1 for the first ten elements, but bends towards more neutrons per proton as the nucleus gets larger. These two observations are enough to give us a rule for nuclear stability that goes something like Unstable isotopes must decay towards the zone of stability, finally falling below 209 Bi. Consider some of the known isotopes of carbon 11 6 C 12 6 C 13 6 C 14 6 C 15 6 C Unstable nucleus N/Z = 0.83 too low Stable nucleus; N/Z = 1 Stable nucleus; N/Z = 1.17 Unstable nucleus; N/Z = 1.33 too high Unstable nucleus; N/Z = 1.5 too high Nuclear Stability - Origin of Decay Mechanisms The stability of a nucleus involves the competition between two forces. 1. Coulomb or electrostatic repulsion between protons acts to push these nucleons apart over a long range. 2. The strong nuclear force is a short range attraction between all nucleons. This is the main function of neutrons in the nucleus. They contribute to the binding of the nucleus without also contributing to the electrostatic destabilisation. How does this explain our observations? 4

6 1. In nuclides with too few neutrons, the electrostatic repulsions overwhelm the strong nuclear attractions. 2. As the nucleus gets larger, the long-range electrostatic repulsion between protons accumulates and eventually overwhelms the strong nuclear attraction, even if N/Z is optimised. This microscopic model does not explain how nuclides with too many neutrons can be unstable. To do so will involve quantum mechanics. Rate of Nuclear Decay Unstable nuclides are present in nature for two reasons. Some unstable nuclides have long half-lives, so they simply haven t decayed yet. Some unstable nuclides continue to be formed by nuclear reactions. The decay of an unstable nuclide is characterised by a half-life. This is the time required for half of the nuclei present to undergo a decay event. E.g. 32 P decays into 32 S with a half-life of 14.7 days. S P + e The number of 32 P nuclei halves in 14.7 days, and halves again after a further 14.7 days... So, after 14.7 days, half of an initial 10 g of 32 P will have decayed, leaving 5 g. At the same time 5 g of 32 S will have formed. After a further 14.7 days, only 2.5 g of 32 P will remain, and 7.5 g of 32 S will be present This also tells us that the rate of decay, the number of nuclei that disintegrate each second, also halves every 14.7 days. The rate of decay halves after every half-life. Nt ( ) Nexp( t) 0 The activity, A, of a radionuclide is simply the rate of emission, or minus the rate of disappearance of the nuclide. i.e. dn d A N0 exp( t) dt dt N0 exp( t) N 5

7 Units of Activity Fundamental unit of activity - Disintegrations per second, also known as the becquerel (Bq) Curie (Ci) 1 Ci equals the number of nuclei disintegrating each second in 1g of 226 Ra = 3.70 x counts per second (or Bq). Activity and Half-Life What is the molar activity of 13 N, which has a half life of 9.96 minutes? Answer minutes = 598s A N N M A A t12 A M = x x /598 = 6.98 x disintegrations mol -1 s -1 (or Bq mol -1 ) or 6.98 x /3.70 x = 1.88 x Ci mol -1 Radiocarbon Dating 14 C is an example of an isotope that is continuously produced in our environment. 99.9% of the naturally abundant 14 C is produced in the upper atmosphere by neutrons reacting with 14 N, which then enters the carbon cycle. N + n C + p The production rate is 2.5 atom cm -2 s -1 with a global inventory of 3 x C atoms (90% oceans, 8% biosphere and soils, 2% atmosphere). Typical 14 C concentration in sea waters is 1.2 x C atoms/l (2 x M). As noted before, 14 C undergoes decay. How is the amount of 14 C determined? Radiocarbon dating can be achieved either by measuring the concentration of 14 C present in a sample, or by measuring the activity due to emission. (Recall that activity is proportional to the number of decaying nuclei: A N ) The activity is proportional to the number of nuclei present. Thus the ratio of the activity after death to activity while alive is equal to the ratio of the number of 14 C nuclides. 6

8 A dn dn N N A N N 0 0 dt dt 0 0 exp( t) To determine the age of a sample we compare the activity A with the activity of a stillliving (or recently dead) sample, A 0, and use the half-life or decay constant. This method assumes that the concentration of 14 C in living matter has been constant over the dating period. This assumption is known not to be exactly true, so a number of qualifications and corrections are applied to 14 C dates, and a standard method is always used to report radiocarbon age. 1. The age of a sample is reported as its radiocarbon age. This may be reported as years BP (before present, where present = AD1950 when radiocarbon dating was invented). 2. An uncertainty or error range is often reported based on known changes in 14 C levels as well as on experimental uncertainty. 3. The radiocarbon age may be corrected using a calibration graph obtained from independent data. 4. Variations in natural isotopic ratios between sources are also corrected. Willard Libby, who invented 14 C dating in 1946 (Nobel Prize, 1960), prepared a primary calibration graph using samples with independently-determined ages. The curve shows the Libby half-life of 5568y, which is used to determine the radiocarbon age of materials and effectively assumes a constant rate of 14 C production. Radiocarbon Dating - worked example E.g. A one gram sample of carbon from peat moss has an activity of mci. A reference or modern standard sample yields mci. What is the radiocarbon age of the sample? A0 t 8033ln A ln

9 Biological Effects of Radiation (for reference only) How do various forms of radiation interact with (biological) matter? The basic characteristic of radiation produced by radioactivity is that it is high energy, and causes the ionization of matter by ejecting an electron from an atom. (It s generally called ionizing radiation.) Ionization produces free radicals. These are highly reactive chemical species. E.g. Gamma irradiation of water ejects an electron creating a radical ion + H 2 O H 2 O +. + e - Both products lead to the production of more free radicals H 2 O +. + H 2 O H 3 O + + OH. and e - + H 2 O H. + OH - Penetrating power of, and radiation: are heavy, highly charged particles. are lighter, and more penetrating. are highly penetrating. + are highly ionizing and penetrating. (Human) Radiation dosage is measured in rems (or millirems) or in Sieverts (Sv). Dosage attempts to include all the factors that can affect a living organism - activity, energy, penetration, and the mass of living matter irradiated. Source Activity Energy of Radiation Energy Absorbed per unit mass (dose) Relative Biological Effectiveness 10 1 Bq or Ci Joule Gray (J/kg) or Rad Q-factor Effective Dosage Equivalent rem = rad x Q Sievert =Gy x Q The total expected dosage for an average person is about 360 mrem/year. 25,000 mrem in 24h No detectable effects 50,000 mrem in 24h Slight temporary blood change 100,000 mrem in 24h Nausea & fatigue 200,000 mrem in 24h First death (no medical intervention) 500,000 mrem in 24h LD 50 (50% of humans exposed die.) N.B. The probability of longer-term effects increases with dose. Most health physicists use a linear no-threshold model. That is, they assume that there is no level of exposure 8

10 that is free from effects. However the time-scale and statistical nature of the effects make low-dose response hard to determine. Medical Imaging (for reference only) Basic principles of medical imaging. Use a radioisotope to specifically target a chemical agent, organ or process in the body with high selectivity. Isotope should emit low-energy, highly-penetrating radiation to minimise effective dosage equivalent to patient. In practice this usually means γ. Image distribution of radioisotope (by its activity) using scintillation counting gamma camera (planar image like an x-ray) or computer-assisted tomography (CAT or CT scan - cross section or threedimensional reconstruction) Images may be a simple gray scale density or pseudo-colour signal. Pseudo colour is especially common in computer-reconstructed imaging. Positron Emitting Isotopes are generally formed in a cyclotron, which bombards a stable sample with protons or deuterons. Charged protons or deuterons are generated and accelerated in electric field and magnetic fields along a spiral path until they strike their target (stable) nuclide. N + H C + α ( C t 1/2 = 20.3 min) O + H N + α ( N t 1/2 = 9.97 min) C + H N + n N + H O + n ( O t 1/2 = 2.07 min) N e + H F + α ( F t 1/2 = min) Nuclear imaging is useful because it allows us to radiolabel molecules that specifically target organs, molecules or chemical processes for diagnosis or biochemical research. The synthetic chemistry to design these target molecules differs widely:- Cyclotron-produced PET isotopes ( 11 C, 18 F ) are often exploited in the synthesis of organic molecules (drugs, peptides, carbohydrates, steroids, vitamins ) Metals ( 99m Tc, 82 Rb, ) may be used as soluble or insoluble salts, or as coordination compounds, to mimic biological molecules, toxins, as heavy metal tracers 9