Nuclear Physics & Radioactivity What holds a nucleus
Nuclear Physics & Radioactivity What holds a nucleus together? What drives radioactive decay? What sets the timescale for radioactive decay? What are the statistics of radioactive decay? Lecture outline: 1) nuclear physics 2) radioactive decay 3) counting statistics Nuclear Structure: Z A E (or AE or EA); e.g. 12C Number of protons = Z (Atomic number) Number protons + neutrons = A (Mass #) Same Z, different A -- Isotope particles in a cloud chamber
1 Particles: Proton, Neutron, Alpha, Leptons 2 The Four Forces of Nature Force Strength Range Occurrence Strong nuclear 1 <<1/r2 (finite, v. short) inter-nucleon
Electromagnetic 10-2 1/r2 (infinite, but shielded) nucleus, atom Weak nuclear 10-13 <<1/r2 (finite, v. short) -decay, neutrinos Gravity 10-39 1/r2 (infinite)
everywhere Isotopes 330 natural isotopes 25 unstable, long halflife 35 unstable, short halflife More than 1000 artificial isotopes 3 Binding energy Lets revisit the fusion of four protons to form a 4He nucleus: 4( 11H ) 1( 24 He) 2e 2 e E 4(1.007277) 1(4.00150) m m 0.02761amu *these masses come from the table of nuclides 56 Fe
We have calculated the mass deficit --> i.e. the whole is less than sum of the parts The mass deficit is represented by a HUGE energy release, which can be calculated using Einsteins famous equation, E=mc2, and is usually expressed in MeV. The energy difference can be termed a binding energy, often given on a per nucleon basis. 4 Contributions to Binding Energy EB = strong nuclear force binding -surface tension binding + spin pairing +shell binding-Coulomb repulsion 1) strong nuclear force -- the more nucleons the better 2) surface tension -- the less surface/volume the better (U better than He) 3) spin pairing -- neutrons and protons have + and - spins, paired spins better 4) shell binding -- nucleus has quantized shells which prefer to be filled (magic numbers) 5) Coulomb repulsion -- packing more protons into nucleus comes at a cost (although neutron addition will stabilize high Z nuclei) 5 Radioactive Decay - a radioactive parent nuclide decays to a daughter nuclide - the probability that one nucleus will decay in a unit time is defined as (units of s-1, y-1) - If we have N unstable nuclei, the number of decays in time dt is
dN = - N dt Thus dN/N = - dt ln N = - t + Const N = N0e-t - where N0 is the number of nuclei present at t = 0 t1 / 2 life is defined as = 1/ - the decay constant is time independent; the mean N N 0 / 2 N 0e Define halflife t1/2 : Note that t1/2 = ln(2) / Activity A: Number of decays per unit time. A = |dN/dt| = N = A0e-t where A0 is the initial activity 6 Decay plot for 14C dN
N dt N N 0e t ln(2) t1/ 2 14 Number of C atoms N0 1000000 900000 800000 700000 t1/2 = 5730y
600000 500000 400000 300000 1/ 2 1/ 2 1/ 2 N 0 t N 0 / 2 t N 0 / 4 t N0 / 8 200000 100000 0 0 5730 10000 20000
30000 40000 50000 Years 7 Activity calculations Activity N - usually reported in Bq (disintegrations per second), example: 14C activity = 0.226 Bq / gram (Old Unit: Curie (Ci) = = 3.7x1010 Bq (1 g of radium) A A0 e t
- because activity is linearly proportional to number N, then A can be substituted for N in the equation t N N 0e Example activities: Radium in watch dial: 4 x 104 Bq = 1 Ci Sealed sources in lab: < 1 Ci Cancer treatment source: 4 x 1013 Bq = 1000 Ci 8 Four types of radioactive decay 1) alpha () decay - 4He nucleus (2p + 2n) ejected; ZZ-2, AA-4 2) beta () decay electron ejected; ZZ+1; no change in A 3) gamma () decay - photon emission, no change in A or Z 4) spontaneous fission - for Z=92 and above, generates two smaller nuclei 9 decay
241 95 Am 237 93 Np 24 He - involves strong and Coloumbic forces - alpha particle and daughter nucleus have equal and opposite momenta (i.e. daughter experiences recoil) 10 decay - three types 1) - decay 3 1 3
2 H He e e - converts one neutron into a proton and electron - no change of A, but different element - release of anti-neutrino (no charge, no mass) 2) + decay 11 6 C 115 B e e - converts one proton into a neutron and positron - no change of A, but different element - release of neutrino 3) Electron capture
7 Be e 4 EC 37 Li e - converts one proton into a neutron - no change of A, but different element - release of neutrino 11 decay 3 2 *
3 2 He He - conversion of strong to coulombic E - no change of A or Z (element) - release of photon - usually occurs in conjunction with other decay Spontaneous fission 256 100 Fm sf 140 54 Xe 112 46 Pd 4n
- heavy nuclides split into two daughters and neutrons - U most common (fission-track dating) Fission tracks from 238U fission in old zircon 12 Radiation Dose, Dose Rate When radiation (electromagnetic or particles) is absorbed by any material, energy is absorbed by the material (photon energy or kinetic energy). The physical unit of absorbed radiation dose is the gray (Gy), equal to 1 J per kg of mass. Dose rate is the rate of dosage, the dose per unit time interval, for example, 10 Gy/h. This is a physical measurement, and does not correctly quantify the long-term biological effect.
Biologically Equivalent Dose = Dose x Weight Factor 13 Weighting factor (wR) The weighting factor (wR) is 1 for beta particles. The weighting factor (wR) is also 1 for X-rays and gamma rays. The weighting factor (wR) is 20 for alpha particles and 5-20 for neutrons, depending on energy. Some beta particles may not be much hazard because they have low energy and will not penetrate the skin (for example, from tritium). Alpha particles also will not penetrate skin. 14
Dose = dose rate x time For example, if dose rate D = 500 Gy/h then the dose after 2 hours is 1000 Gy = 1 mGy. The conventional (old) unit of dose is the rad 1 Gray = 1 Gy = 100 rad. The absorbed physical radiation dose of 1 mGy is equal to 100 millirad. (1 milli x 100 rad) The unit of biologically equivalent dose is the Sievert; conventional (old) unit of equivalent dose is the rem 1 Sievert = 1 Sv = 100 rem. E.g, 1 mG dose of beta particles (wR = 1), has biologically equivalent dose 1 mSv = 100 millirem. 15 Counting Statistics The radioactive decay process follows Poisson statistics (special case of binomial statistics). If we count decays for time T for a sample with (parent) average number of decays in time T, then the probability of observing x counts in that time is x
e PP ( x) x! The standard deviation for # counts in T is = For a large number of decays in time T, the Poisson distribution approaches a Gaussian distribution with = 1 PG ( x) e 2 ( x )2 2 The uncertainty in an average (random) count is 16 17 18
Permitted Radiation Dose & Natural Background Permitted Dose 19 Doses Due to Ionizing Radiation Natural background (cosmic rays & radiation from naturally radioactive material): San Francisco 120 mrems/yr New York 135 mrems/yr Denver 300 mrems/yr Pocos de Caldos, Brazil 7,000 mrems/yr Natural radioactive materials in the body: K40 Whole body 17 mrems/yr K40 Brain
30 mrems/yr Ra226 Whole body 2.8 mrems/yr Ra226 Bone 28 mrems/yr U238 Kidneys 1.2 mrems/yr Rn222 (Radon gas) Lung 2001,100 mrems/yr (depending on location) Twoweek vacation in the mountains 3 mrems (due to an increase in cosmic rays at higher elevation) Crosscountry jet flight >1 mrem/hr Radiumdial watch (close to wrist area) 0.1 mSv/day (10 mrems/day) Wholebody diagnostic Xray up to 250 mSv (25,000 mrems) Chest Xray up to 1 mSv/film (100 mrems/film) Complete dental Xray up to 50 mSv (5,000 mrems)
NRC, NCRP & EPA wholebody limit General Public 1 mSv/yr (100 mrems/yr) 20 How radioactive is your body? 1.2 radioactive atoms of 40K for every 10,000 non-radioactive atoms of potassium. There is of the order of 140 g of potassium in an adult who weighs 70 kg, and 0.0169 g consists of the 40K isotope. This amount of 40K disintegrates at the rate of 266,000 atoms per minute. 89% result in the release of beta particles with maximum energy of 1.33 MeV 11% result in gamma photons with an energy of 1.46 MeV. All of the beta particles and about 50 percent of the gamma rays are absorbed in the body, giving annual doses of 16 mrad from the beta particles and 2 mrad from the gamma rays. 21
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