Nuclear physics 1. Structure • • At the center of an atom there is a tiny but massive nucleus. Nuclei are made up of protons and neutrons Proton has a positive charge with the same magnitude as electron (+e=1.6x10-19C) and a mass mp = 1.67262x10-27 kg Neutron is electrically neutral (q=0) and has a mass mn = 1.67493x10-27 kg that is very slightly lager the mass of the proton Nucleons: protons and neutrons Different nuclei are referred as nuclides 2. Terminology Z - the atomic number or proton number (the number of protons in the nucleus) N - the neutron number (the number of neutrons in the nucleus) A - the atomic mass number (the number of nucleons in the nucleus) A=Z+N X - chemical symbol for the element; it contains the same information as Z but in a more easily recognizable form A Standard notation: Z X Isotopes – nuclei that contain the same number of protons but different number of neutrons 3. Radius Because of wave-particle duality, the size of the nucleus is somewhat fuzzy. V 43 r 3 A r 1.2 10 15 mA 1 3 Example: Estimate the diameter of the following nuclei: d H 2rH 21.2 10 m 235 15 10 15 dU 2rU 21.2 10 15 m 1 2.4 10 15 m 1 1 H, 1 3 1 3 15 m dU 6.17 dH Example: Compare the density of nuclear matter to the density of normal solids nucl mnucl / Vnucl r atom matom / Vatom r 3 atom 3 nucl 3 10 15 1015 10 10 235 92 U. 4. Atomic mass units Masses of atoms are measured with reference to the carbon-12 atom 12 A neutral 6 C atom is given the precise value 12.000000 u (unified atomic mass units) 1 u = 1.6605x10-27 kg = 931.5 MeV/c2 Proton: mp = 1.67262x10-27 kg = 1.007276 u = 938.27 MeV/c2 Neutron: mn = 1.67493x10-27 kg = 1.008665 u = 939.57 MeV/c2 1H atom: mH = 1.67353x10-27 kg = 1.007825 u = 938.78 MeV/c2 (proton +electron) Electron: me = 9.1094x10-31 kg = 0.00054858 u =0.51100 MeV/c2 What it is MeV/c2 ? E mc 2 8.98740 1016 J 1kg c 1kg(2.9979 10 m / s ) 8.98740 10 J 19 1.6022 10 J / eV 1kg 8.98740 1016 J / c 2 5.6094 1035 eV / c 2 560.94 10 27 MeV / c 2 2 8 2 16 Binding Energy The total mass of a stable nucleus is always less than the sum of the masses of its separate protons and neutrons. Where has the mass gone? It has become energy, such as radiation or kinetic energy, released during the formation of the nucleus. This difference between the total mass of the constituents and the mass of the nucleus is called the total binding energy of the nucleus. Binding Energy and Nuclear Forces •The higher the binding energy per nucleon, the more stable the nucleus. •More massive nuclei require extra neutrons to overcome the Coulomb repulsion of the protons in order to be stable. •The force that binds the nucleons together is called the strong nuclear force. •It is a very strong, but short-range, force. It is essentially zero if the nucleons are more than about 10-15 m apart. •The Coulomb force is long-range; this is why extra neutrons are needed for stability in high-Z nuclei. •Nuclei that are unstable decay; many such decays are governed by another force called the weak nuclear force. Radioactivity (Discovered in 1896 by Henry Becquerel) Most of the known nuclides are unstable (radioactive). A radioactive nuclide spontaneously emits particles (radioactive rays), transforming itself into a different nuclide. Radioactive rays were observed to be of three types: 1. Alpha rays, which could barely penetrate a piece of paper 2. Beta rays, which could penetrate 3 mm of aluminum 3. Gamma rays, which could penetrate several centimeters of lead Alpha and beta rays are bent in opposite directions in a magnetic field, while gamma rays are not bent at all. 1. Alpha rays are helium nuclei 2. Beta rays are electrons 3. Gamma rays are electromagnetic radiation Detection of Radiation Individual particles such as electrons, neutrons, and protons cannot be seen directly, so their existence must be inferred through measurements. The Geiger counter When a charged particle passes through, it ionizes the gas. The ions cascade onto the wire, producing a pulse. A scintillation counter uses a scintillator – a material that emits light when a charged particle goes through it. The scintillator is made light-tight, and the light flashes are viewed with a photomultiplier tube, which has a photocathode that emits an electron when struck by a photon and then a series of amplifiers. A cloud chamber contains a supercooled gas; when a charged particle goes through, droplets form along its track. Similarly, a bubble chamber contains a superheated liquid, and it is bubbles that form. In either case, the tracks can be photographed and measured. Alpha Decay Alpha decay can be written as (transmutation of one element into another) M P c 2 M D c 2 m c 2 Q parent nucleus daughter nucleus disintegration energy Example: Radium-226 will alpha-decay to radon-222 parent nucleus daughter nucleus Alpha decay occurs when the strong nuclear force cannot hold a large nucleus together. The mass of the parent nucleus is greater than the sum of the masses of the daughter nucleus and the alpha particle; this difference is called the disintegration energy. Alpha decay is so much more likely than other forms of nuclear disintegration because the alpha particle itself is quite stable. Beta Decay Beta decay occurs when a nucleus emits an electron or positron. Example 1: the decay of carbon-14: •The Greek letter v is the symbol for neutrino - another particle born in this process. The symbol means antineutrino. •The nucleus still has 14 nucleons, but it has one more proton and one fewer neutron. •This decay is an example of an interaction that proceeds via the weak nuclear force. •The electron in beta decay is not an orbital electron; it is created in the decay. •The fundamental process is a neutron decaying to a proton, electron, and neutrino: n p e •The need for a particle such as the neutrino was discovered through analysis of energy and momentum conservation in beta decay – it could not be a twoparticle decay. •Neutrinos are notoriously difficult to detect, as they interact only weakly, and direct evidence for their existence was not available until more than 20 years had passed. Example 2: Beta decay can also occur where the nucleus emits a positron rather than an electron: Example 3: A nucleus can capture one of its inner electrons: Gamma Decay Gamma rays are very high-energy photons. They are emitted when a nucleus decays from an excited state to a lower state, just as photons are emitted by electrons returning to a lower state. Conservation of Nucleon Number and Other Conservation Laws A new law that is evident by studying radioactive decay is that the total number of nucleons cannot change. Decay Series A decay series occurs when one radioactive isotope decays to another radioactive isotope, which decays to another, and so on. This allows the creation of nuclei that otherwise would not exist in nature. Half-Life and Rate of Decay Nuclear decay is a random process; the decay of any nucleus is not influenced by the decay of any other. Therefore, the number of decays in a short time interval is proportional to the number of nuclei present and to the time: using calculus N N N e t t t 0 N 0 λ - decay constant (characteristic of that particular nuclide) N / t N ln 2 N T1 2 ln 2 1.0 10 22 7 5730 yr 3.156 10 s / yr 3.8 1010 The half-life is the time it takes for half the nuclei in a given sample to decay. It is related to the decay constant: 1 Radioactive Dating Radioactive dating can be done by analyzing the fraction of carbon in organic material that is carbon-14. The ratio of carbon-14 to carbon-12 in the atmosphere has been roughly constant over thousands of years. This ratio is about 1.3x10-12. N0 C N C N C N C 1.3 10 14 6 12 0 6 14 0 6 12 6 12 A living plant or tree will be constantly exchanging carbon with the atmosphere, and will have the same carbon ratio in its tissues. When the plant dies, this exchange stops. Carbon-14 has a half-life of about 5730 years; it gradually decays away and becomes a smaller and smaller fraction of the total carbon in the plant tissue. This fraction can be measured, and the age of the tissue deduced. Objects older than about 60,000 years cannot be dated this way – there is too little carbon-14 left. Other isotopes are useful for geologic time scale dating. Uranium-238 has a half-life of 4.5 x 109 years, and has been used to date the oldest rocks on Earth as about 4 billion years old. Ex: The mass of carbon in an animal bone fragment found in an archeological site is 200 g. If the bone registers an activity 16 decays/s, what is its age? m 200 g N t 16 s N0 1 m C N C 14 6 1.3 10 12 6 N 12 T 1 5730 y 2 12 6 C 12.0 g N A 6.02 10 C m C m 14 6 12 6 C 1.3 10 14 0 6 N 12 N t 0 N 0 N C N 12 6 C 1.3 10 12 6 12 m A NA m 1.00 10 25 1.3 1013 ln 2 m 1.3 10 12 N A 50 s 1 T1 2 23 t ? N t N t 0 e t N t 0 T12 N t 0 t ln ln N t ln 2 N t 1 5730 y 50s 1 3 t ln 9 . 4 10 yr 1 ln 2 16s Stability and Tunneling When a nucleus decays through alpha emission, energy is released. Question: Why is it that these nuclei do not decay immediately? Answer: Although energy is released in the decay, there is still an energy barrier The alpha particle can escape through the barrier - quantum mechanical phenomenon called tunneling. As stated in the Heisenberg uncertainty principle, energy conservation can be violated as long as the violation does not last too long: The higher the energy barrier, the less time the alpha particle has to get through it, and the less likely that is to happen. This accounts for the extremely wide variation in half-lives for alpha decay.