PHYS 221 Recitation Kevin Ralphs Week 14 Overview • Nuclear Physics – Structure of the Nucleus – Nuclear Reactions Nuclear Physics • Structure of the Nucleus – The nucleus of made of two types of particle called nucleons: protons and neutrons – A nucleus is specified with the following notation 𝐴 𝑍𝑋 Z: Atomic Number – Number of protons A: Mass Number – Number of nucleons X: Element Symbol • Examples 6 3 4 2𝐻𝑒 2𝐻𝑒 2𝐻𝑒 • Nuclei with the same number of protons, but different number of neutrons are called isotopes Nuclear Physics • Structure of the Nucleus – Atomic Mass • The atomic mass of an atom is the mass of the nucleons plus the mass of the electrons • The periodic table records average values of the atomic mass weighted by the natural abundance of the isotopes – Size of the Nucleus • Scattering experiments have shown that nuclei are approximately spherical with the following approximate radius 𝑟 = 𝑟𝑜 𝐴1/3 Nuclear Physics • Structure of the Nucleus – Forces within the Nucleus • Electric Forces due to repulsion between protons • The strong nuclear force is an attractive force that binds nucleons together, but only acts over short distances – Stability of the Nucleus • The above forces work together to create an equilibrium within the nucleus • Although neutrons add stability by spacing the protons further apart to counterbalance their electric repulsion, adding too many create an unstable nucleus that will split Nuclear Physics • Nuclear Reactions – Radioactive decay is a spontaneous process where a nuclei splits into two or more particles – The original nucleus is referred to as the parent nucleus with the final result being called decay products Nuclear Physics • Nuclear Reactions – There are 3 kinds of decay that we will concern ourselves with: • Alpha Particles – An alpha particle is a cluster of 2 protons and 2 neutrons, essentially a helium nuclei – In this type of decay, the alpha particle is ejected with the appropriate numbers adjusted in the daughter nucleus • Beta Particles – Beta decay occurs when a proton turns into a neutron or the other way around – When this happens, additional particles are kicked out to conserve charge and some other properties that are beyond the scope of our class • Gamma Decay – Nucleons can become excited and emit photons, gamma rays, when they return to their ground state just like electrons Nuclear Physics • Nuclear Reactions – Conservation Rules • • • • Conservation of Mass-Energy Conservation of Momentum Conservation of Electric Charge Conservation of Nucleon Number Nuclear Physics • Nuclear Reactions – Binding Energy • If we were to total up the individual masses of the nucleons and compare this to the atomic mass of them together, we would notice that some of the mass is missing • We should expect this: The nucleus is stable so it should be a lower energy system than the individual nucleons • Due to relativity, we know that this lower energy has to be accounted for with lower mass • Note that when doing binding energy calculation, you have to carry many digits since the change is mass is very small Nuclear Physics • Nuclear Reactions – Half-life • We cannot predict when a decay process will occur for a specific nucleus, but if there are many nuclei then we can estimate the average number of reactions that should occur in a span of time • It would make sense if the likelihood of a decay event (which is essentially the rate of decay) was proportional to the amount of nuclei that could possibly decay which suggests an exponential kind of decay 𝑁 𝑡 = 𝑁𝑜 𝑒 −𝜆𝑡 𝑇1 2 ln 2 = 𝜆 • 𝑇1 2 is the half-life of the element and is the period of time where we would expect that nearly half of the material had decayed • Note that N(t) is the number of nuclei left not that number that have decayed. Likewise No is the number at t=0. Nuclear Physics • Nuclear Reactions – Measuring Radiation • The “strength” of a radioactive sample is called its activity and describe how many decay events occur in a span of time • Two common units of activity are the curie (Ci) and the becquerel (Bq) 1 Ci = 3.7 × 1010 decays/s 1 Bq = 1 decays/s Nuclear Physics • Nuclear Radiation – Measuring Radiation • Radiation can also be measured in the amount of energy absorbed weighted by the amount of material that absorbed it • Dosage can be measure in rems or rads • Rads give the raw energy absorbed 1 𝑟𝑎𝑑 = 0.01 𝐽 𝑘𝑔 • The same dosage in rads can have different effects on biological material, so the rem accounts for that Dose in rem = (dose in rads) x (RBE)