PHYS 221 Lecture Kevin Ralphs 29 July 2013

Overview Exam Information Nuclear Physics Structure of the Nucleus Nuclear Reactions

Exam Information The final will be on Wednesday 31 July at 8:00 am A final review session will be conducted tomorrow at the same time and location as your recitations There are prior year finals posted on the PHYS 221 web site already, although I am trying to pull together another one to help you guys prepare The questions in the lecture slides probably give the best idea of the kinds of questions that will be asked. I will have hand worked solutions for those before this evening

Exam Information There will be 12 questions on the exam 2/3 of the questions will require calculations with formulas 2 of those will require the use of two formulas to get the answer The rest will be conceptual questions that may require simple calculations dealing with notation I am writing it to take about an hour with you having two hours to take it

Nuclear Physics Structure of the Nucleus 𝑍 𝐴 𝑋 The nucleus of made of two types of particle called nucleons: protons and neutrons A nucleus is specified with the following notation 𝑍 𝐴 𝑋 Z: Atomic Number – Number of protons A: Mass Number – Number of nucleons X: Element Symbol Examples 2 3 𝐻𝑒 2 4 𝐻𝑒 2 6 𝐻𝑒 Nuclei with the same number of protons, but different number of neutrons are called isotopes

Nuclear Physics Structure of the Nucleus 𝑟= 𝑟 𝑜 𝐴 1/3 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= 𝑟 𝑜 𝐴 1/3

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 Binding Energy Conservation of Mass-Energy Conservation of Momentum Conservation of Electric Charge Conservation of Nucleon Number 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

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 loss of mass has to be accounted for with gained energy 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 𝑁 𝑡 = 𝑁 𝑜 𝑒 −𝜆𝑡 𝑇 1 2 = ln 2 𝜆 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 = 𝑁 𝑜 𝑒 −𝜆𝑡 𝑇 1 2 = ln 2 𝜆 𝑇 1 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

Nuclear Physics Nuclear Reactions 1 Ci =3.7× 10 10 decays/s 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× 10 10 decays/s 1 Bq =1 decays/s

Dose in rem = (dose in rads) x (RBE) 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)

Quiz Question At t = 0, 950 g of a radioactive material is present. Twenty-five years later it is found that only 23 g of the material remains. What is its half-life? 2.81 years 9.47 years 4.66 years 10.3 years 1.52 years

Quiz Question Which of the following forces is (most) crucial for holding a nucleus together? Electric force Magnetic force The strong force Friction Gravity