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Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open. The values of the emf, resistance R, and the capacitance C for each of the circuits are circuit 1: 18 V, R = 3, C = 1 µF circuit 2: 18 V, R = 6, C = 9 µF circuit 3: 12 V, R = 1, C = 7 µF circuit 4: 10 V, R = 5, C = 7 µF Which circuit has the largest current right after the switch is closed? Which circuit takes the longest time to charge the capacitor to ½ its final charge? Which circuit takes the least amount of time to charge the capacitor to ½ its final charge?

Units in Nuclear Physics Different units are used to describe masses in Nuclear physics An atomic mass unit (u) is particularly convenient For particle physicists, it is common to use units of MeV/c 2 Distances in nuclear physics are typically around m = 1 fm Occasionally called a Fermi, usually called a femtometer Einstein’s most famous equation is important in nuclear science:

Antiparticles For every particle there is an antiparticle same mass and spin, opposite charge Name is usually denoted by putting the word anti- in front of it Symbol is the same with either charge reversed or a bar on it For some particles, the antiparticle is the same as the particle The eta is its own anti-particle. What is its mass and charge? A)Insufficient information, insufficient information B)Zero, insufficient information C)Insufficient information, zero D)Zero, Zero Name SymbolChargeSpinMass (MeV/c 2 ) Proton p +e ½ 938 Anti-Proton p –e ½938 Electron e - –e ½0.511 positron e + +e ½0.511

Three quantities describe a nucleus Nuclei The number of protons is called the atomic number Z The number of neutrons is called N The number of nucleons is called the atomic mass number A We normally describe nuclei by specifying which element it is, its Z – value, and its A - value AZAZ Which two pieces of information are redundant? A)Fe and 56B) Fe and 26C) 56 and 26 Hence, the Z – value is often omitted

Forces in Nuclei There are electromagnetic interactions among the protons and neutrons The only one important for our purposes is the repulsion of protons There is an additional force, called the nuclear force, the strong nuclear force, or the strong force It is attractive – protons and neutrons attract each other It is very strong – much stronger than electric forces It is short-range – only adjacent nucleons affect each other The strong force does not depend on charge!

Sizes in Nuclei Thanks to scattering experiments (practice exam II, the conservation of energy problem), we have an upper bound on the size of a nucleus It turns out that nuclei have sizes on the order of femtometers, and most nuclei are spherical.

Binding Energy of a Nucleus Factors that go into figuring out how stable a nucleus is Strong nuclear force – each nucleon that is added gets to “bind” to its neighbor Electric Force – protons repel each other This force accumulates as you add more and more protons Large nuclei don’t like having too many protons Very large nuclei become unstable Quantum Mechanics – the Pauli Exclusion Principle Because the nucleons are spin ½, you can fit two into every state Prefer even number of protons and neutrons Prefer roughly equal numbers of the two (two nucleons of the same spin can’t occupy the same space)

Best and Worst Bound Nuclei Well- bound Most Well- bound High energy The most stable – lowest energy nuclei – have moderate numbers of nucleons, and a little more than half neutrons 4 He is a very well bound nucleus Very heavy nuclei – like Uranium – tend to also have lots of energy

Trends in Stability Because of the forces involved, there are tends in stability. For light particles, when the number of protons equals the number of neutrons, the nuclei are more stable For larger nuclei, a higher proportion of neutrons is required. The most stable nuclei obey magic numbers: Z or N=2,8,20,28,50,82 This is due to shell filling just like with electrons

Binding Energy and mass The mass of a nuclei is less than the mass of its parts. There must exist a binding energy, i.e., an energy keeping the nuclei together. The binding energy is so large that there is a measurable mass difference. (Unlike binding due to other forces!) E b (MeV)=(Zm p +Nm n -M A ) x MeV/amu Binding energy per nucleon is the binding energy divided by the mass number

Binding Energy

Lithium 7: 3 protons, 3 electrons and 4 neutrons, mass of Binding energy= c 2 =39.246MeV Binding energy per nucleon=5.6MeV Binding energy =(3* )c 2 +4*( )c 2 -( )c 2

Radioactivity Some substances will decay naturally and emit particles There are multiple types of radioactive decay: alpha, beta and gamma. Alpha particles barely penetrate a sheet of paper Beta particles penetrate a few millimeters of aluminum Gamma particles penetrate several centimeters of lead! The rate at which a particular decay process occurs in a radioactive sample is proportional to the number of radioactive nuclei present Each atom has a probability to decay irregardless of the other nuclei

Radioactivity If N is the number of the radioactive nuclei present then, This means that the number of nuclei decays exponentially The rate The half-life (the time it takes for ½ the nuclei to decay)

Radioactivity Starting with a pure sample of nuclide A which decays, what is the number of atoms of A as a function of time: