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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 to½ its final charge?

Which circuit takes the least amount of time to charge the capacitor to½ 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/c2

27 2u 1.66 10 kg 931.5 MeV / c •Distances in nuclear physics are typically around 10-15m = 1 fm•Occasionally called a Fermi, usually called a femtometer

151 fm 10 m

•Einstein’s most famous equation is important in nuclear science:

2mcE

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 informationB) Zero, insufficient informationC) Insufficient information, zeroD) Zero, Zero

Name Symbol ChargeSpin Mass (MeV/c2) Proton p +e ½ 938Anti-Proton p –e ½ 938Electron e- –e ½ 0.511positron e+ +e ½ 0.511

•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

A Z N •We normally describe nuclei by specifying which element it is, its Z – value, and its A - value 56

26 FeAZ

Which two pieces of information are redundant?A) Fe and 56 B) Fe and 26 C) 56 and

2656 Fe•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

d

Zeek

r

qkqmv ))(2(

221

2

•It turns out that nuclei have sizes on the order of femtometers, and most nuclei are spherical.

3/1)2.1( Afmr

Binding Energy of a NucleusFactors 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 Nuclei42 He

Well-bound

5626 Fe

MostWell-bound

23892 U

High energy

•The most stable – lowest energy nuclei – have moderate numbers of nucleons, and a little more than half neutrons

•4He 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!)

•Eb(MeV)=(Zmp+Nmn-MA) x 931.494MeV/amu

•Binding energy per nucleon is the binding energy divided by the mass number

Binding Energy

Binding Energy

•Lithium 7: 3 protons, 3 electrons and 4 neutrons, mass of 7.016003

•Binding energy=0.042132c2=39.246MeV•Binding energy per nucleon=5.6MeV

•Binding energy =(3*1.007825)c2+4*(1.008665)c2-(7.016003)c2

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,

Ndt

dN dtN

dN

toeNN

•This means that the number of nuclei decays exponentially

to eNR •The rate

•The half-life (the time it takes for ½ the nuclei to decay)

2ln

2/1 T

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

toeNN