Transcript Lecture #14 03/17/05

Announcements
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:
circuit 3:
18 V, R = 6 , C = 9 µF
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/c2
u  1.66 10
27
kg  931.5 MeV / c
2
•Distances in nuclear physics are typically around 10-15m = 1 fm
•Occasionally called a Fermi, usually called a femtometer
1 fm  10
15
m
•Einstein’s most famous equation is important in nuclear science:
E  mc
2
Antiparticles
•For every particle there is an antiparticle
•same mass and spin, opposite charge
•For some particles, the antiparticle is the same as the particle
•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
Name
Symbol Charge Spin Mass (MeV/c2)
Proton
p
+e
½
938
Anti-Proton
p
–e
½
938
Electron
e–e
½
0.511
positron
e+
+e
½
0.511
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
Nuclei
•Three quantities describe a nucleus
•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
A
56
Z
26 Fe
Which two pieces of information are redundant?
A) Fe and 56
B) Fe and 26
C) 56 and 26
•Hence, the Z – value is often
omitted
56
Fe
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
mv 2 kq1q2 k (2e)( Ze)


2
r
d
•It turns out that nuclei have sizes on the order of femtometers, and
most nuclei are spherical.
r  (1.2 fm) A1/ 3
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
•Quantum Mechanics – the Pauli Exclusion Principle
•(two nucleons of the same spin
can’t occupy the same space)
•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
•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
Best and Worst Bound Nuclei
4
2
He
Wellbound
56
26
Fe
Most
Wellbound
238
92
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 =(3*1.007825)c2+4*(1.008665)c2-(7.016003)c2
•Binding energy=0.042132c2=39.246MeV
•Binding energy per nucleon=5.6MeV
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,
dN
 N
dt
dN
 dt
N
•This means that the number of nuclei decays exponentially
N  N o e  t
•The rate
R  N o e  t
•The half-life (the time it takes for ½ the nuclei to decay)
T1/ 2 
ln 2

Radioactivity
•Starting with a pure sample of nuclide A which decays, what
is the number of atoms of A as a function of time:
N  N o e  t