10-15 m
Physics 116
World’s largest popcorn ball
Session 38
Nuclei
Dec 2, 2011
www.thepopcornfactory.com/
R. J. Wilkes
Email: [email protected]
Announcements
•! Final exam is NOT droppable! Everyone must take the final.
•! Usual format. YOU must bring bubble sheet and pencil and
calculator.
•! Exam will be designed for 1 hr but you can take 2 hrs.
•! Final will be about 1/3 on material since exam 3, remainder covers
all material discussed during the course
•! Textbook sections skipped in previous exams will also be skipped
for the final. ONLY material covered in class (and not labelled
“cultural supplement” or equivalent) will be on the exam.
•! As usual we will have practice questions posted Weds next week,
and go over the practice questions in class next Friday.
Lecture Schedule
(to end of term)
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3
A bit more on atomic physics
•! Pauli exclusion principle (Wolfgang Pauli, Austria, c. 1925)
–! Only one electron in an atom can have any possible quantum state
(specific set of quantum numbers n, l, ml and ms )
–! Once a particular quantum state is occupied, other electrons are
excluded from that state
–! Exclusion principle applies to all fermions (particles with half-integer spin
angular momentum, in units of !): protons in nuclei obey same rules
Quantum rules for atomic electrons:
n = 1, 2, 3… principal quantum number, energy
level (n=1=“ground state”)
l = 0, 1, 2… (n-1) orbital angular momentum, in
units of ! (total of n states possible)
ml = -l … 0 … +l “magnetic quantum number”, zcomponent of L (total 2l+1 states)
ms = -1/2, +1/2 spin angular momentum, in units
of ! (only 2 states possible)
Hydrogen atom’s
electron levels:
2 in n=1 (l=0)
8 in n=2 (l=0,1)
18 in n=3 (l=0,1,2)
4
Periodic Table today: organizes elements by properties
and atomic weight
Yesterday
Z and A increase as you go across and down.
Elements in same column have similar properties.
http://www.molres.org/MRI_DownloadPT.html
Z
(# of protons)
A
(total n+p)
“Noble
gases”:
refuse to
mix with
other
elements!
(they have
electrons
filliing all
allowed
states)
“Rare earth”
Uranium is heaviest elements go
natural element
in here
(white numbers =
synthetic elements)
(Parenthesis means unstable element)
5
Nuclear (please, not “nuke-ular”!) physics
FYI: physics terminology
•! “Chemistry” = study of molecules as systems; size scale ~10-9 m
•! Atomic physics = study of atoms as systems – lasers, low
temperature states of matter; size scale ~10-10 m
•! Nuclear physics = study of atomic nuclei as systems – nuclear
reactions, radioactivity, properties of isotopes; size scale 10-15 m
•! Particle (“High Energy”) physics = study of “elementary” particles
as systems; size scale << 10-15 m (=1 femtometer [fm] or fermi)
–! recall: EP’s = things made when you smash nuclei with high energy
projectiles; not the same as “fundamental” particles like quarks
–! Why “high energy”? Recall de Broglie: ! = h / p !
•! high momentum (= high energy) means short wavelength
–! Use HE particles like microscopes, to study structure of particles
•! Energy scale corresponds to size scale (eV = electron volt)
–! Atoms ~ few eV, nuclei ~ few million eV, quarks ~ billions of eV
6
What holds nuclei together?
•! Recall basics of nuclear structure:
–! Nucleus = Z protons (Z=“atomic number”: 1=hydrogen, 2=helium…) and
N neutrons; Z + N = A (atomic mass number)
–! Protons have + charge: they repel each other via 1/r2 Coulomb’s Law
•! Remember nuclear size scale: incredibly small r = huge force!
A = atomic mass number = total number of protons + neutrons
Z = atomic number, # of protons (determines which element it is)
N = A – Z =number of neutrons (determines which isotope it is)
Isotopes have same Z but different A’s.
Example: 6C12 = “carbon-12”, has 6 protons (like all carbon) and 6
neutrons (unlike “carbon-14”, which has 8 neutrons)
–! Nuclear “glue” holds protons and neutrons into nuclei
•! “strong nuclear force” is carried by particle called (what else?) gluon
–! But strong force has limited range: not infinite like electromagnetic force
•! Nucleus is like a compressed spring, held together by a rope
–! Cut the rope, and stored “binding energy” is released
•! Energy taken up to bind nucleus is reflected in mass
E=mc2 + conservation of energy
7
Radioactivity
•! H. Becquerel (1896): discovered radioactivity
–! Sample of mineral containing uranium fogged photographic plate
•! Marie Walenska-Curie (“Madame Curie”, c. 1900): with P. Curie,
made many important early discoveries (Nobel Prize 1903)
–! “Radiation” from radioactive elements takes 3 main forms
•! Alpha rays are positively charged, heavy (actually: helium nuclei)
–! Cannot penetrate much matter (piece of paper stops them)
•! Beta rays are negatively* charged, very low mass (electrons)
–! More penetrating than alphas, but stopped by a thin lead sheet
•! Gamma rays are uncharged, massless (high energy photons)
–! Able to penetrate even thick lead sheets
–! Later (1932) another form was identified: neutrons
•! Uncharged, so not subject to electrical forces: can percolate
through shielding for a long distance (dangerous: hard to stop!)
–! Neutrons decay to proton + electron + neutrino, mean life ~ 15 min
–! All these particles can be produced by radioactive decay of nuclei
* Nuclei can also emit anti-electrons = positrons, + charge
8
Binding energy curve
•! The whole is not equal to the sum of its parts !
–! Mass of helium nucleus (2p+2n) is less than 2*Mproton + 2*Mneutron
•! Difference = binding energy (stored energy)
•! Fuse p’s and n’s to make He, and energy is released: nuclear fusion
–! Mass of uranium nucleus is more than sum of its p’s and n’s
•! Break uranium nucleus into lighter nuclei and E is released: nuclear
fission
–! Iron nucleus has minimum binding energy per particle: most stable
Energy of
an isolated
proton
Energy of proton
bound inside nucleus
of mass number A
Energy is released when heavy nucleus
is broken up, or light nuclei are fused
Uranium
Atomic mass number, A
9
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•! Every 10 sec, 1% of the
survivors decay
•! Rate of decay is constant
per nucleus, but number
of decays per second
(Geiger counter ticks/sec)
drops because population
diminishes!
•! This is an example of
"exponential behavior“:
applies to many different
phenomena
Statistics for this example:
•! half-life = 690 sec
= time to drop to 500,000
•! avg lifetime = 1000 sec.
(Longer than half-life,
because a few nuclei remain
for a long time: distribution
has a "long tail")
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12/2/11
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Examples of radioactive decay processes
•! Standard way to write isotopes: ZElementA
•! Uranium alpha decay: 92 U238 ! 90Th234 + #!
–! Remember, # = 2He4
–! Notice the A’s and Z’s balance on both sides of the equation
•! U loses 2 from Z and 4 from A: becomes thorium
–! However, exact masses don’t add up: some goes into KE of the #!
MU =238.051 MeV, MTh = 234.044 MeV, Ma = 4.002 MeV
U nucleus is heavier than sum of thorium nucleus and alpha
•! Carbon-14 beta decay: 6 C14 ! 7N14 + $
–! This is an example of weak nuclear force in action
•! Neutron turns into a proton by emitting an electron
–! More about this process later!
•! carbon gains 1 in Z, A stays the same: becomes nitrogen
–! Electron has KE, which carries away some energy
–! “invisible” neutrinos carry away more energy
14
Describing radioactive decay rates
•! Average (mean) lifetime = just what it says
–! Watch a million nuclei and find the average time to decay
–! Mean lifetime = , “decay constant” =
–! Nuclei decay at random times according to an “exponential law”:
the number remaining at time t is given by
•! Half-life T1/2 = time for 50% of nuclei in a sample to decay
–! So
•! Decay rate
Initial decay rate:
- sign means: losing nuclei!
= decay rate at time t
15
Example
•! Decay constant of radon* (Rn) is 0.181 days-1
•! What is Rn’s mean lifetime?
•! What is the half-life?
*Rn is produced in the decay of
uranium, which is a common
elementt – eg, in granite (or
concrete made from granite).
Because it is a noble gas, Rn
percolates out and gets into the air.
Unventilated basements can be
dangerous!!
•! What is decay rate for a sample of 0.001 mole (9 grams) of Rn ?
–! Note: this is 1.2! 1015 becquerel (Bq) activity (1Bq = 1 count/sec)
–! Older unit of activity: curie (Ci) = 3.7 ! 1010 Bq, so this would be
32,000 Ci, a huge amount of radioactive material!
16
Radioactivity
•! Table of isotopes shows all known varieties of all elements
Increasing N
A=Z+N
Increasing Z
Line of stability:
Stable isotopes have Z and A about equal
Other isotopes undergo radioactive decay
Isotope = varieties of the same element (Z) with different numbers of
neutrons (so, different values of A)
17