Physics 116 Worlds largest popcorn ball Session 38 Nuclei Dec 2, - - PowerPoint PPT Presentation

• R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Session 38

Nuclei

Dec 2, 2011

10-15 m

www.thepopcornfactory.com/

World’s largest popcorn ball

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.

3

Lecture Schedule

(to end of term)

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4

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”, z- component of L (total 2l+1 states) ms = -1/2, +1/2 spin angular momentum, in units

• f (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)

5

Periodic Table today: organizes elements by properties and atomic weight

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 A

“Rare earth” elements go in here

(Parenthesis means unstable element) Uranium is heaviest natural element (white numbers = synthetic elements) “Noble gases”: refuse to mix with

• ther

elements! (they have electrons filliing all allowed states)

(# of protons) (total n+p)

Yesterday

6

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

7

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!

– 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

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)

8

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

9

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 is released when heavy nucleus is broken up, or light nuclei are fused

Energy of an isolated proton Energy of proton bound inside nucleus

• f mass number A

Atomic mass number, A Uranium

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• Every 10 sec, 1% of the

survivors decay

• Rate of decay is constant

per nucleus, but number

• f 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.

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More than you need to know

14

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

15

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
• sign means: losing nuclei!

Initial decay rate: = decay rate at time t

Example

• Decay constant of radon* (Rn) is 0.181 days-1
• What is Rn’s mean lifetime?
• What is the half-life?
• 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

*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!!

17

Radioactivity

• Table of isotopes shows all known varieties of all elements

Increasing N Increasing Z Line of stability: Stable isotopes have Z and A about equal A = Z + N Other isotopes undergo radioactive decay

Isotope = varieties of the same element (Z) with different numbers of neutrons (so, different values of A)