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)

!"#$%&

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

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)

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

other

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

of mass number A

Atomic mass number, A

Uranium

!"#$%"&'($)*+$,+)-./*+-"0#%1+2-%&3,,+!"#$%"&'($)*+$//.,)-")3,+$0)3-3,'04+53").-3,+%5+!"#$%&#'(()

60+"+,"12/3+%5+7,"*8+"+9$//$%0+:;<=+")%1,>+

•! *!%+"+,-,./+%5+-"#$%"&'(3+#3&"*+5%-+"0*+$0#$($#."/+0.&/3.,+$,+

,1"//+5%-+"0*+2"-'&./"-+23-$%#+%5+'13+7,"*?+@+,3&%0#8+

–! A7#3&"*8+B+,"13+5%-+"#/+,3&%0#+%5+'13>+0%C?+)%1%--%C?+*3"-+<D@@+

–! A7#3&"*8+$,+0%)+"E3&)3#+$5+,%13+%.0'!+0.&/3.,+&F%%,3,+)%+#3&"*+0%C+

•! G3&"*,+"-3+,#$'1'#$'#.+%5+%03+"0%)F3->+0%+H131%-*I+

–! 2%."-)#3&+'!)%4)$'5"/(+&%.0)3#+$0+"0*+'13+$0)3-("/+$,+1!%1%!6%#"-)

.%)("&1-')(,7'+7)%)"/+0.193-+%5+:+")%1,8>+1%-3+")%1,?+1%-3+#3&"*,+

JF$,+K$0#+%5+-"0#%1+93F"($%-+$,+&"//3#+"+*%,((%#)1!%5'((+7LM+A%$,,%0?+

@NO@P@O=D8+"0#+"22/$3,+$0+1"0*+%)F3-+2F30%130"+

•! !313193->+%0&3+"+0.&/3.,+#3&"*,?+$)+$,+0%+/%043-+.-"0$.1Q++

–! J"K30+%.)+%5+)F3+-.00$04R+0.193-+%5+&"0#$#")3,+5%-+#3&"*+

$,&,#,(0'(+C$)F+'13+

•! MMM:0/3,,+,%13+%)F3-+#3&"*+2-%&3,,+$,+&"8,#9+.-"0$.1+)%%Q+

@D+

L)"','&,+%5+-"#$%"&'(3+#3&"*+

•! !3&"//>+(."6(65+B+"+,$04/3+0.193-?+#3-$(3#+5-%1+"+/"-43+9%#*+

%5+#")"?+)F")+#3,&-$93,+,%13+53").-3+%5+)F3+:0%-')#")"+,3)+

–! S3"0+7"(3-"438+/$53'13+J"(4+%5+"+0.&/3.,+$,+"+.,35./+,)"','&+

–! T0%)F3-+$,+)F3+F"/5P/$53>+J@U;+B+'13+$)+)"K3,+5%-+0"-4+%5+0.&/3$+)%+#3&"*+

–! VW"12/3>+,)"-)+C$)F+@?DDD?DDD+-"#$%"&'(3+0.&/3$+C$)F+"(3-"43+/$53'13+

@DDD+,3&%0#,M++

•! L%+3"&F+,3&%0#?+"0*+0.&/3.,+F",+2-%9"9$/$)*+@U@DDD+%5+#3&"*$04+

–! X%-+"+@D+,3&%0#+$0)3-("/?+A7#3&"*8+B+@Y++PP+)F$,+13"0,>++

»! "Z3-+@D+,3&?+[[Y+%5+%-$4$0"/+0.&/3$+,.-($(3>+[[D?DDD+

»! "Z3-+;D+,3&?+[[Y+%5+[[Y+B+[OY+-31"$0+

»! "Z3-+<D+,3&?+[[Y+%5+[OY+B+[NY+-31"$0MMM3)&+

•! S"K3+"+4-"2F+%5+0.193-+%5+-31"$0$04+0.&/3$+(,+'13R+

@@+

+L.-($("/+&.-(3+•! \.193-+%5+0.&/3$+-31"$0$04+7.0#3&"*3#8+(,+'13>+

@;+

•! 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")

13"0+/$53'13+B+@DDD+,3&+

]"/5P/$53+B+^[D+,3&+

VW"12/3>+,.22%,3+#3&"*+2-%9"9$/$)*+B+DMDD@+23-+,3&%0#+

L)"-)+C$)F+"+1$//$%0+%5+)F3,3+0.&/3$R

!"#$%"&'(3+#3&"*+1")F+

•! !"#$%"&'(3+#3&"*+/"C++$;<$.))B+P!;)=):0'!')! ,().0')$'5"/)

5%#(."#.=)0"().0')(%-36%#)

)))))))))))))));>.?)@);A'B1>C.<"?)

•! D'"#)-,4'C6&')" @)E<!+

•! ]"/5P/$53+.@U;B+7/0;8"+B+DM^[<"!

•! _03+`.-$3+7`$8+$,+<MN+a+@D@D+#$,$0)34-"'%0,+23-+,3&%0#+

12/2/11 @<+

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 ! 7N

14 + $

–! 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)