Download - Nuclear Physics and Radioactivity - Princeton Universitygrothserver.princeton.edu/~groth/phys102s02/lectures/lecture_10.pdf · no lecture next Thursday! ... The strong force balances

25 Apr 2002 Physics 102 Lecture 10 1

Nuclear Physics and Radioactivity

Physics 102

25 April 2002

Lecture 10

Wilhelm RoentgenX-rays

Marie & Pierrre Curie Radioactivity

Ernest RutherfordNucleus

James ChadwickNeutron

From: http://www.th.physik.uni-frankfurt.de/~jr/portraits.html


Announcements

� This is the last lecture; no lecture next Thursday!

� The Final Exam will be Monday, May 20, at 7:30 pm inMcDonnell A02 (this room). Please arrive early.

� Make-up labs: Monday, May 6.

� Exam will cover all material from the term, with aboutmore weight on the material since the midterm. Theremay be a “lab” question and a “demo” question or two.

� Review sessions:� Individual preceptors will hold review sessions in addition

to their standard office hours over break.

� Also, May 16, 7:30 pm -- , McDonnell A02 (here).


The Nucleus

� An atomic nucleus contains Z protonsand N neutrons. Its atomic mass numberis A=Z+N.

� All atoms of the same elements havethe same number of protons (by definition),but various isotopes of an elements (with different N)often exist.

� Isotopes are writtenfor example:

XAZ

U23892He4

2 U23592


The sizes of things

❈A typical molecule is 10-9 meters

❇An atom is roughly 10-10 meters in diameter and has a binding energy of order eV (e.g., 13.6 eV for n=1 in H)

✮The nucleus has a diameter 10-14 to 10-15 meter and has a binding energy of ~10 MeV per nucleon

nucleus nucleon


The Strong Nuclear Force

� The strong nuclear force is a strong (duh!), short range(10-15 m) attractive force between nucleons.

� The strong force balances the repulsive electrostaticforce to hold nuclei together.

� When adding a proton to a large nucleus,� it is attracted to its nearest neighbors (a force independent

of the size of the nucleus) and

� repelled by the other protons (a force that increases withthe size of the nucleus)

� » there is a maximum stable nuclear size.


Let us call the radius of the nucleus and the mass of theproton . Which of the following expressions gives anenergy most closely associated with the strong force (e is thecharge on the electron and k is the electromagnetic constant).

rnmp

A. ke

rn

D. ke

rn

2

E. m cp2

B. m gp

C. X-rayshν


� A bound nucleus weighs less than the sum of its parts

� Two hydrogen atoms and two neutrons together havemass 4.0330u, but a helium atom is only 4.0026u.

� The “mass defect” is 0.0304u, and the “binding energy”is (∆m)c2=4.5x10-12 J=28.3 MeV or 7.1 MeV/nucleon.

Mass Defect


The Curve of Binding Energy

� We can plot the average binding energy per nucleonversus the number of nucleons

(8.7 MeV/nucleon)

(1 MeV/nucleon)

He42

H21

U23892

C126

Fe5626

O168

Bin

ding

ene

rgy/

nucl

eon→

Number of nucleons→

83209 Bi

Largest stablenuclei

Schematic


Radioactivity

� Three basic types of radioactive “decay” occur:� Alpha decay (emission of a helium nucleus)

� Beta decay (emission of electron or positron from nucleus)

� Gamma decay (emission of photon)

HeRnRa 42

22286

22688 +→

γ+→ AgAg 11047

*11047

ν++→ν++→

+

−

enp

epnν++→ −eXeI 13154

13153 only in nuclei

α β γ (multiply length by 10)

Penetration depth in lead

0.01mm 0. 1mm 100 mm


Decay of 238U

From Sears, Zemansk, Young, &Freedman “University Physics”


Lead and Bismuth are the endpoints

Found on the Web Elements site


And wemeasurepulses ofcurrent

Incidentionizingparticle

Breaksdowngas Geiger

counter

Radioactivity is everywhere!

The dose in REM = 100*(energy absorbed per mass)*RBE

A 1 MeV beta particle (RBE~1) into1kg of tissue at 100 counts/minutegives a dose of 0.8 mrem/year

Average dose of a US residentis 360 mrem/yr.

200 mrem/yr is from Radon,about 70 mrem/yr is fromman-made sources.

Correction here from 0.01 !


Decay products are charged

Geiger counter

Radioactivesource

Lead shield

Magnetic fieldout of pagebends particlesinto Geigercounter.

What is the sign of thedecay products?

N S

A. PositiveB. NegativeC. Not enough information to tell


X-rays from the lown orbits of high Zatoms

0.3 to 300 keVGamma rays fromnuclear transitions andradioactivity

0.3 MeV to 104 MeV

Visible light fromthe transitions oflow Z atoms.

~2 eV


Forces in Nature

Gravity

Electromagnetic

Weak

Strong

Electroweak

Relative strength

10-2 to 10-12

10-40

1

Can these forces be unified into a single picture?

If so, we would have a TOE: theory of everything!


Half-life and Radioactive Dating� Radioactive decays are spontaneous and individually

unpredictable (quantum events!).

� Given a collection of some radioactive element with N0

atoms, on average half of the atoms will decay in somecharacteristic time T1/2.

� If we know the original fraction of a radioactive isotope,then measuring the current fraction gives us the sample’sage. E.g., 14C has a 5730 yr half-life. Also, Rb and Srare used to date the Earth (age = 4.54 Billion years).

N N e t T== −−0

2 1 2ln / /


Let us imagine that we have an atom with 120nucleons each with a binding energy of 8 MeV. Thissplits into two nuclei each with 60 nucleons and eachwith a binding energy of 9 MeV.

A. The total binding energy after the split is largerand so there is a net increase in kinetic energy.

B. The total binding energy after the split is largerand so there is a net loss of kinetic energy.

C. This process is not possible because the bindingenergy cannot increase.


Nuclear Energy: Fission

� Heavy elements, when broken apart, yield binding energy.

� Neutrons can be used to induce these “fission” reactions.

� Heavier elements are more “neutron rich”: 235U has 143neutrons and 92 protons, compared with 8 and 8 foroxygen.

� Hence a typical fission reaction releases several neutrons,that can each induce another fission, etc, leading to a“chain reaction.”

n3KrBaUUn 10

9236

14156

23692

23592

10 ++→→+

01

92235

92236

54140

3894

012n U U Xe Sr n+ → → + +


The Atomic Bomb

� The Atomic Bomb is based on the fission of about 15 kgof (about a 3” diameter sphere). Each fissionreaction releases about 250 MeV of energy.

235 U


Power

� The fission reaction also powers much of the country.

� One drawback is that fission reactors use rare, expensivefuel (235U is only 0.3% of natural U) and leaveradioactive waste products.

Three Mile Island inPennsylvania.

There was a leak ofradioactive materialin 1979.


Technetium 99

� “Radioactive Tracer” for medical uses.

� Bone Scans, Cardiac Stress Tests, ...

� Molybdenum 99 is a fission product (reactors!).

� Technetium is attached to a drug that’s bound by thetissue under study.

� Take “photograph” in 142 keV gamma rays.

4299 66Mo Tc hours43

99 *→ + +−β ν

4399 142 6Tc Tc keV) hours*

4399→ +γ (

4399 210 000Tc Ru years44

99→ + +−β ν ,

Technetium Bone ScanJ. Wallis, M.D.

102 student afterstudying for final


The Sun: fusion reactor

� Fusing light elements together also releases bindingenergy!

� However, nuclei must be squeezed close enough toovercome electrostatic repulsion.

� The Sun gets its energy from fusing H to He.

UV , the n=3 ton=2 Balmer lineHα


� At Princeton Plasma PhysicsLab (and elsewhere), peopletry to recreate the conditions

in the Sun.

� If it can be made to work,fusion gives a very high energyyield from cheap, abundant fuel.

� So far, all fusion devices usemore energy than they yield.

� The reaction yields 17 MeV, or about 4 times as muchenergy per nucleon as fission.

Nuclear Energy: Fusion


Elementary particles

� Primarily in this course we have been concerned withprotons, neutrons, and electrons. The stuff of which weare made.

� There are many more “elementary particles” which wefind in Nature. A couple of weeks ago we showed thatmuons rained down on us from the upper atmosphere.

� The first “elementary particle” discovered was theelectron (1897), then the proton and neutron (1932)

� The Standard Model of Particle Physics can predict theproperties of these particles to amazing accuracy. This isone of the intellectual triumphs of the past 50 years.


The cloud chamber

A mist of alcohol is produced in the chamber.

An ionizing particle (beta) leaves a trail ofnucleating agents around which droplets form.We see the drops.


Tracks in a cloud chamber


The Constituents of Matter� All matter is made up of a small number of particles:

� six quarks (in three pairs: {u, d}, {c, s}, {t,b})� three charged leptons: e-, µ-, τ-

� three uncharged neutrinos� antiparticles for all of these.

� Only the lightest family ({u, d}, e, ν) are seen in ordinary matter.

� Baryons (p, n, …) are made up of three quarks.

� Mesons (pion,…) are made of quark-antiquark pairs.


The Origin of the Elements� The early Universe was very hot and dense: a stew of

isolated charged particles. After the first 100 seconds,about 25% of protons are fused into alpha particles, anda tiny fraction into deuterium, tritium, and lithium.

� Stars like our Sun fuse H into He; more massive starsfuse He into C, O, etc, up to Fe.

� More massive elements are formed in dense, neutron richenvironments (e.g., supernova explosions)

� “We are , billion year old carbon

… and we’ve got to get ourselves back to the garden”Joni Mitchell, 1970


Cosmology

� Using nuclear physics, we can predict the abundances ofthe light elements and the predictions match theobservations. This is amazing physics !amazing physics !

� We can look at the motions of galaxies--usingNewtonian mechanics-- and tell that most of the matterin the universe is of a sort of which we are unfamiliar.

� After accounting for the matter, we find that most of theenergy density in the universe is of a sort that will causethe expansion of the universe to accelerate and cool.

“This is the way the world endsNot with a bang but a whimper”

T.S.Eliot The HollowMen


Where have we been? Where are we going?We have traveled through all of physics from Galileo and

Newton to Maxwell, Einstein, Bohr, and Gell-Mann.We have seen that we can quantify Nature and predict the

outcome of experiments and that there are preciseprinciples that tell us how Nature acts. The technologicalfruits of the physics we have discussed define how youexperience life.

Building on the last three hundred years, physicists nowquantitatively address questions such as: What are thecontents and fate of the universe? Could elementaryparticles be manifestations of hidden dimensions?

Physics is dynamic, new questions continually arise: “There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.” -Hamlet

Download - Nuclear Physics and Radioactivity - Princeton Universitygrothserver.princeton.edu/~groth/phys102s02/lectures/lecture_10.pdf · no lecture next Thursday! ... The strong force balances

Top Related