Nuclear Physics

This Lecture: Nuclear structure, Strong Force, Radioactivity

Previous lecture: More on Atomic PhysicsElectron Spin and Exclusion PrincipleEmission and absorption spectra for atoms with more electrons Lasers

FinalMon. May 12, 12:25-2:25, Ingraham B10

New material: Particle in a box (Ch 40.4-5, 40.10)Hydrogen Atom quantum numbers, wave functions, probability(Ch 41.1-2)Electron Spin and Pauli exclusion principle (Ch 41.3-6)Lasers (Ch 41.8)Nuclear Physics: nuclear structure (Ch 42.1-3) and Radioactivity (Ch 42.5-7) MTE1-3 material (see past lecture notes and Exam web page)

Final Exam

• Final is 25% of final grade• In the final about 30% on new material, rest is

material in MTE1-3• 2 sheets allowed (HAND WRITTEN!)

Notify NOW any potential and VERY serious problem you have with this time

From last lecture: building atoms

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http://eclipse.gsfc.nasa.gov/SEhelp/ApolloLaser.html

Measuring the Moon-Earth distance with a laser

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NASA Apollo Laser Ranging Experiment: begun 25 yrs ago when Apollo 11 deployed a reflector in the Sea of tranquillity

Lunar ranging involves sending a laser beam through an optical telescope

At the Moon's surface the beam is roughly four miles wide

Highly collimated beam from stimulated emission, almost monochromatic

Neutron

Proton

Nuclear Structure

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Size of electron orbit is 5x10-11 m

Nucleus is 5,000 times smaller than the atom!

Neutron: zero charge (neutral)Proton: positive charge

(equal and opposite to electron)

Nucleus size ~10-14 m

Spacing betweennucleons 10-15 m1 fermi = 10-15m

Nucleons are not building blocks of matter

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• We now know thatprotons and neutronsare not fundamentalparticles.

• They are composedof quarks, whichinteract byexchanging gluons.

• Zero net charge -># protons in nucleus = # electrons orbiting.

• The number of electrons determines which element.– 1 electron → Hydrogen– 2 electrons → Helium– 6 electrons → Carbon

• How many neutrons?Li63

A

Z

Nucleus =Protons+ Neutronsnucleons

A=N+Z

Notation for nuclei

8A = # of nucleons=atomic mass number

Z = atomic number (# of protons or # of electrons)N = # of neutrons

•Carbon has 6 electrons (Z=6)•Zero net charge => 6 protons in

the nucleus.•Most common form of carbon

has 6 neutrons in the nucleus.

Example: Carbon

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C12

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Another form of Carbon has6 protons, 8 neutrons in the nucleus. This is 14C.

different mass

Tritum is an isotope of hydrogen with threetotal nucleons: two neutrons and oneproton. How many electrons does it have?

A. OneB. TwoC. Three

Quiz

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Isotopes of Hydrogen

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D2O has 20 nucleons and H2O has 18. So heavy water is heavier than water by (20-18)/18= 10%Number of nucleons determines the mass of atoms

Women Nobel PrizesThe only 2 female Nobel Prizes in Nuclear

Physics! (we need more!!!)

Maria Goeppert-Mayer 1963 Shell Model of Nucleus

1903 Marie Curie (with Pierre)in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel

• So what holds the nucleus together?

• Coulomb force? Gravity?

• Coulomb force only acts oncharged particles– Repulsive between protons,

and doesn’t affect neutrons at all.

• Gravitational force is much too weak.Showed before that gravitational force ismuch weaker than Coulomb force.

Nuclear Force (Strong Interaction)

Gravitational effects are negligible at atomic and nuclear level

• New attractive force.• Dramatically stronger than Coulomb force at

short distances.• Doesn’t depend on sign of charge.• This is the ‘strong interaction’, one of the four

fundamental interactions:

electromagnetic interactionstrong interactionweak interactiongravitational interaction

The Strong Nuclear Force

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The Coulomb attraction energy (~10 eV) binds thehydrogen atom together.

Protons in nucleus are 50,000 times closer togetherthan electron and proton in hydrogen atom.

Attractive energy must be larger than the Coulomb repulsion, so nuclear binding energies are at least

A. 5000 eV

B. 500,000 eV

C. 5,000,000 eV

Experimentally, nucleons bound by ~ 8 MeV / nucleon(8,000,000 eV / nucleon)

Estimating the Strong Force

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=0.5 MeV

• It is convenient to use atomic mass units, u, toexpress masses– 1 u = 1.660 539 x 10-27 kg– mass of one atom of 12C = 12 u ⇒ 1 u = 1.66 x 10-27 kg

• Mass can also be expressed in MeV/c2

– From rest energy of a particle ER = mc2

– 1 u = 931.494 MeV/c2

A convenient unit of Mass

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• Experimentally,– radius of nucleus r = roA1/3 (A=mass # = # nucleons)– says that volume V proportional to A.– says that nucleon density is constant

• Nuclear matter is ~ incompressible– More nucleons -> larger nucleus– Nucleons ~ same distance apart in all nuclei

Nuclear density

r0=1.2 fm

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ρnuc =mV

=Au43πr3

=Au

43πr0

3A=

u43πr0

3=1.66 ×10−27kg43π (1.2 ×10−15)

= 2.3×1017kg /m3

Nuclear Binding Energy

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mp=1.6726 x 10-27kg/1.66 x 10-27 kg/u= 1.0078u

2 protons &2 neutrons

• Mass of nucleus is less thanmass of isolated constituents!

• Helium nucleus energy < energy isolated nucleons.

Arises from E=mc2

Equivalence of massand energy.

Heliumnucleus

• Energy difference isbinding energy.

1.0078u

1.0078u

mn=1.6749 x 10-27kg/1.66 x 10-27 kg/u= 1.0087u

Binding energy

• Binding energy: energy you would need to supply to disassemble the nucleus into nucleons: Ebinding = (Zmp+Nmn-mnucleus)c2

• Example: deuteron = 1 proton and 1 neutron bounded together• Free particles: mp = 1.0078u, mn= 1.0087u, mp+mn=2.01649u• Atomic mass of deuteron 2H = 2.01410u• Binding energy =0.002388u x 931.494MeV/u = 2.224MeV• Binding energy/nucleon = 2.224/2

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Nucles massmnucleus

Mass of Z protons and N neutrons: Zmp + Nmn

Experiment says:mnucleus < Zmp + Nmn

Binding energy of different nuclei

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For nuclei smaller than Fe the binding energy increases with A: you have to supply more energy to win nuclear bounds.Fe with A = 56 nucleons has 8.79 MeV/nucleon (amount of energy to remove one nucleon from Fe nuclei)Peaks at 4He, 12C and 16O because these nuclei are more tightly bond.Nuclear force is short range: as nucleus grows nuclear bonds are saturated and nuclei interact only with neighbors => Ebinding almost constant

Binding energy released: fusion and fission

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Combine p and n to form 4He

7MeV/nucleonbinding energy is released

smaller energyis released in fission of a heavy nuclei into 2 lighter nuclei

fusionof 2 light nuclei ina heavier one

Stable and Unstable Isotopes

Isotope = same ZIsotone = same NIsobar = same A

Stability of nuclei• Dots: naturally occurring isotopes.• Shaded region: isotopes created in

the laboratory.• Light nuclei are most stable if N=Z• Heavy nuclei are most stable if N>Z• As # of p increases more neutrons are

needed to keep nucleus stable• No nuclei are stable for Z>83

Radioactivity

• Discovered by Becquerel in 1896 • spontaneous emission of radiation as result of

decay or disintegration of unstable nuclei• Unstable nuclei can decay by emitting some

form of energy• Three different types of decay observed:

Alpha decay ⇒ emission of 4He nuclei (2p+2n)Beta decay⇒ electrons and its anti-particle (positron)Gamma decay⇒ high energy photons

Penetrating power of radiation

• Alpha radiation barely penetrate a piece of paper (but dangerous!)

• Beta radiation can penetrate a few mm of Al• Gamma radiation can penetrate several cm of

lead

Is the radiation charged?

• Alpha radiation positively charged• Beta radiation negatively charged• Gamma radiation uncharged

Decay: an exponential decrease

• 232Th has a half-life t1/2=14 x109 yr

• Sample initially contains: N0 = 106 232Th atoms

• Every 14 billion years, the number of 232Th nuclei goes down by a factor of two.

N0

N0/2N0/4

N0/8

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N(t1/ 2) =N0

2= N0e

−rt1/2

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N(t) = N0e−rt

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−rt1/ 2 = ln(1/2)⇒ r = ln2 / t1/ 2

The Decay Rate• probability that a nucleus decays during Δt

• number of decays (decrease)= NxProb=rNΔt = =-ΔN N=number of independent nuclei

Constant of proportionality r = decay rate (in s-1)

The number of decays per second is the activity

# radioactive nuclei at time t

# rad. nuclei at t=0

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Prob(in Δt) = rΔt

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ΔNΔt

= −rN

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N(t) = N0e−rt

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R =ΔNΔt

= rN

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τ =1r

time constant