Dr. Bill Pezzaglia

Nuclear Physics

Updated: 2010May17

Modern Physics Series1

INCOMPLETE DRAFT

Nuclear Physics

A. Nuclear Structure

B. Nuclear Decay

C. Nuclear Reactions

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A. Nuclear Structure

1. Parts of the Atom

2. Isotopes

3. Nuclide Table

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1. Parts of Atom

• Electron orbit diameter approximately 10-10 m

• Nucleus size 10-15 m

• Nucleus made of Protons Neutrons

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2. Isotopes 5

21H

11H

31H

Isotopes have same atomic number (number of protons)

2b. Nomenclature 6

• Z: Atomic NumberNumber of ProtonsTells what is chemical “X”

• N: Neutron NumberNumber of Neutrons

• A: Mass NumberNumber of NucleonsA=Z+N

AZX

Don’t really need “Z”: You know Carbon 14 has 6 protons, because its carbon.

14C

2c. Atomic Mass 7

011.12)12(989.)00335.13(011.

• AMU: Atomic Mass UnitCarbon 12 is exactly 12 amu

• Or 1 mole of C12 is 12 grams

• Naturally occurring carbon• 98.9% C12 (12.00000 amu)• 1.1% C13 (13.00335 amu)

• Average:

3. Nuclide Table• G. Seaborg 1940

• Atomic number is on vertical axis, Neutron number on the horizontal

• Isotopes: same ZC12, C13

• Isotones: same NC14, N15, O16

• Isobars: same AC14, N14, O14

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Nuclide Table (Small Z) 9

Nuclide Table (BIG Z)10

B. Nuclear Decay

1. Activity

2. Decay Law

3. Modes (Alpha, Beta, Gamma)

4. Dosage

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1. Radioactivity

(a) Phenomena

• 1898 Term coined by Pierre & Marie Curie (radiation-active)

• 1896 Becquerel discovers radioactive emissions (“Becquerel Rays”) of uranium salts (using photographic plates)

(b) Units

• Activity: decays per second (emissions per second)

• new SI unit Bq=becquerels= decays per second

• Old Unit: Curie: 1 Ci = 3.7×1010 Bq (activity of 1 gram of radium 226)

(c) Decay Constant

• Activity is proportional to number of nuclei present “N”

• Activity = N

• Decay Constant “” is probability of decay per second.

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Antoine Henri Becquerel (1852-1908), 1903 Nobel Prize for discovery of radioactivity

2. Decay Law• 1902 Rutherford & Soddy realized that all

radioactive decays obeyed the same exponential decay law

• Half Life: time for half of sample to decay. It is related to decay constant :

•

• This “emination law” showed radioactive decay was not deterministic, but statistical (indeterminant) in nature.

)2(

2/1

Lnt

13

teNtN 0)(

3. Decay Modes

• Rutherford (1897) clarifies that there are two types of “Becquerel Rays”, alpha (which he identifies as a Helium nucleus), and beta which is 100x more penetrating.

• By emitting any of these, the element undergoes “transmutation” into another element.

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3. Decay Modes 15

3b. Beta Decay

• Beta particle is actually an electron, identified in 1897 by Thomson.

• Beta decay involves a “neutrino” (described by Enrico Fermi in 1930s)

• DISCUSSED IN CLASS

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3c. Gamma Decay

• “Gamma Rays” discovered 1900 by Villard (later identified as high energy photons, which were what Becquerel originally saw)

• For example: A beta+ (positron) which annihilates with beta- (electron) will create 2 gamma rays

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4. Dosage

Radiation does damage to tissue:• Dose: energy absorbed per mass

• New SI unit: Gray: 1 Gy = 1 Joule/ke• Old Unit: rad: 1 rad = 0.01 Gy

• RBE: Relative Biological Effectiveness• Gamma 1, Beta 1-2, Alpha 10-20

• Dose Equivalent:• Dose equiv = Dose x RBE• SI unit: sievert: 1 Sv = Gy x RBE• Old unit: rem: 1 rem = 0.01 Sv= rad x RBE

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C. Nuclear Reactions

1. Stability

2. Fission

3. Fusion

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1. Nuclear Stability(a) Binding Energy: the energy required to remove

one nucleon from the nucleus

The mass of an atom is LESS than the sum of its parts due to negative potential energy of nuclear force.

• Mass Defect: m=(Zmp+Nmn-matom)

• Binding Energy: BE=m(931.49 MeV/u)

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1b. Binding energy per nucleon

• Low Z: more nucleons means more nuclear force, hence more stable

• High Z: nuclear force is short range, big nuclei unstable

• Iron is most stable

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1c. Nuclear Force

• Aka “strong force”. This is what holds the protons together in a nucleus

•Nucleons attract each other

•Force is short range, hence big nuclei are unstable

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2. Nuclear Reactions

(a) Terms

• Q=(mass reactants-mass products)c2

• Efficiency: Q/(mass reactants)c2

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2b Fusion

• Combine two (or more) small nuclei to make a bigger, more stable, nuclei

• Fusion of 4 Hydrogen to Helium is how sun produces energy

• Fusion of 3 Helium to Carbon is how “red giants” create energy

• All elements up to iron in the universe were made this way inside of stars (“nucleosynthesis”).

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2c Fission

• Large, unstable nucleus is split into two (or more) smaller, more stable nuclei

• Fission can be induced by tossing a slow neutron at a nucleus.

• During fission, often 2 or more neutrons are released, which can create more fissions (chain reaction)

• Nuclear reactors generate power from fission of U235.

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3. Shell Model of Nucleus 26

3c. Shell Model

Note prediction of stable nuclei for Z=126 (not discovered yet!) [highest element so far is what?]

Nuclei with “magic” numbers of neutrons and protons are very stable:

2

Notes28

• Knight: does not cover “Q” is chap 30, although it appears in several problems. Certainly does not do the kinematics correctly to get the KE

References/Notes29

• Physics Today, Feb (1996) 21-26, “The Discovery of Radioactivity”