The unleashed power of the atom has changed everything save our modes of thinking and we thus drift toward unparalleled catastrophe.

-Albert Einstein

Bronze Buddha at Hiroshima

Nuclear Powe

Nuclear Weapons

Nuclear PowerIs it Green & Safe?

Nuclear Waste250,000 tons of Spent Fuel10,000 tons made per year

Health Effects of Ionizing Radiation

Radiocarbon Dating

Atomic Notation

AZ X

Atomic Mass NumberA = # protons + neutrons

Atomic #

1 3 2381 1 92H, H, U

Atomic NumberZ = # protons

Neutron Number NN = # neutronsN = A - Z

Atomic Mass Units1u = 1/12 mass of Carbon-12

27 21 1.6605 10 931.5 /u x kg MeV c−= =

238.0508u 234.0436u 4.0026u

( )238.0508 234.0436 4.0026 0.0046m u uΔ = − − =2 2 2.0.0046 (931.5 / ) 4.3E mc u MeV c c MeV= Δ = =

Some Masses in Various Units

All Elements Have IsotopesSame # of protons - different # of neutrons

Atomic Mass of an Element is an average of all IsotopesIsotopes have the same chemistry as the atom.

This is why radioactive isotopes can be so dangerous.The body doesn’t see the difference between water made

with hydrogen and water made with tritium.

The Size of the Nucleus

• First investigated by Rutherford in scattering experiments• He found an expression for d: how close an alpha particle

moving toward the nucleus can come before being turned around by the Coulomb force

• d is called the distance of closest approach– d gives an upper limit for the size of the nucleus– For gold, he found d = 3.2 x 10-14 m– For silver, he found d = 2 x 10-14 m

2

24 ek Zedmv

=

Nuclei• The volume of the nucleus (assumed to be spherical) is directly proportional to the total number of nucleons

• This suggests that all nuclei have nearly the same density– Since r3 would be proportional to

A• Nucleons combine to form a

nucleus as though they were tightly packed spheres

• Average radius is

• ro = 1.2 x 10-15 m• A is the mass number

1 3or r A=

Protons repel each other!How is an Atomic Nucleus Stable?

Strong Force is STRONGER than the Coulomb Force over short distances: Short Range Force

~ 100Strong CoulombF F

Over a range of 10-15 m.

Why are Atoms Not Stable?Why do Atoms Decay?

As nuclear size increases, the distance between nucleons increases and the strong force becomes too weak to overcome the Coulomb electrical repulsion.

The nucleus is unstable and can decay.

Stable NucleiNeutrons:

Nuclear GlueWith few exceptions, naturally occurring stable nuclei have N ≥ Z.

For Z ≤ 20, N = Z is stable.

Elements with Z ≥83 are unstable and spontaneously decay until they turn into stable lead with Z = 82.

Heavy elements FISSION into lighter elements, releasing energyin the process by E = Δmc2, where Δm is the difference in mass

between the parent and products.

~ 25 MeV is released in this reactionMost of the Energy is released in the form of Kinetic Energy (heat).

Fission

Light elements FUSE into larger elements, releasing energyin the process by E = mc2.

Fusion

Nuclear RadiationAtomic decay by Alpha and Beta radiation causes atomic transmutation.Gamma radiation does not transmutate the atom, it changes its energy.

Alpha DecayAtomic Mass Number, A, and charge is conserved for all reactions!

Beta DecayAtomic Mass Number, A, and charge is conserved for all reactions!

Neutrino: Weak ForceMass ~ 0, conserves momentum

Spontaneous Nuclear Decay: Fission

Beta DecayNeutron Decay into a Proton

(Neutron Half life ~ 12 minutes)

Alpha Decay

Only in very extreme conditions like the interior of a star or in a fusion bomb or reactor can you overcome the Coulomb

repulsion and force nucleons to fuse.

There is NO Spontaneous Fusion

Natural TransmutationSpontaneous Fission

Elements with Z ≥83 are unstable and spontaneously decay by alpha and beta radiation until they turn into stable lead with Z = 82.Note: some elements can decay by both modes.

Decay Series for U-238

Decay Series of 232Th

• Series starts with 232Th• Processes through a

series of alpha and beta decays

• The series branches at 212Bi

• Ends with a stable isotope of lead, 208Pb

Radioactive SeriesNatural radioactivity: Unstable nuclei found in nature

Artificial radioactivity: Nuclei produced in the laboratory by bombarding atoms with energetic particles in nuclear reactions.

Activity: Rate of Disintegration

( ) ( )dN tA N tdt

λ= = −

[

N(t) is the # of radioactive atoms in the sample at time t.The activity, A, is the rate at which they decay.

λ is the “decay constant”.

] ( ) 1 disintegration/secondA Becquerel Bq= =

A CURIE is the activity of 1 gram of Radium.

101 3.7 10 ~ Ci x Bq billion Bq=

Example: Activity of 1Kg of Carbon is ~250 Bq ~ 7nCiInhaling a sample with 1μCi of activity will kill you.

Chernobyl released 50 million curies into the atmosphere.

The decay rate R of a sample is defined as the number of decays per second:

Ro = Noλ is the decay rate at t = 0.

( ) −= λtoR t R e

( ) −= λtoN t N e

The amount of undecayed radioactive particles present in the sample at any time t is:

•λ is called the decay constant and determines the rate at which the material will decay•No is the number of undecayed nuclei at time t = 0

( ) ( )dN tA N tdt

λ= = −

From the activity we derive the following useful items:

The half life of a radioactiveelement is the time it takes for a quantity to decay to 1/2 its original amount, N0.

Half Life ( ) −= λtoN t N e

Activity & Half Life dNA Ndt

λ= = −

0( ) tN t N e λ−=The # of radioactive nuclei present at any time t since t = 0 when the # was N0:

0( ) / 2N t N=Decay Constant:

1/ 2 1/ 2te λ− =

1/ 2ln ln1/ 2te λ− =

1/ 2 ln 2tλ− = −

1/ 2

ln 2t

λ = (ln2=0.693)

Carbon Half-LifeCarbon-14 decays with a halflife of about 5730 years by the

emission of an electron of energy 0.016 MeV. At equilibrium with the atmosphere, a gram of carbon shows an activity of about 15

decays per minute. There is 1 atom of C-14 for every 8.3x1011 atoms of C-12.

14 146 7C N β −→ +

Activity: Rate of DisintegrationDetermine the activity of C-14 in a gram of a living organism.

There is 1 atom of C-14 for every 8.3x1011 atoms of C-12.

# C-14 atoms in 1 gram of C:23

1011

6.02 10 12 1 141 6.0 10 1412 8 10 12mol x C Cg x C atoms

g mol x C⎛ ⎞⎛ ⎞ ⎛ ⎞= =⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠⎝ ⎠⎝ ⎠

A Nλ=

107

0.693 1 6 105730 3.15 10

yr x atomsyr x s⎛ ⎞= ⎜ ⎟⎝ ⎠

.23Bq=

1/ 2

0.693t

λ = 0.6935730yr

=

Carbon DatingWhile alive, an organic material absorbs radioactive C-14 from the atmosphere and has a fixed percent of C-14 in it with a fixed rate of radioactivity. Once the plant dies, it stops absorbing C-14 and so the radioactivity is reduced. Measuring the Activity gives a measure of the amount of C-14 remaining and thus the date when the object died.

Neolithic IcemanMaterial found with the body had a C-14 activity of about 0.121 Bq per gram of carbon. Determine the age of the Iceman’s remains.

0 0.23 @ 0A Bq t= =0.121 @ A Bq t now= =

1/ 2 5730t yr

Given:

=

5730 ln .23/ .121 53100.693

yr yr= =

0tA A e λ−=

0ln / ln tA A e tλ λ−= = −

01 ln /t A Aλ

=

1/ 2

0.693t

λ =

Moon Rock ProblemIn a piece of rock from the Moon, the 87Rb content is assayed to be 1.82 × 1010 atoms per gram of material, and the 87Sr content is found to be 1.07 × 109 atoms per gram. Calculate the age of the rock. What assumption is implicit in using the radioactive dating method? The half‐life of the decay is 4.75 × 1010 yr. 87Rb decays by:

ve ++→ −Sr Rb 8787

The Apollo missions sampled ancient lunar crustal rocks. These rocks are about 4.5 billion years old.

Why can’t we see Atoms?

How do we know they exist?