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 Power

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.

If Helium loses a proton, it becomes a different element

If Helium loses one of its neutrons, it becomes an isotope

Isotopes and Elements

pnn

e

3He

ppn

e

e3H =T

The Hydrogen Atom

• One electron orbiting a nucleus

• 1 proton = Z = atomic number

• 0 neutrons = N• Total mass = A = Z+N =1• Singly ionized Hydrogen is

missing one electron = 1H+

• Add a neutron and you have Deuterium = 2H = D

• Add 2 neutrons and you have Tritium = 3H = T

p

e

1H

The Helium Atom• Two electrons orbiting a nucleus with:

2 protons = Z = atomic number

2 neutrons = N

• Total mass = A = Z+N

• Singly ionized Helium is missing one electron = 4He+

• Doubly ionized Helium is missing both electrons = α particle = 4He++

ppn

n

e

e

4He

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

More about Fusion in Chapter 45!

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 Force

Binding EnergyIt takes energy to break up an atom.

Energy must be put into a system to break it apart.That energy is converted to mass.

That energy is called the Binding Energy.

Eb = (Zmp + Nmn – MA) x 931.494 MeV/u

The masses are expressed in atomic mass units.Add the atomic mass of the electron to the proton.

Binding Energy per NucleonThe most stable atoms have the most Binding Energy per nucleon.

Radioactive Atoms mutate by fission or fusion until they have maximum Binding Energy per nucleon which occurs at Iron.

Mass per NucleonThe smaller the mass per nucleon, the greater the binding energy.Elements fission down or fuse up to Iron, the most stable element,

releasing energy by E = Δmc2.

Fission

Fusion

Spontaneous Nuclear Decay: Fission

Beta DecayNeutron Decay into a Proton

(Neutron Half life ~ 12 minutes)

Alpha Decay

E = Δmc2

Energy Released: The Mass DefectParent atoms have more mass than product atoms.

The difference is released in the form of Kinetic energy.

( )parents productsm m mΔ = −

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 @

Given:

A Bq t now= =1/ 2 5730t yr=

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 =

You Try: Problem 74In 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? Could the material in the rock actually be much older? 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.

Alpha Decay• Decay of 226 Ra

• If the parent is at rest before the decay, the total kinetic energy of the products is 4.87 MeV

• In general, less massive particles carry off more of the kinetic energy

• In general for alpha decay:– N decreases by 2– Z decreases by 2– A decreases by 4

HeRnRa 42

22286

22688 +→

Parent

Daughter

How do you calculate the KE of the alpha particle?

See example 44.8

Q: Disintegration Energy

• The disintegration energy Q of a system is defined as

Q = (Mx – My – Mα)c2

• The disintegration energy appears in the form of kinetic energy in the daughter nucleus and the alpha particle

• A negative Q value indicates that such a proposed decay does not occur spontaneously

Beta Decay• During beta decay, the daughter nucleus has

the same number of nucleons as the parent, but the atomic number is changed by one

• Symbolically 1

1

X Y eX Y e

A AZ ZA AZ Z

−+

+−

→ +

→ +

Beta Decay & The Neutrino•The emission of the electron or positron is from the nucleus•The process occurs when a neutron is transformed into a proton or a proton changes into a neutron•The electron or positron is created in the process of the decay•Energy must be conserved BUT it wasn’t! Experiments showed a range in the amount of kinetic energy of the emitted particles•To account for this “missing” energy, in 1930 Pauliproposed the existence of another particle•Enrico Fermi later named this particle the neutrino, meaning, “little neutron”

Neutrino• Properties of the neutrino

– Zero electrical charge– Mass much smaller than the electron, probably not zero– Spin of ½ - it is a lepton.– Very weak interaction with matter and so is difficult to detect– in beta decay, the following pairs of particles are emitted

1

1

X Y eX Y e

A AZ ZA AZ Z

νν

−+

+−

→ + +

→ + +

–An electron and an antineutrino–A positron and a neutrino

Neutrinos are LeptonsThey come in 3 Flavors.

They have antiparticles too.

Detecting Neutrinos50 trillion solar neutrinos pass through your body every second. Can you detect them?

Because of the reluctance of neutrinos to react with atomic nuclei and thus allow themselves to be captured, very large number of neutrinos and very large detector volumes are required.

Frederick Reines and his colleage Clyde L. Cowan, Jr. proposed in 1953 a reactor experiment to capture neutrinos through the reaction:

antineutrino + proton –› neutron + positron.

The target in the Reines-Cowan experiment consisted of approximately 400 litres of water containing cadmium chloride placed between large liquid scintillation detectors. The neutrino collides with a proton in the water and creates a positron and a neutron. The positron is slowed down by the water and destroyed together with an electron, whereupon two photons are created. These are recorded simultaneously in the two detectors. The neutron also loses velocity in the water and is eventually captured by a cadmium nucleus, whereupon photons are emitted. These photons reach the detectors a microsecond or so later than those from the destruction of the positron and give proof of neutrino capture.

The Nobel Prize in Physics 1995

Solar Neutrino Measurement

Detecting solar neutrinos would be PROOF that the sun shines from nuclear fusion.

Raymond Davis Jr’s detector, which for the first time in history proved the existence of solar neutrinos. Over a period of 30 years he succeeded in capturing a total of 2,000 neutrinos from the Sun and was thus able to prove that fusion provided the energy from the Sun. The tank, which was placed in a gold mine, contained more than 100,000 gallons of tetrachloroethylene. A neutrino interacts with a chlorine nucleus to produce an argon atom.

The Nobel Prize in Physics 2002

Solar Neutrino ProblemFrom the Davis experiment, it became clear that the number of solar neutrinos detected was lower than that predicted by models of the solar interior. In various experiments, the number of detected neutrinos was between one third and one half of the predicted number. This came to be known as the solar neutrino problem.

The solution to the problem is called Neutrino Oscillations:The neutrinos change into each other!

According to quantum mechanics, particles sometimes behave like waves (and vice versa). When neutrinos "mix" as described above, they combine in the same way that waves combine. When sound waves combine, they "beat", as depicted in the picture to the right. Neutrinos do a similar sort of thing, except we say that they "oscillate".

It is the flavor of the neutrino that oscillates. If a neutrino starts out as 100% νe, as it moves along its "νe-ness" will begin to fade, while its νμ-ness or ντ-ness grows. The νe-ness soon reaches a minimum, and begins to increase again. Then the neutrino once again becomes a pure νe before fading away again. The amplitude and frequency of the oscillation depends on the particular values of the three masses and the mixing parameters, which are still being studied.

The Main Injector Neutrino Oscillation Search (MINOS) experiment studies a neutrino beam using two detectors. The MINOS near detector, located at Fermilab, records the composition of the neutrino beam as it leaves the Fermilab site. The MINOS far detector, located in Minnesota, half a mile underground, again analyzes the neutrino beam. This allows scientists to directly study the oscillation of muon neutrinos into electron neutrinos or tau neutrinos under laboratory conditions.

Super Kamiokande

Super-K is located 1,000 m underground in MozumiMine in Japan. It consists of 50,000 tons of pure watersurrounded by about 11,200 detectors. A neutrino interaction with the electrons or nuclei of water producing a flash of light which can be detected. In 1998 discovered neutrino oscillations and mass.

The Nobel Prize in Physics 2002

Masatoshi Koshiba

Koshiba confrimed Davis’s results and in 1987 detected the first cosmic neutrinos from a supernova explosion, capturing twelve of the total of 1016 neutrinos that passed through the detector.

AMANDA: Neutrino Telescopeat the South Pole

The Cherenkov Effect Muons breaking the 'light barrier'

Cosmic GallJohn Updike

Neutrinos they are very small.They have no charge and have no mass

And do not interact at all.The earth is just a silly ball

To them, through which they simply pass,Like dustmaids down a drafty hall

Or photons through a sheet of glass.They snub the most exquisite gas,Ignore the most substantial wall,

Cold-shoulder steel and sounding brass,Insult the stallion in his stall,

And, scorning barriers of class,Infiltrate you and me! Like tall

And painless guillotines, they fallDown through our heads into the grass.

At night, they enter at NepalAnd pierce the lover and his lass

From underneath the bed – you callIt wonderful; I call it crass.

• The fundamental process of e- decay is a neutron changing into a proton, an electron and an antineutrino

• In e+, the proton changes into a neutron, positron and neutrino– This can only occur within a nucleus– It cannot occur for an isolated proton since its mass is

less than the mass of the neutron

Q Values for Beta Decay

• For e- decay and electron capture, the Q value is Q= (Mx – MY)c2

• For e+ decay, the Q value is Q = (Mx – MY - 2me)c2

– The extra term, -2mec2, is due to the fact that the atomic number of the parent decreases by one when the daughter is formed

– To form a neutral atom, the daughter sheds one electron• If Q is negative, the decay will not occur

Gamma Decay• Gamma rays are given off when an excited

nucleus decays to a lower energy state• The decay occurs by emitting a high-energy

photon

– The X* indicates a nucleus in an excited state

X X*A AZ Z γ→ +

• Decay sequence–The first decay is a beta emission–The second step is a gamma emission

Cerenkov light from gamma rays due to Cobalt-60 decay in water