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 Power

Nuclear Weapons

Nuclear Waste

250,000 tons of Spent Fuel

10,000 tons made per year

Health Effects of Ionizing Radiation

Radiocarbon Dating

Atomic Notation

A

Z X

Atomic Mass Number

A = # protons + neutrons

Atomic #

1 3 238

1 1 92H, H, U

Atomic Number

Z = # protons

Neutron Number N

N = # neutrons

N = A - Z

E = mc2

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 m

Heavy elements FISSION into lighter elements, releasing energy

in the process by E = mc2, where m is the difference in mass

between the parent and products.

~ 4.3 MeV is released in this reaction

Most of the Energy is released in the form of Kinetic Energy (heat).

Fission

Light elements FUSE into larger elements, releasing energy

in the process by E = mc2.

Fusion

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 u

2 2 2.0.0046 (931.5 / ) 4.3E mc u MeV c c MeV

Some Masses in Various Units

191 1.6 10eV x J

27 21 1.6605 10 931.5 /u x kg MeV c

131 1.6 10MeV x J

Super Useful

ANN m

M

(M is the atomic mass which is also the number of

moles in 1 gram. Avogadro’s Number is the number

of particles in a mole, N is the number of particles

present with Activity A)

Number Particles:

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

Atomic Mass of an Element is an average of all Isotopes

Isotopes 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

Isotopes and Elements

If Helium loses one of its

neutrons, it becomes an

isotope

p

nn

e

3He

p

pn

e

e

3H =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 = a particle = 4He++

p

pn

n

e

e

4He

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 3

or 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 Nuclei

Neutrons:

Nuclear Glue

With 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.

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 Ni-62.

Eb = (Zmp + Nmn – MA) x 931.494 MeV/u

The Curve of Binding Energy

Slide 42-46

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 = mc2.

Fission

Fusion

Binding Energy per Nucleon

For energy release in fusion or fission, the products need to have a

higher binding energy per nucleon (proton or neutron) than the

reactants. As the graph above shows, fusion only releases energy for

light elements and fission only releases energy for heavy elements.

https://www.youtube.com/watch?v=UkLkiXiOCW

U

https://www.youtube.com/watch?v

=HCRBPZM0O1E&index=13&list

=PLaSHX1Y3kE0yjGNcRSsPhA_

ZEHIXYIE0Z

The Liquid Drop Model

1936 Bohr: Provides good agreement with observed nuclear

binding energies

2

2 3

1 2 3 41 3

1b

Z Z N ZE C A C A C C

A A

For A 15, C1 = 15.7 MeV; C2 = 17.8 MeV; C3 = 0.71 MeV; and C4 = 23.6 MeV

Magic Numbers

• The disagreement between the semiempirical formula and

experiments is plotted

• The peaks are reminiscent of the peaks in graphs of

ionization energy of atoms and lead to the shell model of

the nucleus

• These peaks are at the magic numbers of

Z or N = 2, 8, 20, 28, 52, 82

The shell model of

the nucleus, using

multielectron atoms

as an analogy, was

proposed in 1949 by

Maria Goeppert-

Mayer.

The shell model

considers each

nucleon to move

independently with an

average potential

energy due to the

strong force of

all the other nucleons.

The Shell Model

Slide 42-52

Maria Goeppert-Mayer received the

1963 Nobel Prize in Physics for her

work in nuclear physics.

The figure shows the energy diagram for 12C.

Exactly six protons are allowed in the n 1 and n 2

energy levels.

Likewise for the six

neutrons.

Thus 12C has a

closed n 2

proton shell and

a closed n 2

neutron shell.

Low-Z Nuclei

Slide 42-56

The figure shows the energy diagram for 12B.

The sixth neutron fills the n 2 neutron shell, so the

seventh neutron has to go into the n 3 energy level.

The n 2 proton shell

has one vacancy

because there are

only five protons.

12B has significantly

more nuclear energy

than 12C.

Low-Z Nuclei

Slide 42-58

Marie Curie

• 1867 – 1934

• Polish scientist

• Shared Nobel Prize in 1903 for

studies in radioactive

substances

– Prize in physics

– Shared with Pierre Curie and

Becquerel

• Won Nobel Prize in 1911 for

discovery of radium and

polonium

– Prize in chemistry

Our Friend The Atom

https://youtu.be/QDcjW1XSXN0?t=34m00s

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!

4 4

2 2X Y HeA A

Z Z

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

H eR nR a 4

2

2 2 2

8 6

2 2 6

8 8

In Fission, the alpha

particle escapes the

nucleus by Quantum

Tunneling.

In Fusion, protons fuse

to form helium by

Quantum Tunneling

through the repulsive

coulomb barrier.

Quantum

Tunneling

Beta DecayA neutron turns into a proton by emitting an electron!

Neutrino: Weak Force

1

1

X Y e

X Y e

A A

Z Z

A A

Z Z

ν

ν

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 e

X Y e

A A

Z Z

A A

Z Z

ν

ν

–An electron and an antineutrino

–A positron and a neutrino

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 A

Z Z γ

12 12

5 6

12 12

6 6

B C e

C C

*

*

ν

γ

Summary of Decays

https://www.youtube.com/watch?v=aJkx6hAD-4E

The half life of a

radioactive

element is the time it

takes for a quantity

to decay to 1/2 its

original amount, N0.

Half Life ( ) λt

oN t N e

Activity: Rate of Disintegration

( )( )

dN tA N t

dt

N(t) is the # of radioactive atoms in the sample at time t.

The activity, A, is the rate at which they decay.

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 ~ 7nCi

Inhaling a sample with 1Ci 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.

( ) λt

oR t R e

( ) λt

oN 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 t

dt

From the activity we derive the following useful items:

Activity & Half Life dNA N

dt

0( ) tN t N e 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/ 2t

e

1/ 2ln ln1/ 2t

e

1/ 2 ln 2t

1/ 2

ln 2

t (ln2=0.693)

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.

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 14

6 7C N

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:

2310

11

6.02 10 12 1 141 6.0 10 14

12 8 10 12

mol x C Cg x C atoms

g mol x C

A N

10

7

0.693 16 10

5730 3.15 10

yrx atoms

yr x s

0.23Bq

1/ 2

0.693

t

0.693

5730yr

Neolithic Iceman discovered in

1991 in Italy

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 Given:

0.121 @ A Bq t now 1/ 2 5730t yr

5730ln.23/ .121 5310

0.693

yryr

0

tA A e

0ln / ln tA A e t

0

1ln /t A A

1/ 2

0.693

t

Natural Transmutation

Spontaneous FissionElements 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.

Induced Nuclear Fission

Nuclear Reactions

https://www.youtube.com/watch?v=9gERUtbtkRc&index=12&l

ist=PLaSHX1Y3kE0yjGNcRSsPhA_ZEHIXYIE0Z

Nuclear Reactions The structure of nuclei can be changed by bombarding

them with energetic particles

The changes are called nuclear reactions

As with nuclear decays, the atomic numbers and mass

numbers must balance on both sides of the equation

A target nucleus, X, is bombarded by a particle a, resulting in a daughter nucleus Y and an outgoing particle b

a + X Y + b

The reaction energy Q is defined as the total change in mass-energy resulting from the reaction

Q = (Ma + MX – MY – Mb)c2

Q Values for Reactions

The Q value determines the type of reaction An exothermic reaction

There is a mass “loss” in the reaction

There is a release of energy

Q is positive

An endothermic reaction

There is a “gain” of mass in the reaction

Energy is needed, in the form of kinetic energy of the incoming particles

Q is negative

The minimum energy necessary for the reaction to occur is called the threshold energy

Nuclear Reactions

• If a and b are identical, so that X and Y are

also necessarily identical, the reaction is

called a scattering event

– If the kinetic energy before the event is the

same as after, it is classified as elastic

scattering

– If the kinetic energies before and after are not

the same, it is an inelastic scattering

a + X Y + b

Our Friend The Atom

https://youtu.be/QDcjW1XSXN0?t=34m00s

Problem

Nuclear Magnetic Resonance

(NMR)

A nucleus has spin angular momentum

Shown is a vector model giving possible orientations of the spin and its projection on the zaxis

The magnitude of the spin angular momentum is

For a nucleus with spin ½,

there are only two allowed

states

Emax and Emin

It is possible to observe

transitions between two spin

states using NMR

( 1)I I h

MRI

An MRI (Magnetic Resonance Imaging) is based on NMR

Because of variations in an external field, hydrogen atoms in different parts of the body have different energy splittings between spin states

The resonance signal can provide information about the positions of the protons

https://www.youtube.com/watch?v=hlR

pl_GMPPc

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 Pauli proposed the existence of another particle

•Enrico Fermi later named this particle the neutrino, meaning, “little neutron”

Neutrinos are Leptons

They come in 3 Flavors.

They have antiparticles too.

Detecting Neutrinos

50 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 Problem

From 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 Mozumi Mine in

Japan. It consists of 50,000 tons of pure water surrounded

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 Telescope

at the South Pole

The Cherenkov Effect Muons breaking the 'light barrier'

Neutrino Experiments at CERN

The Oscillation Project with Emulsion-

Racking Apparatus (OPERA)

OPERA is an instrument used

in a scientific experiment for

detecting tau neutrinos from

muon neutrino oscillations.

The experiment is a

collaboration between CERN in

Geneva, Switzerland, and the

Laboratori Nazionali del Gran

Sasso (LNGS) in Gran Sasso,

Italy and uses the CERN

Neutrinos to Gran Sasso

(CNGS) neutrino beam.

Neutrino Experiments at CERN

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 fall

Down through our heads into the grass.

At night, they enter at Nepal

And pierce the lover and his lass

From underneath the bed – you call

It wonderful; I call it crass.

http://www.youtube.com/watch?v=dhkCMO1lG7g