Do Now (5/2/12):

• What is an istope?• What makes an isotope different than its

element?

Nuclear Reactions

5/2/12

Lesson Objectives

–Describe nuclear reactions and perform balancing of nuclear reactions by solving problems.

–Apply radioactivity equations by solving problems.

Sub-atomic particles

The numbers:• Protons and neutrons are approximately equal

in size– mp = 1.67 x 10-27 kg

– mn = 1.67 x 10-27 kg

– me = 9.11 x 10-31 kg

Isotope

• Atomic nuclei having the same number of protons but different number of neutrons

Vocab Review:

• Nuclear reaction: the number of protons or neutrons in the nucleus of an atom changes.

• Atomic number: Number of protons in the nucleus of the atom

• Mass number: Sum of protons and neutrons in the nucleus of the atom

Nuclear Structure

Z = Atomic number N = Number of neutronsA = Atomic massA = Z + N

Relative Size of Nuclei

One fermi (f) = 10-15 m

Radius versus Atomic Mass

r = 1.2 A1/3 (in f)-------------------------Helium: A = 4 r = 1.2 (4)1/3

= 1.9 f-------------------------Uranium: A = 238 r = 1.2 (238)1/3

= 7.4 f

Atomic Mass Units

• From carbon-12 as the basis.

• Neutron = 1.008u• Proton = 1.007u• An amu = 1.66 x 10-27 kg = 931MeV/c2

• Also expressed in MeV from E=mc2

Einstein's Equation • Mass is just a type of energy where one is

measured in Joules, J, and one in kilograms, kg.

• The conversion factor between mass and energy is just the square of the speed of light.

• E = mc2

Einstein's Equation cont.

• E = mc2 • Mass of a proton, m, is 1 atomic mass unit =

1.7 x 10-27kg • Speed of light, c, is 3 x 108m/s• What is E?• E = 15.3 x 10-11Joules• 1eV = 1.6 x 10-19J so what is E in eV.• E = 9.56 x 108eV = 956MeV

Albert Einstein’s E = mc2 Is Called Mass-Energy Equivalence

Mass is energy: E = mc2 Energy is mass: m = E /c2

Binding energy

• Mass of a single nucleon is higher than its mass when incorporated into a nucleus.

• Mass defect is reflective of the binding energy (how tightly are the nucleons bound.)

http://universe-review.ca/I14-01-bindingenergy.jpg

Nuclear Force

• No precise mathematical formula known…yet.• Short-range force (10-15 m)• Related to ratio of protons and neutrons in the

nucleus.

http://universe-review.ca/I14-02-pnratio.jpg

Nuclear Decay

• Natural process occurring in some atoms/isotopes because the nucleus is unstable (too big).

• Increases stability of the nucleus.• New (daughter) elements form.• Half life varies from fractions of a second to

thousands of years.

Radioactivity vs Radiation

• Radioactivity – The property of an atom that describes spontaneous changes in its nucleus that create a different nuclide (isotope).

• Radiation - The energy that is released as particles or rays, during radioactive decay.

The Nucleus

Radioactivity• 3 types of radioactive

emission:

x x x x x x x x

x x x x x x x x

x x x x x x x x

Pb

Types of radiation

• Alpha – a helium nucleus (two neutrons, two protons)

• Beta – a high energy electron• Gamma – high energy photons

Penetrating Power

e-

He (nucleus)

Alpha (α) Decay• The parent nucleus loses a cluster of 2 protons and 2

neutrons.

Ra22688

+

+

+

+

+

+

+ +

++

++

++

HeRn 42

22286 Z = # of protons + neutrons

A = # of protons

Beta (β) Decay• The parent nucleus has a neutron turn into a proton and

an extra electron is created to conserve charge.

+

+ +

+

+

+

Watch this neutron

+ e

C146

eN147

Energy Release in Decay

• Mass of Parent Atom = 14.003242 u• Combined mass of products = 14.003074 u

C146

um 000168.0

2cmE eVorJxsmx

u

kgxuE 870,1561051.2/103

1

1066.1000168.0 1428

27

                                           

  

Alpha decay

•the nucleus of an atom emits an alpha particle

Alpha Particle

• Nucleus of a helium atom

Beta decay

• occurs when a neutron is changed to a proton within the nucleus of an atom, and a beta particle and an antineutrino are emitted

Gamma decay

• Radioactive process of decay that takes place when the nucleus of an atom emits a gamma ray.

• http://library.thinkquest.org/17940/texts/radioactivity/radioactivity.html

Mass Defect: • The difference between the sum of the mass of the individual

nucleon (proton or neutron) and the actual mass.

€

m = matom −Z mp +me( )

+(A − Z)mn

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Example #1:

Fermium-253 has a half-life of 0.334 seconds. A radioactive sample is considered to be completely decayed after 10 half-lives. How much time will elapse for this sample to be considered gone?

Binding Energy

• The energy equivalent of the mass defect; it is always negative

It is the minimum amount of energy needed to break the nucleus into its component nucleons.€

Ebinding =

(massdefect(inu))(931.49MeV /u)

Example #2:

• The half life of Zn-71 is 2.4 minute. If one had 100 g at the beginning, what is the decay rate of Zn-71?

Mass remaining

• m=mass remaining• Original mass

€

m = m0e−λ t

Example #3:

• The half life of Zn-71 is 2.4 minute. If one had 100 g at the beginning, how many grams would be left after 7.2 minutes elapsed?

Practice:

•Use the rest of class to work on the paper: Radioactivity; problems: #2,5,6, and 7

Do Now (4/24/12):

• Pd-100 has a half-life of 3.6 days. If one had 6.02x1023 atoms at the start, how many atoms would be present

Decay Sequence

Alpha decay sequence:

235

U92

209

Po84

4 231

He + Th2 90

4 205

He + Pb2 82

Decay Sequence

Beta decay sequence:

14

C6

228

Ra88

14 0

N + e7 -1

228 0

Ac + e89 -1

Natural Transmutation

The changing of one element to another is called transmutation.

Half-life

• Time for half of a radioactive sample to undergo decay.

• First order decay process.

• T1/2 = 0.693/ where =decay constant

• N = N0e-t

The Strong Force Protons which would otherwisestrongly repel at close distancesare held in place by an extremelystrong, but extremely short rangeforce called the strong force. Other names for the strong forceare strong nuclear force, or nuclear force.

The strong force between two protons is about the same asthe strong force between twoneutrons, or a proton and a neutron.

Beyond about one fermithe strong force declinesextremely rapidly.

As more protons areadded to the nucleus, more neutrons are needed to bind theprotons together, butthe larger the nucleusbecomes, the farther apart are the protonsand the less effectiveis the strong force

Protons and neutrons in the nucleus are collectively referred to as nucleons.

Neutron Number versus Proton Number

Electric force is longer range than the strong force.

Eventually separation becomes too great for the strong force to compensate for the repulsive forces. Nuclei spontaneously disintegrate for proton numbers larger than 83.

The release of light and or particles which accompanies the disintegration is called radiation, first discovered by Henri Becquerel in 1896.

The Binding Energy of a Nucleus

The larger the binding energy of a nucleus, the more stable it is.

The binding energy is the difference between the rest energies.

Atomic Mass Unit

One atomic mass unit (amu) = 1.6605 x 10-27 kg -------------------------------------------------------------------- E = (1.6605 x 10-27 kg) (3 x 108 m/s)2

= 1.49 x 10-10 J

1.49 x 10-10 J / 1.6 x 10-19 J /eV = 9.31 x 108 eV 931 x 106 eV = 931 MeV

  one amu = 931 MeV  

An amu is often abbreviated u

The Binding Energy of Helium

Dm = 4.0330 - 4.0026 = 0.0304 u

E = (931 MeV /u) 0.0304 u = 28.3 MeV

There are four nucleons, sothe binding energy per nucleonis about 28/4, or about 7 MeVper nucleon.

Binding Energy per Nucleon

Nuclei with the largest binding energyper nucleon are the most stable.-----------------------------------------------------

The largest binding energy per nucleon is 8.7 MeV, for mass number A = 60.

Beyond bismuth, A = 209, nucleiare unstable.

Atoms in the Middle of the Periodic Table are the Most Stable

• The most tightly bound of the nuclei is 62Ni

• The most tightly bound nuclides are all even-even nuclei

Binding Energy of Alpha Particle

For the alpha particle Δm= 0.0304 u which gives a binding energy of 28.3 MeV

It Takes a Lot More Energy to Split a Nucleus Than to Ionize an Atom

Uranium Decays via Alpha-Particle Emission

The first particle that was recognized as having been ejected from an unstable nucleus was called an alpha particle because alpha is the first letter of the Greek alphabet.   It's now known to consist of two protons and two neutrons, which is the same as a helium nucleus.

Carbon-14 Decays by Beta Emission

The beta particleis now known tobe just an electron.

Is the nucleon count conserved?

Is the total chargeconserved?

Reaching Stability Through Gamma Ray Emission

Nuclei with excessenergy emit gamma-rays, whichare extremely short-wavelength electro-magnetic waves, i.e.,very high energy photons.

Nuclear Notation

Alpha Particle Emission

The alphaparticleis a heliumnucleus.

Balancing Nuclear Decay Equations

92U238 --------> 90Th234  +  2He4

Subscripts are "proton numbers"

Superscripts are "nucleon numbers"

Proton and nucleon counts must be the same:

92 = 90 + 2 238 = 234 + 4

Distribution of Energy in Alpha Emission

Dm = 0.0046 u

E = 0.0046 x 931 = 4.3 MeV-----------------------Which particlehas the greaterkinetic energy?

Energy Distribution in Radioactive Decay

Ratio of kinetic energies: KEm / KEM:

(1/2 mV2) / (1/2 Mv2) = (m/M)(V2/v2) = (m/M)(V/v)2 (1)

Conservation of momentum: Mv = mV (2)

Rearranging, we getV/v = M/m (3) Substitute (3) into (1):

Ratio = (m/M)(M/m)2 (4) = M/m

Smaller mass gets more energy

Marie Curie

Marie Sklodowska Curie          (1867-1934)

Lithograph entitled "Radium"appeared in the December 22, 1904 issue of Vanity Fair.

Marie and Pierre Curie isolated 1/30 ounce ofradium from one ton ofuranium ore.

Marie died fromradiation-inducedleukemia.

The pages of her labnotebook were laterfound to becontaminated withradioactivefingerprints.

Radioactivity in Radium

In "balancing" a nuclear disintegration equation, note that the subscripts and superscripts add up.

Plutonium Powered Spacecraft

94Pu238 -----> 92U234 + a

Smoke Detectors Use Radiation Sources

Alpha particles emitted from source ionize the air and provide the charge necessary to conduct current through the air.

Charges stick to the heavy smoke particles and the current decreases, causingthe alarm to buzz.

Beta Particle (Electron) Emission

90Th234 ------> 91Pa234 + -1e0

The neutron number of anelectron is zero, and theproton number is negative one.

Negative beta particlesare emitted when a neutronis transformed into a proton and an electron.

Beta Particle (Electron) Emission by Carbon-14

6C14 -----> 7N14 + -1e0

The subscripts representthe "proton" number (electrons have a negative)proton number.

Superscripts represent thenucleon number; electronsare not nucleons, so theirnucleon number is zero.

Beta Particle (Positron) Emission by Oxygen-15

A positron has the same mass as the electron, but opposite charge.

8O15 -----> 7N15 + 1e0

The subscripts representthe "proton" number (a positron has a positiveproton number)

Superscripts represent thenucleon number; positronsare not nucleons, so theirnucleon number is zero.

15

PET Imaging of Brain Is Based On Positron Annihilation

Healthy brain Brain with Alzheimer's disease

Wavelength of a Gamma Ray

What is the wavelength of a 1 MeV gamma ray?

Using the 1240 rule: l = 1240 eV-nm / E = 1240 eV-nm / 1 x 106 eV = 1.24 x 10-6 nm = 1.24 x 10-15 m = 1.24 fermiThis gamma radiation is extraordinarily harmfulto humans and other living things since its wavelength is comparable to the diameter ofa nucleon; transmutations are likely whensuch radiation reaches nuclei.

Brain Surgery with the Gamma Knife

The Geiger Counter

Hans Geiger inventedthe "Geiger counter".----------------------------------It was Hans Geiger who,while working in Ernest Rutherford's lab, was the first to see the alpha particles reverse direction in the alpha particle experiment, but it was Rutherford's calculation which proved theexistence of the nucleus

The Scintillation Counter

Scintillator is material which willemit photons when struck byhigh energy charged particlesor high energy photons.

Photon strikes metal plate,ejecting electrons which arepulled toward 100 V anode.The anode is coated with amaterial which is easilyionizable and releases two ormore electrons for each onethat strikes it.

Transmuting Uranium to Neptunium

Neutron enters nucleus and is transformed into a proton and an electron (which leaves the nucleus).

Nuclear Energy Map

Nuclear Fission Produces Far More Energy Than Combustion

Average number of neutronsreleased is 2.5.

Combined kinetic energy of particles is about 200 MeV.

100,000,000 times more energy than is released when coal is burned: C + O2 => CO2

(about 2 eV)

Estimating Energy Released During Fission

About 7.5 MeVto about 8.5 MeVper nucleon.

Mass differenceis about one MeVper nucleon.

If A = 235, thenenergy releasedis about 235 MeV

Calculating Binding Energies—What is the binding energy of C12?

One atom of C12 consists of 6 protons, 6 electrons, and 6 neutrons. The mass of the uncombined protons and electrons is the same as that of six H1 atoms (if we ignore the small binding energy of the electron proton pair).

Mass of six H1 atoms = 6 x 1.0078 u = 6.0468 uMass of six neutrons= 6 x 1.0087 u = 6.0522 uTotal mass of particles= 12.0990 uMass of C12= 12.0000 uLoss in mass on forming C12= 0.0990 uBinding energy= 931 MeV x 0.0990= 92 MeV

Slow Neutrons Cause Chain Reactions

Slow neutrons are required.

A chain reaction occurs ifmore than one neutrongoes on to cause anotherfission.

Neutrons can be slowed bybouncing them off of smallobjects, such as carbonnuclei.One pound of U-235, ifcompletely fissioned, yieldsthe same energy as100,000,000 pounds of coal.

Cadmium Control Rods Absorb Neutrons

Enrico Fermisupervised construction of theworld's first nuclearreactor.

Cadmium is a good absorber of neutrons.

World's First Controlled Nuclear Chain Reaction

Handball court under the bleachers at the University of Chicago, 1942.  Uranium-235 is at the center of the stack of graphite blocks; the carbon acts as a moderator, slowing neutrons.

The Manhattan Project

 Oak Ridge, Tennessee.  60,000 workers worked for three years to separate 2 kilograms of uranium-235 from uranium-238.

World's First Fission Explosion

Trinity Site--5:30 am, July 16, 1945, Alamogordo, New Mexico.

Dr. Robert J. Oppenheimer and Maj. Gen. Leslie L. Groves,

The First Atomic Bomb

"Little Boy", two feet in diameter, ten feet long, 9000  pounds, dropped on Hiroshima, Japan, was a uranium  bomb, equivalent to 20,000 tons of explosive.

“Gun” Bomb Concept

Two sub-critical massesare smashed together tocreate a super-criticalmass.

The Two Bombs Used In WWII Were of Different Types

Little Boy and Fat Man

Implosion Weapon Concept

Pu “pit” 4.5 cm with 2.5 cm centerhole

Energy From Fission

165 MeV7 MeV6 MeV7 MeV6 MeV9 MeV

200 MeV

~kinetic energy of fission products~ gamma rays~ kinetic energy of the neutrons~ energy from fission products~ gamma rays from fission products~ anti-neutrinos from fission products

Atomic Bomb Targets

The only nuclear weapons ever used in anger were the two atomic bombs dropped in 1945.

The Scorched Remains

Nagasaki, Japan Nagasaki survivor. (Click here for panoramic view of Hiroshima.)

Modern Nuclear Reactors

The water in the reactor vessel has three purposes.

The water, being composed of relatively light molecules, acts as a moderator. In Fermi's reactor, carbon in the form of graphite was the moderator.

Water also acts to remove heat from fuel rods which otherwise would melt.

The heated water, converted to steam, is then converted into electrical energy.

A Nuclear Reactor

Heat generated by fissionin uranium rods createssteam which turns turbineblades connected to acoil of wire in magnetic field.

Uranium Fission

• If a massive nucleus like uranium-235 breaks apart (fissions), then there will be a net yield of energy because the sum of the masses of the fragments will be less than the mass of the uranium nucleus.

• If the mass of the fragments is equal to or greater than that of iron at the peak of the binding energy curve, then the nuclear particles will be more tightly bound than they were in the uranium nucleus, and that decrease in mass comes off in the form of energy according to the Einstein equation.

Fission Energy Release

Fission Particle and Energy Yields

Fission Fragments

• When uranium-235 undergoes fission, the average of the fragment mass is about 118, but very few fragments near that average are found.

• It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 and 137.

• Most of these fission fragments are highly unstable (radioactive), and some of them such as cesium-137 and strontium-90 are extremely dangerous when released to the environment.

Fission Fragment Example

• A common pair of fragments from uranium-235 fission is xenon and strontium:

• Highly radioactive, the xenon decays with a half-life of 14 seconds and finally produces the stable isotope cerium-140.

• Strontium-94 decays with a half-life of 75 seconds, finally producing the stable isotope zirconium-94.

• These fragments are not as dangerous as intermediate half-life fragments such as cesium-137.

Fission Fragment Decay

This particular set of fragments from uranium-235 fission undergoes a series of beta decays to form stable end products

Chain Reactions

• If at least one neutron from each fission strikes another U-235 nucleus and initiates fission, then the chain reaction is sustained.

• If the reaction will sustain itself, it is said to be "critical", and the mass of U-235 required to produced the critical condition is said to be a "critical mass". A critical chain reaction can be achieved at low concentrations of U-235 if the neutrons from fission are moderated to lower their speed, since the probability for fission with slow neutrons is greater.

• The smaller the sphere, the greater the ratio of surface area to volume, and the greater the percentage of neutrons which escape the sphere before causing fission.  

• Critical mass--or, critical size--is that mass value at which an average of more than one neutron per fission is used to cause another fission.

Uranium 235 Fission for Energy

Uranium As Fuel

• Natural uranium is composed of 0.72% U-235 (the fissionable isotope), 99.27% U-238, and a trace quantity 0.0055% U-234 . The 0.72% – U-235 is not sufficient present in suficient cocentration to produce a

self-sustaining critical chain reaction in U.S. style light-water reactors. For light-water reactors, the fuel must be enriched to 2.5-3.5% U-235.

– It can be used in Canadian CANDU reactors.

Fusion in Stars

10 million degrees at the core causes fusion of hydrogen into helium.

Proton-Proton Fusion

This is the nuclear fusion process which fuels the Sun and other stars which have core temperatures less than 15 million Kelvin. A reaction cycle yields about 25 MeV of energy.

P-P Fusion

• The fusing of two protons which is the first step of the proton-proton cycle created great problems for early theorists because they recognized that the interior temperature of the sun (some 14 million Kelvins) would not provide nearly enough energy to overcome the coulomb barrier of electric repulsion between two protons.

With the development of quantum mechanics, it was realized that on this scale the protons must be considered to have wave properties and that there was the possibility of tunneling through the coulomb barrier.

Fusion Options on Earth

Deuterium Fusion Cycle

These equations can be combined as:

Which can be written as:

D-D Fusion

Deuterium must be moving extremely fast to fuse.

D-T Fusion

• The most promising of the hydrogen fusion reactions which make up the deuterium cycle is the fusion of deuterium and tritium.

• The reaction yields 17.6 MeV of energy but requires a temperature of approximately 40 million Kelvins to overcome the coulomb barrier and ignite it.

• The deuterium fuel is abundant, but tritium must be either bred from lithium or gotten in the operation of the deuterium cycle.

Deuterium-Tritium Fusion Using Lasers

Laser evaporates D-T, creating a "plasma" of charged particles which push away from one another.  The reaction force compresses and heats core

Thermonuclear Weapons

The hydrogen bomb uses an atomic bomb as the heat source to fuse hydrogen into helium.  The so-called H-bomb is vastlymore destructive than fission bombs.  The Hiroshima bomb hadhad explosive power of about 20,000 tons of TNT; H-bombs commonly have 50-500 times the power (1-10 megatons).

Bikini Atoll, in the Marshall Islands (1954)

Fusion Compared with Fission

If the final products have less mass than the reactants, energy is released.

Fission versus Fusion

A Binding Energy Comparison of Fission and Fusion

The buildup of heavier elements in the nuclear fusion processes in stars is limited to elements below iron, since the fusion of iron would subtract energy rather than provide it.

Comparison of Fission and Fusion Yields

Fuel• U-238 – 99 % of uranium on Earth, • U-235 - 0.7 %• Both decay naturally by alpha radiation, but U-235 can

undergo induced fission. • Plutonium-239 is created by bombarding U-238 with

neutrons• Uranium must be enriched so it contains more U-235.

– 3% for nuclear power plants – 90% for weapons-grade uranium

Fuel

• Splitting an atom releases large amounts of heat and gamma radiation.

• The difference in mass between products and the original U-235 atom is converted to energy according to Einstein’s famous E = mc².

Fission vs. Fusion

• Fission – the splitting of a nucleus; used for reactors and weapons

• Fusion – the fusing of two nuclei; used in weapons and occurs in outer space (stars)

Drill

If an atom of nitrogen-13 releases a positron, what particles would be present in the nucleus?

What type of decay is this?

Objectives

Compare nuclear force with other forces.Describe fission and fusion.Apply mass-energy equivalence.

Nuclear Fission

Nuclear Fission

Average number of neutronsreleased is 2.5.

Average combined kinetic energy of particles is about 200 MeV.

100,000,000 times more energy than is released when coal is burned:

C + O2 => CO2

(about 2 eV)

Critical Mass

The smaller the sphere, the greater the ratio of surface area to volume, and the greater the percentage of neutrons which escape the sphere before causing fission. Critical mass--or, critical size--is that mass value at which each fission event produces an average of one more fission event.

Fusion

Fusion is the opposite of fission. Deuterium must be moving extremely fast to fuse.

Deuterium-Tritium Fusion

Neutrons carry away 80 %of the energy released

Fusion versus Fission

If the final products have less mass than the reactants, energy is released.

Nuclear fission

• http://library.thinkquest.org/17940/texts/fission/fission.html

Nuclear reactors

What is Happening in Japan

• http://www.nytimes.com/interactive/2011/03/12/world/asia/the-explosion-at-the-japanese-reactor.html?ref=asia