Do Now (5/2/12): What is an istope? What makes an isotope different than its element?

Nuclear Reactions 5/2/12 

Apply radioactivity equations by solving problems. 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 neutrons A = Atomic mass A = 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 E = mc2 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.)

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

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 Pb

Types of radiation Alpha – a helium nucleus (two neutrons, two protons) Beta – a high energy electron Gamma – high energy photons

Penetrating Power He (nucleus) e-

Alpha (α) Decay The parent nucleus loses a cluster of 2 protons and 2 neutrons. 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. + + + + + + e + Watch this neutron

Energy Release in Decay Mass of Parent Atom = 14.003242 u Combined mass of products = 14.003074 u

                                             

the nucleus of an atom emits an alpha particle Alpha decay the nucleus of an atom emits an alpha particle

Nucleus of a helium atom 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.

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.

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

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 U 92 4 231 He + Th 2 90 209 4 231 He + Th 2 90 209 Po 84 4 205 He + Pb 2 82

Decay Sequence Beta decay sequence: 14 C 6 14 0 N + e 7 -1 228 Ra 88 14 0 N + e 7 -1 228 Ra 88 228 0 Ac + e 89 -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

Protons and neutrons in the nucleus  are collectively referred to as  nucleons. The Strong Force Protons which would otherwise strongly repel at close distances are held in place by an extremely strong, but extremely short range force called the strong force. Other names for the strong force are strong nuclear force, or nuclear force. The strong force between two protons is about the same as the strong force between two neutrons, or a proton and a neutron. Beyond about one fermi the strong force declines extremely rapidly. As more protons are added to the nucleus, more neutrons are needed to bind the protons together, but the larger the nucleus becomes, the farther apart are the protons and the less effective is the strong force

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, so the binding energy per nucleon is about 28/4, or about 7 MeV per nucleon.

Binding Energy per Nucleon Nuclei with the largest binding energy per nucleon are the most stable. ----------------------------------------------------- The largest binding energy per nucleon is 8.7 MeV, for mass number A = 60. Beyond bismuth, A = 209, nuclei are 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 particle is now known to be just an electron. Is the nucleon count conserved? Is the total charge conserved?

Reaching Stability Through Gamma Ray Emission Nuclei with excess energy emit gamma-rays, which are extremely short- wavelength electro- magnetic waves, i.e., very high energy photons.

Nuclear Notation

Alpha Particle Emission The alpha particle is a helium nucleus.

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 particle has the greater kinetic energy?

Energy Distribution in Radioactive Decay Conservation of momentum: Mv = mV                              (2) Rearranging, we get V/v = M/m                           (3)     Substitute (3) into (1): Ratio = (m/M)(M/m)2          (4)          = M/m Smaller mass gets more energy Ratio of kinetic energies:  KEm / KEM:   (1/2 mV2) / (1/2 Mv2) = (m/M)(V2/v2)                                      = (m/M)(V/v)2    (1)

Marie Curie Marie and Pierre Curie isolated 1/30 ounce of radium from one ton of uranium ore. Marie died from radiation-induced leukemia. The pages of her lab notebook were later found to be contaminated with radioactive fingerprints. Lithograph entitled "Radium" appeared in the December 22, 1904 issue of Vanity Fair. Marie Sklodowska Curie           (1867-1934)

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

Plutonium Powered Light Sphere Six ounces (170 grams) of plutonium dioxide inside graphite-iridium container. Alpha particles colliding with graphic casing heats it to 1000 degrees centigrade. Sphere radiates about 100 watts of light energy, and will continue to do so for decades. 94Pu239 -----> 92U235 + a

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, causing the alarm to buzz.

Beta Particle (Electron) Emission The neutron number of an electron is zero, and the proton number is negative one.   Negative beta particles are emitted when a neutron is transformed into a proton and an electron. 90Th234   ------>  91Pa234  + -1e0

Beta Particle (Electron) Emission by Carbon-14 6C14 -----> 7N14 + -1e0 The subscripts represent the "proton" number (electrons have a negative) proton number. Superscripts represent the nucleon number; electrons are not nucleons, so their nucleon number is zero.

Beta Particle (Positron) Emission by Oxygen-15 8O15 -----> 7N15 + 1e0 The subscripts represent the "proton" number (a positron has a positive proton number) Superscripts represent the nucleon number; positrons are not nucleons, so their nucleon number is zero. 15 A positron has the same mass as the electron, but opposite charge.

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 fermi This gamma radiation is extraordinarily harmful to humans and other living things since its wavelength is comparable to the diameter of a nucleon; transmutations are likely when such radiation reaches nuclei.

Brain Surgery with the Gamma Knife

The Geiger Counter Hans Geiger invented the "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 the existence of the nucleus

The Scintillation Counter Scintillator is material which will emit photons when struck by high energy charged particles or high energy photons. Photon strikes metal plate, ejecting electrons which are pulled toward 100 V anode. The anode is coated with a material which is easily ionizable and releases two or more electrons for each one that 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 neutrons released 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 MeV to about 8.5 MeV per nucleon. Mass difference is about one MeV per nucleon. If A = 235, then energy released is 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 u Mass of six neutrons= 6 x 1.0087 u = 6.0522 u Total mass of particles= 12.0990 u Mass of C12= 12.0000 u Loss in mass on forming C12= 0.0990 u Binding energy= 931 MeV x 0.0990= 92 MeV

Slow Neutrons Cause Chain Reactions Slow neutrons are required. A chain reaction occurs if more than one neutron goes on to cause another fission. Neutrons can be slowed by bouncing them off of small objects, such as carbon nuclei. One pound of U-235, if completely fissioned, yields the same energy as 100,000,000 pounds of coal.

Cadmium Control Rods Absorb Neutrons Enrico Fermi supervised construction of the world's first nuclear reactor. 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 Dr. Robert J. Oppenheimer and Maj. Gen. Leslie L. Groves, Trinity Site--5:30 am, July 16, 1945, Alamogordo, New Mexico.

 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 masses are smashed together to create a super-critical mass.

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 center hole

Energy From Fission ~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 165 MeV 7 MeV 6 MeV 7 MeV 6 MeV 9 MeV 200 MeV

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

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

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 fission in uranium rods creates steam which turns turbine blades connected to a coil 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

Uranium Fission Process

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 Bikini Atoll, in the Marshall Islands (1954) The hydrogen bomb uses an atomic bomb as the heat source to fuse hydrogen into helium.  The so-called H-bomb is vastly more destructive than fission bombs.  The Hiroshima bomb had had explosive power of about 20,000 tons of TNT; H-bombs commonly have 50-500 times the power (1-10 megatons).

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 neutrons released 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