Nuclear Powe Bronze Buddha at Hiroshima
Nuclear Weapons
Nuclear Power Is it Green & Safe?
Nuclear Waste 250,000 tons of Spent Fuel 10,000 tons made per year
Health Effects of Ionizing Radiation
Radiocarbon Dating
Atomic Notation Atomic Mass Number A = # protons + neutrons A Z X Atomic # 1 3 238 1H, 1H, 92U Atomic Number Z = # protons Neutron Number N N = # neutrons N = A - Z
Atomic Mass Units 1u = 1/12 mass of Carbon-12 1u = 1.6605x10 kg = 931.5 MeV / c 27 2 238.0508u 234.0436u 4.0026u Δ m= 238.0508 234.0436 4.0026 u = 0.0046u ( ) 2 2 2. E =Δ mc = 0.0046 u(931.5 MeV / c ) c = 4.3MeV
Some Masses in Various Units
All Elements Have Isotopes Same # 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.
The Size of the Nucleus d = 4 e kze 2 mv 2 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
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 r 3 would be proportional to A Nucleons combine to form a nucleus as though they were tightly packed spheres Average radius is Nuclei r = r A o 13 r o = 1.2 x 10-15 m A is the mass number
Protons repel each other! How is an Atomic Nucleus Stable?
Strong Force is STRONGER than the Coulomb Force over short distances: Short Range Force F Strong ~100F Coulomb 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.
Fission Heavy elements FISSION into lighter elements, releasing energy in the process by E = Δmc 2, where Δm is the difference in mass between the parent and products. ~ 25 MeV is released in this reaction Most of the Energy is released in the form of Kinetic Energy (heat).
Fusion Light elements FUSE into larger elements, releasing energy in the process by E = mc 2.
Nuclear Radiation Atomic decay by Alpha and Beta radiation causes atomic transmutation. Gamma radiation does not transmutate the atom, it changes its energy.
Alpha Decay Atomic Mass Number, A, and charge is conserved for all reactions!
Beta Decay Atomic Mass Number, A, and charge is conserved for all reactions! Neutrino: Weak Force Mass ~ 0, conserves momentum
Spontaneous Nuclear Decay: Fission Beta Decay Neutron Decay into a Proton (Neutron Half life ~ 12 minutes) Alpha Decay
There is NO Spontaneous Fusion 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.
Natural Transmutation Spontaneous 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 232 Th Series starts with 232 Th Processes through a series of alpha and beta decays The series branches at 212 Bi Ends with a stable isotope of lead, 208 Pb
Radioactive Series Natural 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 [ 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. dn() t A = = λnt () dt A] = Becquerel( Bq) = 1 disintegration/second A CURIE is the activity of 1 gram of Radium. 10 1 = 3.7 10 ~ Ci x Bq billion Bq Example: Activity of 1Kg of Carbon is ~250 Bq ~ 7nCi Inhaling a sample with 1μCi of activity will kill you. Chernobyl released 50 million curies into the atmosphere.
From the activity we derive the following useful items: The decay rate R of a sample is defined as the number of decays per second: R o = N o λ is the decay rate at t = 0. dn() t A = = λnt () dt Rt ( ) = Re The amount of undecayed radioactive particles present in the sample at any time t is: o N( t ) = N e o λt λt λ is called the decay constant and determines the rate at which the material will decay N o is the number of undecayed nuclei at time t = 0
Half Life N( t ) = N e o λt The half life of a radioactive element is the time it takes for a quantity to decay to 1/2 its original amount, N 0.
Activity & Half Life The # of radioactive nuclei present at any time t since t = 0 when the # was N 0 : Decay Constant: Nt () = N /2 0 dn A = = λn dt e λt 1/2 = 1/2 Nt () = Ne λt 1/2 ln e λt = ln1/ 2 λt 1/2 = ln 2 0 λ = ln 2 t 1/2 (ln2=0.693)
Carbon Half-Life Carbon-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 8.3x10 11 atoms of C-12. C N + β 14 14 6 7
Activity: Rate of Disintegration Determine the activity of C-14 in a gram of a living organism. There is 1 atom of C-14 for every 8.3x10 11 atoms of C-12. # C-14 atoms in 1 gram of C: 23 mol 6.02x10 C12 1C14 10 = 1g 6.0x10 C14atoms 11 = 12g mol 8x10 C12 A = λn 0.693 1yr = 610 x 7 5730yr 3.15x10 s =.23Bq λ = 0.693 t 1/2 = 0.693 5730 yr 10 atoms
Carbon Dating While 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 Iceman Material 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. Given: A0 = 0.23 Bq @ t = 0 A= 0.121 Bq @ t = now A= Ae λt λt ln A/ A = ln e = λt 0 0 0.693 λ = t 1/2 t1/2 = 5730yr 1 t = ln A 0 / A λ 5730yr = ln.23/.121 = 5310yr 0.693
Moon Rock Problem In a piece of rock from the Moon, the 87 Rb content is assayed to be 1.82 10 10 atoms per gram of material, and the 87 Sr content is found to be 1.07 10 9 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 10 10 yr. 87 Rb decays by: 87 Rb 87 Sr + e + v 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?