CHM 123Chapter 19
19.5 Radioactive decay rates - Dating
Radioactive carbon-14 is constantly being generated in the upper atmosphere by neutron bombardment:
Carbon-14 eventually enters the food chain via the formation of carbon dioxide and its uptake by plants via photosynthesis. Eating these plants distributes carbon-14 throughout all living organisms
Because the half-life of any nuclide is constant, the amount of substance remaining in an artifact can serve as a nuclear clock to determine ages of objects. When an animal is alive it maintains a caron-14 to carbon-12 ratio identical to that in the atmosphere. When it dies, this ratio decreases. By measuring this ratio and contrast it to the atmosphere, we can get an approximate age.
Radioactive decay is a first order process
Example: The decay constant for sodium-24, a radioisotope used medically in blood studies, is 4.63 × 10−2h−1. What is the half-life of Na-24?
Example: A wood artifact is found to have a C-14 activity of 9.1 disintegrations per second. Given that the C-14 activity of an equal mass of fresh-cut wood has a constant value of 15.2 disintegrations per second, determine the age of the artifact. The half-life of C-14 is 5730 years.
Example: A rock is found to contain 5.51 mg of U-238 and 1.63 mg of Pb-206. Determine the age of the rock (t ½ of U-238 is 4.51 x 109yrs.)
Example: What is the age of a rock whose Ar-40/K-40 ratio is 1.15? The half-life of K is 1.28 x 109 years.
19.5 – Energy Changes During Nuclear Reactions:
It should be possible to measure the str3ngth of the forces holding a nucleus together by measuring the amount of energy necessary to tear the nuclear apart into its component protons and neutrons. For example,with Helium-4 nucleus,the energy change associated with combining two neutrons and two protons to form Helium-4 is a direct measure of Helium-4 stability.
*Recall: Activation energy is the potential energy barrier that must be surmounted before reactants can be converted to products. The height of the barrier controls the rate of the reaction
Every process that releases energy is accompanied by an equivalent loss of mass. Every process that absorbs energy results in a gain of mass. The mass changes accompanying chemical reactions are too small to measure but mass changes due to nuclear reactions can be measured using a mass spectrometer
Mass Defect: The loss in mass that occurs when protons and neutrons combine to form a nucleus. Thus, the mass of a nucleus is less than the sum of the masses of the protons and neutrons from which it is composed!
Δm = mass of nucleons– actual mass
The loss in mass is converted into energy that is released during the nuclear reaction and is thus a direct measure of the binding energy holding the nucleons together
Nuclear Binding energy of a nucleus is the energy needed to break a nucleus into its individual protons and neutrons. The larger nuclear binding energy, the more stable the nucleus
Einstein discovered that matter could be converted to energy (and vice-versa). The equation that expresses this mass-energy equivalency is:
E = mc2 (c = 3.00x108 m/s)
Or
ΔE = (Δm)c
Example: Determine the nuclear binding energy of the copper-63 atom.
Find the mass defect of a copper-63 nucleus if the actual mass of a copper-63 nucleus is 62.914 amu.
Copper has 29 protons and copper-63 also has (63 - 29) 34 neutrons.
The mass of a proton is 1.00728 amu and a neutron is 1.00867 amu.
- The combined mass or mass of nucleons is calculated:
- Calculate the mass defect.
Δm =
Conversion of Mass Defect into Energy
To convert the mass defect into energy:
- Convert the mass defect into kilograms (1 amu = 1.6606 x 10-27 kg)
- Convert this mass into energy using ΔE = Δmc2, where c = 3.00 x 108 m/s.
The energy calculated in the previous example is the nuclear binding energy. However, nuclear binding energy is often expressed as kJ/mol of nuclei or as MeV/nucleon.
- To convert the energy to kJ/mol of nuclei we will simply employ the conversion factors for converting joules into kilojoules (1 kJ = 1000 J) and for converting individual particles into moles of particles (Avogadro's Number).
To convert the binding energy to MeV (megaelectron volts) per nucleon we will employ the conversion factor for converting joules into MeV (1 MeV = 1.602 x 10-13 J) and the number of nucleons (protons and neutrons) which make up the nucleus.
Example:Determine the nuclear binding energy per nucleon (MeV)for Osmium190.
mass of 190Os = 189.95863 amumass of neutron = 1.008664 amumass of proton = 1.007276 amu
Example:Calculate the binding energy (kJ/mol)
The nuclei in the reaction have the following masses
U-238 = 238.0003 amu, Th-234 = 233.9942 amu and 42He = 4.0015 amu
The binding energy per nucleon for most nuclei falls around 1.3 x 10-12 J (8 MeV). A plot of binding energy per nucleon vs. mass number shows that the most stable nuclei occur around A = 50 to 60. Fe56 is the most stable nucleus in the universe. The existence of a maximum in this curve indicates that energy is released in either a fission or fusion process in which more stable nuclei (i.e., closer to 56Fe) are produced.
Binding energy per nucleon generally increases from small atoms to atoms with mass number around 56. Thus fusing atoms to form medium-size atoms (nuclear fusion) release energy.
Binding energy per nucleon generally decreases from atoms with mass number around 56 and larger. Thus splitting larger atoms to form medium-sized atoms (nuclear fission) also releases energy.
19.6 Nuclear Fission and Nuclear Fusion
Nuclear fission and nuclear fusion are reactions in which nuclei attain size closer to the intermediate range (A = 50)
In nuclear fission,
•a large nucleus is bombarded with a small particle.
•the nucleus splits into smaller nuclei and several neutrons.
•large amounts of energy are released.
When a neutron bombards 235U,
•an unstable nucleus of 236U undergoes fission (splits).
•smaller nuclei are produced, such as Kr-91 and Ba-142.
•neutrons are released to bombard more 235U.
The result is a chain reaction that continues to occur even if the external supply of bombarding neutrons is cut off.
If the sample is too small, many of the neutrons leave the sample before they have a chance to be absorbed
-Critical mass is the smallest mass of fissionable material in which a chain reaction can be sustained
Similarly, a nuclear-powered electicity generation plant can produce lot of electricity froma small amount of fuel. Such plants exploi the heat created by fission, using it to boil water andmake steam, which then turns the turbine on a generator to produce elctricity. The fission reaction occurs in the neclear core of the power plant. The core consists of of about 3.5% U-235 interspersed between retractable neutron-absorbing control rods. Controls rods are needed to absorbed neutrons that would induce fission, shutting down the chain reaction.
Nuclear fusion
The fusion reaction normally takes place in a plasma of deuterium and tritium heated to millions of degrees. It’s the fusion reaction of hydrogen nuclei to produce helium that powers our sun and other stars. To get the nuclei to react, the bombarding nucleus must have enough kinetic energy to overcome the repulsion of electric charges of the nuclei. Because no known material can withstand such high temperatures, fusion reactors use strong magnetic fields to confine the reaction
Advantages: Relatively cheap fuel source and the products are nontoxic.
Disadvantage: A temperature of 40 millionKelvin is needed to initiate the process.
19.7 – Nuclear Transmutation
Nuclear Transmutation: The change of one element into another. Such transmutation is often brought about by bombardment of an atom with a high energy particle such as a proton, neutron or α-particle. In the ensuing collision energy between particle and atom, an unstable nucleus is momentarily created, a nuclear change occurs, and a different element is produced. The first nuclear transmutation was accomplished in 1917 by Ernest Rutherford
Examples:
a)Plutonium-241 can be made by bombarding uranium-238 with alpha particles:
b)In another fission reaction, U-235 bombarded with a neutron produces Sr-94, another small nucleus, and 3 neutrons. Write the complete series of equation for the fission reaction
d) Cobalt-60 is used in radiation therapy for cancer patients. The overall preparation process can be written as
19.4 – Detecting and Measuring Radioactivity
Radioactive emissions are invisible. We can’t see, hear, smell, touch or taste them, no matter how high the dose. We can, however, detect radiation by measuring its ionizing properties.
Radioactivity can be instantly detected with devices such as a Geiger-Muller counter. In this instrument, particles emitted by radioactive nuclei pass through an argon-filled chamber. The energetic particles create a trail of ionized argon atoms. High voltage applied between a wire within the chamber and the chamber itself causes these newly formed ions to produce an electrical signal that can be displayed on a meter
Ionizing Radiation: Radiation that knocks an electron from a molecule, thereby ionizing it.
-Including not only α-particle, β-particle, γ-particle but also X-ray and cosmic ray
Another method is to measure the number of decay events to which a person is exposed, or amount of energy absorbed by body tissue. Radiation intensity is expressed in different ways, depending on what is being measured. See Table 19.2 and 19.4 for some units measure the number of nuclear decay events.
19.9 – Application of Nuclear Chemistry
Medical Application:
Radioisotopes with short half-lives are used in nuclear medicine because
•They have the same chemistry in the body as the nonradioactive atoms.
•In the organs of the body, they give off radiation that exposes a photographic plate (scan), giving an image of an organ.
•In Vivo Procedures
•Determination of whole-blood volume using red blood cells labeled with chromium-51.
•Therapeutic Procedures
•Irradiation of tumors using gamma rays emitted from cobalt-60.
•Beta emission of iodine-131 to treat thyroid disease.
•Imaging Procedures
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