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- At 8:00 a.m., a patient receives a 1.5-mg dose of I-131 to treat thyroid cancer. If the nuclide has a half-life of eight days, what mass of the nuclide remains in the patient at 5:00 p.m. the next day? (Assume no excretion of the nuclide from the body.)
Problem 48
Problem 49
A sample of F-18 has an initial decay rate of 1.5⨉105/s. How long will it take for the decay rate to fall to 2.5⨉103/s? (F-18 has a half-life of 1.83 hours.)
- A wooden boat discovered just south of the Great Pyramid in Egypt has a carbon-14 to carbon-12 ratio that is 72.5% of that found in living organisms. How old is the boat?
Problem 51
- A layer of peat beneath the glacial sediments of the last ice age has a carbon-14 to carbon-12 ratio that is 22.8% of that found in living organisms. How long ago was this ice age?
Problem 52
- An ancient skull has a carbon-14 decay rate of 0.85 disintegrations per minute per gram of carbon (0.85 dis/min/g C). How old is the skull? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min/g C and that carbon-14 has a half-life of 5715 years.)
Problem 53
Problem 54
A mammoth skeleton has a carbon-14 decay rate of 0.48 disintegration per minute per gram of carbon (0.48 dis/min • g C). When did the mammoth live? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min • g C and that carbon- 14 has a half-life of 5715 yr.)
Problem 55
A rock from Australia contains 0.438 g of Pb-206 for every 1.00 g of U-238. Assuming that the rock did not contain any Pb-206 at the time of its formation, how old is the rock?
- A meteor has a Pb-206:U-238 mass ratio of 0.855:1.00. What is the age of the meteor? (Assume that the meteor did not contain any Pb-206 at the time of its formation.)
Problem 56
Problem 57
Write the nuclear reaction for the neutron-induced fission of U-235 to form Xe-144 and Sr-90. How many neutrons are produced in the reaction?
Problem 58
Write the nuclear reaction for the neutron-induced fission of U-235 to produce Te-137 and Zr-97. How many neutrons are produced in the reaction?
Problem 59
Write the nuclear equation for the fusion of two H-2 atoms to form He-3 and one neutron.
Problem 60
Write the nuclear equation for the fusion of H-3 with H-1 to form He-4.
- A breeder nuclear reactor is a reactor in which nonfissionable (nonfissile) U-238 is converted into fissionable (fissile) Pu-239. The process involves bombardment of U-238 by neutrons to form U-239, which then undergoes two sequential beta decays. Write nuclear equations for this process.
Problem 61
- Is the series of nuclear equations to represent the bombardment of Al-27 with a neutron to form a product that subsequently undergoes a beta decay written correctly?
Problem 62
Problem 63
Rutherfordium-257 was synthesized by bombarding Cf-249 with C-12. Write the nuclear equation for this reaction.
- Element 107, now named bohrium, was synthesized by German researchers by colliding bismuth-209 with chromium-54 to form a bohrium isotope and one neutron. Write the nuclear equation that represents this reaction.
Problem 64
Problem 65
If 1.0 g of matter is converted to energy, how much energy is formed?
Problem 66
A typical home uses approximately 1.0⨉103 kWh of energy per month. If the energy came from a nuclear reaction, what mass would have to be converted to energy per year to meet the energy needs of the home?
Problem 67
Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. O-16 (atomic mass = 15.994915 amu) b. Ni-58 (atomic mass = 57.935346 amu) c. Xe-129 (atomic mass = 128.904780 amu)
Problem 68
Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. Li-7 (atomic mass = 7.016003 amu)
Problem 69
Calculate the quantity of energy produced per gram of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to form Xe-144 (atomic mass = 143.9385 amu) and Sr-90 (atomic mass = 89.907738 amu) (discussed in Problem 57).
Problem 70
Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58).
- Calculate the quantity of energy produced per gram of reactant for the fusion of two H-2 (atomic mass = 2.014102 amu) atoms to form He-3 (atomic mass = 3.016029 amu) and one neutron.
Problem 71
- Calculate the quantity of energy produced per gram of reactant for the fusion of H-3 (atomic mass = 3.016049 amu) with H-1 (atomic mass = 1.007825 amu) to form He-4 (atomic mass = 4.002603 amu).
Problem 72
Problem 73
A 75-kg human has a dose of 32.8 rad of radiation. How much energy is absorbed by the person's body? Compare this energy to the amount of energy absorbed by the person's body if he or she jumped from a chair to the floor (assume that the chair is 0.50 m from the ground and that all of the energy from the fall is absorbed by the person).
- If a 55-gram laboratory mouse is exposed to a dose of 20.5 rad of radiation, how much energy is absorbed by the mouse’s body?
Problem 74
- PET studies require fluorine-18, which is produced in a cyclotron and decays with a half-life of 1.83 hours. Assuming that the F-18 can be transported at 60.0 miles/hour, how close must the hospital be to the cyclotron if 65% of the F-18 produced makes it to the hospital?
Problem 75
Problem 76
Suppose a patient is given 1.55 mg of I-131, a beta emitter with a half-life of 8.0 days. Assuming that none of the I-131 is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?
Problem 77
Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each (Be-9 = 9.012182 amu, Bi-209 = 208.980384 amu, He-4 = 4.002603 amu, Li-6 = 6.015122 amu, Ni-64 = 63.927969 amu, Rg-272 = 272.1535 amu, Ta-179 = 178.94593 amu, and W-179 = 178.94707 amu). a. _____ + 94Be → 63Li + 42He
Problem 78a
Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each (Al-27 = 26.981538 amu, Am-241 = 241.056822 amu, He-4 = 4.002603 amu, Np-237 = 237.048166 amu, P-30 = 29.981801 amu, S-32 = 31.972071 amu, and Si-29 = 28.976495 amu).
a. 2713Al + 42He → 3015P + ____