The isotope 238 U decays to 206Pb with a half-life of 4.47 x 10° y. (Although the decay occurs in many individual steps, the first step has by far the longest half-life, so the decay can be considered to go straight to lead.) A rock recovered far underground is found to contain 0.76 mg of 238 U, 0.17 mg of 206pb, and 1.4 mg of 40 Ar. Assume that 40K decays to only 40 Ar with a half-life of 1.25 x 10 y. How much 40K will it likely contain? me
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- In a piece of rock from the Moon, the 8/Rb content is assayed to be 1.89×1010 atoms per gram of material and the 8/Sr content is found to be 1.08x109 atoms per gram. (The relevant decay is 87Rb → 87Sr + e¯. The half-life of the decay is 4.8 x 10 yr.) 10 (a) Determine the age of the rock. yr (b) Could the material in the rock actually be much older? No, it could not be any older. Yes, it could be much older. (c) What assumption is implicit in using the radioactive-dating method? We assume that none of the 8/Sr nuclei came from the decay of 8/Rb nuclei. We assume that all of the 8'Sr nuclei came from the decay of 8'Rb nuclei. We assume that some of the 8Sr nuclei came from the decay of 87 Rb nuclei while the rest was present initially.Potassium-argon dating is used to measure the age of rocks formed from cooled lava by determining the fraction of the original 40K remaining in a sample from the ratio of 40K:40Ar. Unusually, potassium-40 decays into both 40Ca (89.1% of the time) and 40Ar (10.9% of the time) with a half-life of 1:248 x 109 years. What is the calculated age of a sample in which the faction of 40K remaining was found to be 0.0043? Is this result physically plausible and why?An ancient club is found that contains 140 g of pure carbon and has an activity of 4 decays per second. Determine itsage assuming that in living trees the ratio of (14C/12C) atoms is about 1.00*10^-12 . Note that the half life of carbon-14 is 5700 years and the Avogadro number is 6.02*10^23
- In the 1986 disaster at the Chernobyl reactor in eastern Europe, about 1 8 of the 137 Cs present in the reactor was released. The isotope 137 Cs has a half-life of 30.07 y for β decay, with the emission of a total of 1.17 MeV of energy per decay. Of this, 0.51 MeV goes to the emitted electron; the remaining 0.66 MeV goes to a γ ray. The radioactive 137 Cs is absorbed by plants, which are eaten by livestock and humans. How many 137 Cs atoms would need to be present in each kilogram of body tissue if an equivalent dose for one week is 3.5 Sv? Assume that all of the energy from the decay is deposited in 1.0 kg of tissue and that the RBE of the electrons is 1.5.A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 0.8 kg sample of carbon from the wood has an activity of 1550 decays per minute. Find the age of the charcoal. Living material has an activity of 15 decays/minute per gram of carbon present and the half-life of 14C is 5730 y. Answer in units of y.The isotope 1321 decays by ß- emission into stable 132 Xe with a half-life of 2.3 h. (a) How long will it take for of the original 132 I atoms to decay? (b) How long it will take for a sample of 132 I to lose 95% of its activity? 1012 of 14℃ in
- Problem 8: In a living organism, a fixed fraction 1.30 × 10-12 of 12C is the radioactive isotope 14C, which has a half life of 5730 y. What is the activity of the 14C in 1.8 g of 12C found in living tissue in Bq?Numeric : A numeric value is expected and not an expression.R = __________________________________________A particular rock is thought to be 234 million years old. If it contains 4.84 mg of 238U, how much 206 Pb should it contain? Assume 238U decays directly to 206PB with a half-life of 4.47 × 109 y.A nucleus of copper has an atomic mass of 64.93 u (with Z=29 and A=65). Considering that the mass of a neutron and a proton are respectively 1.00866 u and 1.00728 u. What is the total binding energy of that nucleus? (Expressed in MeV)
- The half-life for the a decay of uranium 2U is 4.47 x 10° yr. Determine the age (in years) of a rock specimen that contains 48.6% of its original number of U atoms. t-Number i UnitsA radium source contains 1.00 mg of 226Ra, which decays with a half-life of 1600 y to produce 222Rn, a noble gas. This radon isotope in turn decays by alpha emission with a half-life of 3.82 d. If this process continues for a time much longer than the half-life of 222Rn, the 222Rn decay rate reaches a limiting value that matches the rate at which 222Rn is being produced, which is approximately constant because of the relatively long half-life of 226Ra. For the source under this limiting condition, what are (a) the activity of 226Ra, (b) the activity of 222Rn, and (c) the total mass of 222Rn?98/43Tc decays by emitting a 140 keV gamma ray—a highenergy photon. The mass of the nucleus is approximately 98 u. By what fraction does the mass of the nucleus decrease when the gamma ray is emitted?