A radioactive sample at a lab contains a mixture of 223Ra and 47Ca. There are initially twice as many calcium atoms as there are radium atoms. What is the ratio of calcium atoms to radium atoms 1.50 weeks later? (Note that there are no units in this answer.)
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A radioactive sample at a lab contains a mixture of 223Ra and 47Ca. There are initially twice as many calcium atoms as there are radium atoms. What is the ratio of calcium atoms to radium atoms 1.50 weeks later? (Note that there are no units in this answer.)
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- One method for determining the age of ancient objects is by radiocarbon dating. Natural processes convert nitrogen to Carbon-14, a radioactive isotope with a half-life of 5730 years. When they are alive, animals assimilate Carbon-14 through the food chain. When an animal dies, it stops replacing its carbon and the amount of Carbon-14 decays exponentially. (a) Suppose the minimum detectable amount is 0.1% of the initial amount. What is the maximum age of a fossil that we could date using Carbon-14? (b) Suppose we wanted to date a fossil that was potentially 70 million years old. A radioactive isotope with what half-life would be required?Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32, in milligrams, is left from an original sample of 175 mg of Na "PO, after 38.8 days? Assume that the atomic mass of 32P is 32.0.The rate of decay of a radioactive material is directly proportional to the amount of the material present, with the constant of proportional denoted by k. If the half-life of the material is 2.02 years, find k.
- An unknown radioactive element decays into non-radioactive substances. In 360 days the radioactivity of a sample decreases by 34 percent. (a) Find the decay constant k. (Round your answer to 5 decimal places.) (b) What is the half-life of the element? (Round your answer to two decimal places) half-life: (days) (c) How long will it take for a sample of 100 mg to decay to 59 mg? (Round your answer to two decimal places) time needed: (days)A sample of a radioactive substance has an initial mass of 63.3 mg. This substance follows a continuous exponential decay model and has a half-life of 5 days. (a) Let t be the time (in days) since the start of the experiment, and let y be the amount of the substance at time t. Olno Write a formula relating y to t. Use exact expressions to fill in the missing parts of the formula. Do not use approximations. y = (b) How much will be present in 13 days? Do not round any intermediate computations, and round your answer to the nearest tenth. O mg I Don't Know Submit O2021 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy Center | Accessibility MacBook Ai F11 80 888 F10 FB F9 F7 F6 esc F3 F4 F5 F2 $ 8 9 * 00An accident at a nuclear power plant has left the surrounding area polluted with radioactive material that decays naturally. The initial amount of radioactive material present is 42 su (safe units), and 5 months later it is still 31 su. a.) write a formula giving the amount A(t) of radioactive material (in su) remaining after t months. (Use integers or decimals for any numbers in the expression. Round to three decimal places needed.) b.) what amount of radioactive material will remain after 11 months? c.) how long will it be until A = 1 su, so it is safe for people to return to the area?
- Suppose you are working as a reactor operator in the world’s largest nuclear power station at Kashiwazaki-Kariwa Nuclear Power Plant, Japan. The first unit in this station began to operate in 1985. Suppose the rate at which the nuclear power plant produces radioactive waste is proportional to the number of years it has been operating such that 500 pounds of waste is produced every year. Also, suppose that the waste decays exponentially at a rate of 5% per year. At the beginning of 2011, The Fukushima Daiichi nuclear disaster caused sever damages in the units which released the radiation waste to the atmosphere. Therefore, all the units were closed in 2011 for safety inspection. This left japan completely without nuclear-produced electrical power. Finally, the unit began to operate at the beginning of 2019. As a reactor operator, you are asked to do the following: a. Model the generation of the Kashiwazaki-Kariwa Nuclear Power Plant radioactive waste as a function of time. b.…RADIOACTIVITY. LAW OF RADIOACTIVE DECAY Activity units: 1 Ci = 3.7 × 101º Bq 1. Nuclear decay law: N = Noe¬at, The law of radioactive decay gives the quantitative relationship between the original number of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828... is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s). 2. Relationship between decay constant 2 and isotop half-life T1/2: In(2) 0.693 Radioisotope Half-life Modality T1/2 T1/2 Carbon-11 20 minutes PET where a is decay constant (1/s), T1/2 is isotope half- life (s). 3. Activity or decay rate of a radioactive source A: ΔΝ Fluorine-18 110 minutes PET Copper-64 12.7 hours PET Gallium-67 78.3 hours SPECT Gallium-68 68 minutes PET = AN Technetum-99m 6.02 hours SPECT Δt where A is activity or decay rate of a radioactive source (Bq), N is number of nuclei present at time t (s ), 1 is decay constant (1/s). 4. Activity A of a radioactive source at a time t:…There was a sample of 500 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 2.6% each year. Let & be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between y and t.
- At the beginning of an experiment, a scientist has 252 grams of radioactive goo. After 195 minutes, her sample has decayed to 3.9375 grams. What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. G(t) || How many grams of goo will remain after 32 minutes?The half-life of phosphorus-32 is about 14days. There are 6.6 grams present initially.a. Express the amount of phosphorus-32 remaining as a function of time t.b. When will there be 1 gram remaining?RADIOACTIVITY. LAW OF RADIOACTIVE DECAY Activity units: 1 Ci = 3.7 × 1010 Bq 1. Nuclear decay law: N = Noe¬at, The law of radioactive decay gives the quantitative relationship between the original number of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828... is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s). 2. Relationship between decay constant 1 and isotop half-life T1/2: 0.693 T1/2 1= In(2) Half-life Modality Radioisotope T1/2 where a is decay constant (1/s), T1/2 is isotope half- life (s). Carbon-11 20 minutes PET Fluorine-18 110 minutes PET Copper-64 | 12.7 hours PET 3. Activity or decay rate of a radioactive source A: Gallium-67 AN A = At where A is activity or decay rate of a radioactive lodine-123 source (Bq), N is number of nuclei present at time t Thallium-201 (s ), 2 is decay constant (1/s). 78.3 hours SPECT | 68 minutes Gallium-68 Technetum-99m PET 6.02 hours SPECT Indium-111 | 67.3 hours SPECT…