Conceptual Integrated Science
3rd Edition
ISBN: 9780135197394
Author: Hewitt, Paul G., LYONS, Suzanne, (science Teacher), Suchocki, John, Yeh, Jennifer (jennifer Jean)
Publisher: PEARSON EDUCATION (COLLEGE)
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Chapter 10, Problem 38TS
The formula for the half-life can be expressed as
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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.
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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
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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?
This exercise uses the radioactive decay model.
The half-life of radium-226 is 1600 years. Suppose we have a 29-mg sample.
(a) Find a function m(t) = mo2-t/h that models the mass remaining after t years.
m(t)
1600
29 2
(b) Find a function m(t) = moe-rt that models the mass remaining after t years. (Round your r value to six decimal places
m(t) =
%3D
(c) How much of the sample will remain after 5000 years? (Round your answer to one decimal place.)
1 mg
(d) After how many years will only 17 mg of the sample remain? (Round your answer to one decimal place.)
X yr
Chapter 10 Solutions
Conceptual Integrated Science
Ch. 10 - Prob. 1RCQCh. 10 - Prob. 2RCQCh. 10 - Prob. 3RCQCh. 10 - Prob. 4RCQCh. 10 - What role do neutrons play in the atomic nucleus?Ch. 10 - Prob. 6RCQCh. 10 - Prob. 7RCQCh. 10 - What is the long-range fate of all the uranium...Ch. 10 - What is meant by the half-life of a radioactive...Ch. 10 - What is the half-life of uranium-238?
Ch. 10 - Prob. 11RCQCh. 10 - Prob. 12RCQCh. 10 - Prob. 13RCQCh. 10 - Prob. 14RCQCh. 10 - Prob. 15RCQCh. 10 - How does the mass per nucleons in uranium compare...Ch. 10 - What is the origin of the most of the natural...Ch. 10 - Prob. 18TISCh. 10 - Is radioactivity on Earth something relatively...Ch. 10 - What happens to a nitrogen atom in the atmosphere...Ch. 10 - Prob. 21TISCh. 10 - Why is lead found in all deposits of uranium ores?Ch. 10 - How does the mass of a pair of atoms that have...Ch. 10 - Prob. 24TISCh. 10 - What kind of nuclear power is responsible for...Ch. 10 - Rank these three types of radiation by their...Ch. 10 - Consider the atoms C-12, C-14, and N-14. From...Ch. 10 - Rank these isotopes in order of their...Ch. 10 - Rank the following in order from the most energy...Ch. 10 - Prob. 34TSCh. 10 - Consider a radioactive sample with a half-life of...Ch. 10 - A radioisotope is placed near a radiation...Ch. 10 - Uranium-238 absorbs a neutron and then emits a...Ch. 10 - The formula for the half-life can be expressed as...Ch. 10 - The formula for the half-life can be expressed as...Ch. 10 - Prob. 40TSCh. 10 - Why is it both impractical and impossible to...Ch. 10 - Prob. 42TECh. 10 - Prob. 43TECh. 10 - Prob. 44TECh. 10 - Prob. 45TECh. 10 - Prob. 46TECh. 10 - Prob. 47TECh. 10 - Prob. 48TECh. 10 - Prob. 49TECh. 10 - Prob. 50TECh. 10 - Prob. 51TECh. 10 - Prob. 52TECh. 10 - How is the rate of transmutation related to...Ch. 10 - Why is lead found in all deposits of uranium ores?Ch. 10 - Prob. 55TECh. 10 - Elements heavier than uranium in the periodic...Ch. 10 - If you make an account of 1000 people born in the...Ch. 10 - How does radioactivity allow archeologists to...Ch. 10 - What does the proportion of lead and uranium in...Ch. 10 - Radium-226 is a common isotope on Earth, but it...Ch. 10 - Prob. 61TECh. 10 - Prob. 62TECh. 10 - Prob. 63TECh. 10 - Prob. 64TECh. 10 - Name three fissionable isotopes.Ch. 10 - Prob. 66TECh. 10 - Prob. 67TECh. 10 - Why is carbon better than lead as a moderator in...Ch. 10 - Prob. 69TECh. 10 - Prob. 70TECh. 10 - Prob. 71TECh. 10 - Prob. 72TECh. 10 - Prob. 73TECh. 10 - Prob. 74TECh. 10 - Prob. 75TECh. 10 - How does the mass per nucleon in uranium compare...Ch. 10 - Prob. 77TECh. 10 - Prob. 78TECh. 10 - Prob. 79TECh. 10 - Prob. 80TECh. 10 - How does the energy of the gasoline come from...Ch. 10 - Prob. 82TECh. 10 - Prob. 83TECh. 10 - Prob. 84TECh. 10 - Prob. 85TECh. 10 - Prob. 86TECh. 10 - Prob. 87TECh. 10 - Prob. 88TECh. 10 - Prob. 89TECh. 10 - Prob. 90TECh. 10 - Prob. 91TDICh. 10 - The 1986 accident at the Chernobyl, in which...Ch. 10 - Your friend Paul says that the helium used to...Ch. 10 - Prob. 94TDICh. 10 - Prob. 95TDICh. 10 - Prob. 96TDICh. 10 - Prob. 1RATCh. 10 - Prob. 2RATCh. 10 - A sample of radioactive material is usually a...Ch. 10 - What evidence supports the contention that the...Ch. 10 - When the isotope bismuth-213 emits an alpha...Ch. 10 - Prob. 6RATCh. 10 - Prob. 7RATCh. 10 - Prob. 8RATCh. 10 - Prob. 9RATCh. 10 - If an iron nucleus split in two, its fission...
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- Radioactive substances follow a specific law of decay. Namely, if you have a sample of some radioactive isotope, the quantity left after a certain time, called the half-life and denoted T1/2, is one-half of what you had initially. If you wait a second half-life, then there will be half f what was left at the end of the first half-life. Since 1/2-1/2 = 1/4, you will have one-fourth of the original quantity left after two half-lives. You can continue with this procedure to find the fraction of the original sample that hasn't decayed after any number of half- lives. However, this would become quite cumbersome if you are interested in the quantity left after, say, 10 half-lives. In this case, the quantity you are looking for would be found by multiplying the original quantity by 10 factors or 1/2. To solve this problem, we use exponents. An exponent, a small number written above and to the right, tells you how many copies of a particular number are multiplied together. In our example,…arrow_forwardA sample contains 1,174 nuclei of a radioactive isotope of chromium. If the half-life is 33 days, how many of the radioactive nuclei were present one year earlier? (This year lasted 365 days.) Give your answer to 3 significant figures in scientific notation (e.g. 3.29E6)arrow_forwardAn 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)arrow_forward
- The half-life of a radioactive isotope is the amount of time it takes for a quantity ofradioactive material to decay to one-half of its original amount. (a) The half-life of Carbon 14 (C-14) is 5230 years. Determine the decay-rate parameter λ for C-14.(b) The half-life of Iodine 131 (I-131) is 8 days. Determine the decay-rate parameter for I-131 Thank you for the help. I am hung up on the formula to use.arrow_forwardA certain radioactive material decays exponentially. The percent, P, of the material left after t years is given by P(t) = 100(1.2). a. Determine the half-life of the substance. b. How fast is the substance decaying at the point where the half-life is reached? The substance is decaying at a rate of about -3.8% per year at the time 9.12 years where the half-life is reached The substance is decaying at a rate of about -9.12% per year at the time 6.8 years where the half-life is reached The substance is decaying at a rate of about -9.12% per year at the time 3.8 years where the half-life is reached | None of the abovearrow_forwardA sample from human remains found near Stonehenge in England shows that 71.2% of the carbon-14 still remains. Use the model Q(1) = Qe-0.000121 to determine the age of the sample. In this model, Q(t) represents the amount of carbon-14 remaining t years after death, and Qo represents the initial amount of carbon-14 at the time of death. Round to the nearest 100 yr.arrow_forward
- MI * 00 因 44 -0.00002866t where A(t) is the amount of the isotope at time t (in years) and A, is the original amount. if the original The decay of an isotope is given by A(t)= Ap e amount is 100 pounds, find the half-life of this isotope. The half-life of the isotope is about years. (Do not round until the final answer. Then round to the nearest whole number as needed.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer Copyright © 2021 Pearson Equcation INC. All rignts reserved. | Terms of use | PrIvacy PolicyT Permissions ContaCL US to search PriSc F7 F8 F11 F12 F5 +DD & %23 7. 8. 3. 5. K B. Altarrow_forwardA radioactive nucleus has half-life T1/2. A sample containing these nuclei has initial activity R0. Calculate the number of nuclei that decay during the interval between the times t1 and t2.arrow_forwardA radioactive nucleus has half-life T1/2. A sample containing these nuclei has initial activity R0 at t = 0. Calculate the number of nuclei that decay during the interval between the later times t1 and t2.arrow_forward
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