Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 13, Problem 39P
To determine
To show that mean life time is
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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?
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
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Chapter 13 Solutions
Modern Physics
Ch. 13.4 - Prob. 1ECh. 13 - Prob. 1QCh. 13 - A proton precesses with a frequency p in the...Ch. 13 - Prob. 3QCh. 13 - Prob. 4QCh. 13 - Prob. 5QCh. 13 - Prob. 7QCh. 13 - Prob. 8QCh. 13 - Prob. 9QCh. 13 - What fraction of a radioactive sample has decayed...
Ch. 13 - Prob. 11QCh. 13 - Prob. 12QCh. 13 - Prob. 13QCh. 13 - Prob. 14QCh. 13 - Prob. 15QCh. 13 - Prob. 16QCh. 13 - Prob. 17QCh. 13 - Prob. 18QCh. 13 - Prob. 19QCh. 13 - Prob. 20QCh. 13 - Prob. 21QCh. 13 - Prob. 22QCh. 13 - Prob. 23QCh. 13 - Prob. 25QCh. 13 - Prob. 26QCh. 13 - Prob. 27QCh. 13 - Prob. 28QCh. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - Prob. 5PCh. 13 - Prob. 6PCh. 13 - Prob. 7PCh. 13 - Prob. 8PCh. 13 - Prob. 9PCh. 13 - Prob. 10PCh. 13 - Prob. 11PCh. 13 - Prob. 12PCh. 13 - Prob. 13PCh. 13 - Prob. 14PCh. 13 - Prob. 15PCh. 13 - Prob. 16PCh. 13 - Prob. 17PCh. 13 - Prob. 18PCh. 13 - Prob. 19PCh. 13 - Prob. 20PCh. 13 - Prob. 21PCh. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - Prob. 24PCh. 13 - Prob. 25PCh. 13 - Prob. 26PCh. 13 - Prob. 27PCh. 13 - Prob. 28PCh. 13 - Prob. 29PCh. 13 - Prob. 30PCh. 13 - Prob. 31PCh. 13 - Prob. 32PCh. 13 - Prob. 33PCh. 13 - Prob. 34PCh. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - Prob. 55PCh. 13 - Prob. 56PCh. 13 - Prob. 57PCh. 13 - Prob. 58PCh. 13 - Prob. 59PCh. 13 - Prob. 60PCh. 13 - Prob. 61P
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- 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.arrow_forwardThe 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.arrow_forwardAt the beginning of an experiment, a scientist has 336 grams of radioactive goo. After 60 minutes, her sample has decayed to 42 grams. TRY NOT TO ROUND UNTIL THE VERY END. 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 14 minutes?arrow_forward
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