21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Question
Chapter 8, Problem 41QP
(a)
To determine
The number of half-lives will the sample have remaining only
(b)
To determine
The time taken to complete six half-lives.
(c)
To determine
Whether it is possible to overestimate or underestimate the age of a sample if daughter nuclei were present in the sample when it formed.
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A sample of carbon-14 initially consists of 5 × 10 24 particles. Carbon-14 has a half- life of 5730 years.
a. What is the decay constant for carbon-14? (Answer in units of yr –1 .)
b. How many radioactive particles of the sample remain after 100 years?
c. What percentage of the radioactive particles remains after 500 years?
d. How many radioactive particles of the sample remain after 1000 years?
e. How much time will it take for 50% of the particles to decay?
f. How much time will it take for 99% of the particles to decay?
g. How many half-lives will it take for 99% of the sample to decay?
h. What is the initial decay rate of the sample? (Answer in decays/yr.)
i. After 200 years, what is the decay rate of the sample?
j. How long will it take for the decay rate to decrease to 1015 decays/year?
k. How many half-lives have passed after the time you found in part (j)?
After 30 days of radioactive decay, 100 mg of a radioactive substance was observed to remain. After 120 days, only 30 mg of this substance was left. (a) How much of the substance was originally present? (b) What is the half-life of this radioactive substance?
Assume you found a radioactive isotope that has a 1 million year half-life in an "old" bone. If you were to measure a 20% "parent" to 80% "daughter" ratio, how old is the bone? How would a bone twice as big change the count rate and the half-life?
Chapter 8 Solutions
21st Century Astronomy
Ch. 8.1 - Prob. 8.1CYUCh. 8.2 - Prob. 8.2CYUCh. 8.3 - Prob. 8.3ACYUCh. 8.3 - Prob. 8.3BCYUCh. 8.4 - Prob. 8.4CYUCh. 8.5 - Prob. 8.5CYUCh. 8.6 - Prob. 8.6CYUCh. 8 - Prob. 1QPCh. 8 - Prob. 2QPCh. 8 - Prob. 3QP
Ch. 8 - Prob. 4QPCh. 8 - Prob. 5QPCh. 8 - Prob. 6QPCh. 8 - Prob. 7QPCh. 8 - Prob. 8QPCh. 8 - Prob. 9QPCh. 8 - Prob. 10QPCh. 8 - Prob. 11QPCh. 8 - Prob. 12QPCh. 8 - Prob. 13QPCh. 8 - Prob. 14QPCh. 8 - Prob. 15QPCh. 8 - Prob. 16QPCh. 8 - Prob. 17QPCh. 8 - Prob. 18QPCh. 8 - Prob. 19QPCh. 8 - Prob. 20QPCh. 8 - Prob. 21QPCh. 8 - Prob. 22QPCh. 8 - Prob. 23QPCh. 8 - Prob. 24QPCh. 8 - Prob. 25QPCh. 8 - Prob. 26QPCh. 8 - Prob. 27QPCh. 8 - Prob. 28QPCh. 8 - Prob. 29QPCh. 8 - Prob. 30QPCh. 8 - Prob. 31QPCh. 8 - Prob. 32QPCh. 8 - Prob. 33QPCh. 8 - Prob. 34QPCh. 8 - Prob. 35QPCh. 8 - Prob. 36QPCh. 8 - Prob. 37QPCh. 8 - Prob. 38QPCh. 8 - Prob. 39QPCh. 8 - Prob. 40QPCh. 8 - Prob. 41QPCh. 8 - Prob. 42QPCh. 8 - Prob. 43QPCh. 8 - Prob. 44QPCh. 8 - Prob. 45QP
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