COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 27, Problem 86QAP
To determine
The age of the bone.
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B. Carbon-14 is a radioactive isotope of carbon that has a half-life of 5600 years. It is used extensively in dating
organic material that is tens of thousands of years old.
Model the differential equation of the decay of the isotope if m is the mass and t is the time
Calculate the constant using the half-life time.
What fraction of the original amount of Carbon-14 in a sample would be present after 10,000 years?
i)
ii)
•14 A 236U nucleus undergoes fission and breaks into two mid-
dle-mass fragments, 140Xe and 96Sr. (a) By what percentage does
the surface area of the fission products differ from that of the origi-
nal 236U nucleus? (b) By what percentage does the volume change?
(c) By what percentage does the electric potential energy change?
The electric potential energy of a uniformly charged sphere of ra-
dius r and charge Q is given by
3
514περ
•3 @ A thermal neutron (with approximately zero kinetic energy) is
absorbed by a 23U nucleus. How much energy is transferred from
mass energy to the resulting oscillation of the nucleus? Here are some
atomic masses and the neutron mass.
237U 237.048 723 u
239U 239.054 287 u
238U 238.050 782 u
240U 240.056 585 u
1.008 664 u
Chapter 27 Solutions
COLLEGE PHYSICS
Ch. 27 - Prob. 1QAPCh. 27 - Prob. 2QAPCh. 27 - Prob. 3QAPCh. 27 - Prob. 4QAPCh. 27 - Prob. 5QAPCh. 27 - Prob. 6QAPCh. 27 - Prob. 7QAPCh. 27 - Prob. 8QAPCh. 27 - Prob. 9QAPCh. 27 - Prob. 10QAP
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- A nuclear physicist finds 1.0of 236Uin a piece of uranium ore (T1/2=2.348107y) . (a) Use die decay law to determine how much 236Uwould had to have been on Earth when it formed 4.543109yago for 1.0gto be left today, (b) What is unreasonable about this result? (c) How is this unreasonable result resolved?arrow_forwardConstruct Your Own Problem Consider the decay of radioactive substances in the Earth's interior. The energy emitted is converted to thermal energy that reaches the earth's surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then calculate the power generated. Calculate how much power must cross each square meter of the Earth’s surface if the power is dissipated at the same rate as it is generated. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth.arrow_forwardThe mass (M) and the radius (r) of a nucleus can be expressed in terms of the mass number, A. (a) Show that the density of a nucleus is independent of A (b) Calculate the density of a gold (Au) nucleus. Compare your answer to that for iron (Fe).arrow_forward
- The naturally occurring radioactive isotope 232Th does not make good fission fuel, because it has an even number of neurons; however, it can be bred into a suitable fuel (much as 238U is bred into 239P). (a) What are Z and N for 232Th? (b) Write the reaction equation for neutron captured by 232Th and identify the nuclide AX produced in n+232ThAX+. (c) The product nucleus β decays, as does its daughter. Write me decay equations for each, and identify the final nucleus. (d) Conform that the final nucleus has an odd number of neutrons, making it a better fission fuel. (e) Look up the halflife of the final nucleus to see if it lives long enough to be a useful fuel.arrow_forward(Radiocarbon dating) Carbon taken from a purported relic of the time of Christ contained 4.6 x 1010 atoms of 14C per gram. Carbon extracted from a present-day specimen of the same substance contained 5.0 x 1010 atoms of 14C per gram. Compute the approximate age of the relic. What is your opinion as to its authenticity?arrow_forward6 Carbon-14 (C) dating is a method for finding the age of an organic artifact from the quantity of 14C it contains. Carbon-14, an unstable isotope of carbon, follows a well-known sequence of decay processes. The decay constants of these processes have been well established, allowing researchers to determine the age of an artifact knowing both the original amount of 14C and the current amount. In the lab, it is relatively easy to measure the activity of a sample and to estimate the mass of carbon in the sample. From these measurements, it is possible to find the age of the sample.arrow_forward
- *•58 Two radioactive materials that alpha decay, 238U and 232Th, and one that beta decays, "K, are sufficiently abundant in granite to contribute significantly to the heating of Earth through the de- cay energy produced. The alpha-decay isotopes give rise to decay chains that stop when stable lead isotopes are formed. The isotope 4"K has a single beta decay. (Assume this is the only possible decay of that isotope.) Here is the information: Stable Decay Half-Life End Parent Mode (y) Point (MeV) (ppm) 238U 232Th 4.47 x 10° 206рЬ 51.7 1.41 x 1010 208Pb 42.7 13 1.28 x 10° 40Ca 1.31 4 In the table Q is the total energy released in the decay of one par- ent nucleus to the final stable end point and f is the abundance of the isotope in kilograms per kilogram of granite; ppm means parts per million. (a) Show that these materials produce energy as heat at the rate of 1.0 x 10-9 W for each kilogram of granite. (b) Assuming that there is 2.7 x 102 kg of granite in a 20-km-thick spherical shell at…arrow_forwardThe amount of carbon-14 found in a fossil of a tree is around 0.05% when compared to fresh wood of the same kind. Estimate the age of the fossil.arrow_forward
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