COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 27, Problem 69QAP
To determine
The decay rate per second.
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*•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…
•49 SSM Generally, more massive nuclides tend to be more un-
stable to alpha decay. For example, the most stable isotope of ura-
nium, 28U, has an alpha decay half-life of 4.5 x 10° y. The most stable
isotope of plutonium is 24Pu with an 8.0 x 10' y half-life, and for
curium we have 248Cm and 3.4 x 10 y. When half of an original sam-
ple of 238U has decayed, what fraction of the original sample of (a) plu-
tonium and (b) curium is left?
6
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.
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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- Construct 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_forward•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 uarrow_forward8. The binding energy & d.ee Mev respectively. • of tritium (H) and deuteron (24) released when 340 & Date Page I are what will be energy 24 fuse to form a stable tHe of binding energy 28.3 MeV ? O 2 15 M me AMSarrow_forward
- •22 O An a particle (*He nucleus) is to be taken apart in the fol- lowing steps. Give the energy (work) required for each step: (a) re- move a proton, (b) remove a neutron, and (c) separate the remain- ing proton and neutron. For an a particle, what are (d) the total binding energy and (e) the binding energy per nucleon? (f) Does either match an answer to (a), (b), or (c)? Here are some atomic masses and the neutron mass. "He 4.002 60 u 2H 2.014 10 u 3H 3.016 05 u 'H 1.007 83 u 1.008 67 uarrow_forwardQUESTION 9 _was the first to calculate how much more energy an atom release in radioactive decay that it does in any chemical reaction. J.J.Thompson W.Roentgen Marie Curie O F. Soddyarrow_forward•61 The isotope 238SU decays to 206 Pb with a half-life of 4.47 x 10° y. Although the decay occurs in many individual steps, the first step has by far the longest half-life; therefore, one can often consider the decay to go directly to lead. That is, 238U → 206Pb + various decay products. A rock is found to contain 4.20 mg of 23$U and 2.135 mg of 206PB. Assume that the rock contained no lead at formation, so all the lead now present arose from the decay of uranium. How many atoms of (a) 238U and (b) 206Pb does the rock now contain? (c) How many atoms of 238U did the rock contain at formation? (d) What is the age of the rock?arrow_forward
- Part A Some atomic masses Particle Symbol Mass (u) Electron e 0.00055 Part B Proton 1.00728 Neutron n 1.00866 Part C Hydrogen 1.00783 Helium 4 Не 4.00260 Part D Part E Calculate the binding energy EB of the helium nucleus He. Express your answer in megaelectron volts to three significant figures. • View Available Hint(s) EB = MeVarrow_forwardMY NOTES TEACHER ASK YOUR At t=0 s, you have a pure sample of an unknown substance. At t = 252 s, 36.8% of the substance remains. Determine the half-life and what t will be when 22% of the substance remains. T1/2 -> twarrow_forward•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 514περarrow_forward
- •30 Verify that the fusion of 1.0 kg of deuterium by the reaction ?H + ?H - 'He + n could keep a 100 W lamp burning for 2.5 x 10' y. (Q = +3.27 MeV)arrow_forward19) What is the amount of starting material when 0.35-g remain and the number of half-lives is 2.72 R S=arrow_forwardIn the science section of the newspaper, an article reports the efforts of a group of scientists to create a new nuclear reactor based on the fission of iron (Fe). Is this a good idea?arrow_forward
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