COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Textbook Question
Chapter 32, Problem 59PE
It is estimated that weapons tests in the atmosphere have deposited approximately 9 MCi of 90Sr on the surface of the earth. Find the mass of this amount of 90Sr.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 32 Solutions
COLLEGE PHYSICS
Ch. 32 - In terms of radiation dose, what is the major...Ch. 32 - One of the methods used to limit radiation dose to...Ch. 32 - Isotopes that emit (radiation are relatively safe...Ch. 32 - Why is radon more closely associated with inducing...Ch. 32 - The RBE for lowenergy s is 1.7, whereas that for...Ch. 32 - Which methods of radiation protection were used in...Ch. 32 - What radioisotope could be a problem in homes...Ch. 32 - Are some types of cancer more sensitive to...Ch. 32 - Suppose a person swallows some radioactive...Ch. 32 - Radiotherapy is more likely to be used to treat...
Ch. 32 - Does loud irradiation leave the food radioactive?...Ch. 32 - Compare a low dose of radiation to a human with a...Ch. 32 - Suppose one load irradiation plant uses a 137Cs...Ch. 32 - Why does the fusion of light nuclei into heavier...Ch. 32 - Energy input is required to fuse medium-mass...Ch. 32 - In considering potential fusion reactions, what is...Ch. 32 - Give reasons justifying the contention made in the...Ch. 32 - Explain why the fission of heavy nuclei releases...Ch. 32 - Explain, in terms of conservation of momentum and...Ch. 32 - The ruins of the Chernobyl reactor are enclosed in...Ch. 32 - Since the uranium or plutonium nucleus fissions...Ch. 32 - The cure of a nuclear reactor generates a large...Ch. 32 - How can a nuclear reactor contain many critical...Ch. 32 - Why can heavy nuclei with odd numbers of neutrons...Ch. 32 - Why is a conventional fission nuclear reactor not...Ch. 32 - What are some of the reasons that plutonium rather...Ch. 32 - Use the laws of conservation of momentum and...Ch. 32 - How does the lithium deuteride in the...Ch. 32 - Fallout from nuclear weapons tests in the...Ch. 32 - A neutron generator uses an (source, such as...Ch. 32 - Neutrons from a source (perhaps the one discussed...Ch. 32 - The purpose of producing 99Mo (usually by neutron...Ch. 32 - (a) Two annihilation rays in a PET scan originate...Ch. 32 - Table 32.1 indicates that 7.50 mCi of 99mTc is...Ch. 32 - The activities of 131I and 123I used in thyroid...Ch. 32 - (a) Neutron activation of sodium, which is 100%...Ch. 32 - What is the dose in mSv for: (a) a 0.1 Gy xray?...Ch. 32 - Find the radiation dose in Gy for: (a) A 10mSv...Ch. 32 - How many Gy of exposure is needed to give a...Ch. 32 - What is the dose in Sv in a cancer treatment that...Ch. 32 - One half the rays from 99mTc are absorbed by a...Ch. 32 - A plumber at a nuclear power plant receives a...Ch. 32 - In the 1980s, the term picowave was used to...Ch. 32 - Find the mass of 239Pu mat has an activity of 1.00...Ch. 32 - A beam of 168MeV nitrogen nuclei is used for...Ch. 32 - (a) If the average molecular mass of compounds in...Ch. 32 - Calculate the dose in Sv to the chest at a patient...Ch. 32 - (a) A cancer patient is exposed to rays from a...Ch. 32 - What is the mass of 60Co in a cancer therapy...Ch. 32 - Large amounts of 65Zn are produced in copper...Ch. 32 - Naturally occurring 40K is listed as responsible...Ch. 32 - (a) Background radiation due to 226Ra averages...Ch. 32 - The annual radiation dose from 14C in our bodies...Ch. 32 - If everyone in Australia received an extra 0.05...Ch. 32 - Verify that the total number at nucleons, total...Ch. 32 - Calculate the energy output in each of the fusion...Ch. 32 - Show that the total energy released in the...Ch. 32 - Verify by listing the number of nucleons, total...Ch. 32 - The energy produced by the fusion of a 1.00—kg...Ch. 32 - Tritium is naturally rare, but can be produced by...Ch. 32 - Two fusion reactions mentioned in the text are...Ch. 32 - (a) Calculate the number of grams of deuterium in...Ch. 32 - How many kilograms of water are needed to obtain...Ch. 32 - The power output of the Sun is 41026W. (a) If 90%...Ch. 32 - Another set of reactions that result in the fusing...Ch. 32 - (a) Find the total energy released in MeV in each...Ch. 32 - Verify that the total number of nucleons, total...Ch. 32 - Integrated Concepts The laser system tested for...Ch. 32 - Integrated Concepts Find the amount of energy...Ch. 32 - Integrated Concepts: (a) What temperature gas...Ch. 32 - Integrated Concepts (a) Estimate the years 1hat1he...Ch. 32 - (a) Calculate the energy released in the...Ch. 32 - (a) Calculate the energy released in the...Ch. 32 - (a) Calculate the energy released in the...Ch. 32 - Confirm that each at the reactions listed for...Ch. 32 - Breeding plutonium produces energy even before any...Ch. 32 - The naturally occurring radioactive isotope 232Th...Ch. 32 - The electrical power output of a large nuclear...Ch. 32 - A large power reactor that has been in operation...Ch. 32 - Find the mass converted into energy by a 12.0kT...Ch. 32 - What mass is converted into energy by a 1.00MT...Ch. 32 - Fusion bombs use neutrons from their fission...Ch. 32 - It is estimated that the total explosive yield of...Ch. 32 - A radiationenhanced nuclear weapon (or neutron...Ch. 32 - (a) How many 239Pu nuclei must fission to produce...Ch. 32 - Assume onefourth of the yield of a typical 320kT...Ch. 32 - This problem gives some idea of the magnitude of...Ch. 32 - It is estimated that weapons tests in the...Ch. 32 - A 1.00MT bomb exploded a few kilometers above the...Ch. 32 - Integrated Concepts One scheme to put nuclear...Ch. 32 - Prob. 1TPCh. 32 - Prob. 2TPCh. 32 - Prob. 3TPCh. 32 - Prob. 4TPCh. 32 - Prob. 5TPCh. 32 - Prob. 6TPCh. 32 - Prob. 7TPCh. 32 - Prob. 8TPCh. 32 - Prob. 9TPCh. 32 - Prob. 10TP
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