COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Textbook Question
Chapter 31, Problem 2CQ
What is the difference between (rays and characteristic x rays? Is either necessarily more energetic than the other? Which can be the most energetic?
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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 31 Solutions
COLLEGE PHYSICS
Ch. 31 - Suppose the range for 5.0 MeVa ray is known to be...Ch. 31 - What is the difference between (rays and...Ch. 31 - Ionizing radiation interacts with matter by...Ch. 31 - What characteristics of radioactivity show it to...Ch. 31 - What is the source of the energy emitted in...Ch. 31 - Consider Figure 31.3. If an electric field is...Ch. 31 - Explain how an (particle can have a larger range...Ch. 31 - Arrange the following according to their ability...Ch. 31 - Often, when people have to work around radioactive...Ch. 31 - Is it possible for light emitted by a scintillator...
Ch. 31 - The weak and strong nuclear forces are basic to...Ch. 31 - Define and make clear distinctions between the...Ch. 31 - What are isotopes? Why do different isotopes of...Ch. 31 - Star Trek fans have often heard the term...Ch. 31 - What conservation law requires an electron’s...Ch. 31 - Neutrinos are experimentally determined to have an...Ch. 31 - What do the three types of beta decay have in...Ch. 31 - In a 3109 yearold rock that originally contained...Ch. 31 - Does the number of radioactive nuclei in a sample...Ch. 31 - Radioactivity depends on the nucleus and not the...Ch. 31 - Explain how a bound system can have less mass than...Ch. 31 - Spontaneous radioactive decay occurs only when the...Ch. 31 - To obtain the most precise value of BE from the...Ch. 31 - How does the finite range of the nuclear force...Ch. 31 - Why is the number of neutrons greater than the...Ch. 31 - A physics student caught breaking conservation...Ch. 31 - When a nucleus (decays, does the (particle move...Ch. 31 - The energy of 30.0 eV is required to ionize a...Ch. 31 - A particle of ionizing radiation creates 4000 ion...Ch. 31 - (a) Repeat Exercise 31.2, and convert the energy...Ch. 31 - Suppose a particle of ionizing radiation deposits...Ch. 31 - Verify that a 2.31017kg mass of water at normal...Ch. 31 - Find the length of a side of a cube having a mass...Ch. 31 - What is the radius of an (particle?Ch. 31 - Find the radius of a 238Pu nucleus. 238Pu is a...Ch. 31 - (a) Calculate the radius of 58Ni, one of the most...Ch. 31 - The unified atomic mass unit is defined to be...Ch. 31 - What is the ratio of the velocity of a (particle...Ch. 31 - If a 1.50cmthick piece of lead can absorb 90.0% of...Ch. 31 - The detail observable using a probe is limited by...Ch. 31 - (a) Show that if you assume the average nucleus is...Ch. 31 - What is the radio of the velocity of a 5.00MeV...Ch. 31 - (a) What is the kinetic energy in MeV of a ray...Ch. 31 - In the following eight problems, write the...Ch. 31 - In the following eight problems, write the...Ch. 31 - In the following eight problems, write the...Ch. 31 - In the following eight problems, write the...Ch. 31 - In the following eight problems, write the...Ch. 31 - In the following eight problems, write the...Ch. 31 - In the following eight problems, write the...Ch. 31 - In the following eight problems, write the...Ch. 31 - decay producing 137Ba. The parent nuclide is a...Ch. 31 - ( decay producing 90Y. The parent nuclide is a...Ch. 31 - decay producing 228Ra. The parent nuclide is...Ch. 31 - decay producing 208Pb. The parent nuclide is in...Ch. 31 - When an electron and position annihilate, both...Ch. 31 - Confirm That charge, electron family number, and...Ch. 31 - Confirm that charge, electron family number, and...Ch. 31 - Confirm that charge, electron family number, and...Ch. 31 - Confirm that charge, electron family number, and...Ch. 31 - A rare decay mode has been observed in which 222Ra...Ch. 31 - (a) Write the complete a decay equation for 226Ra....Ch. 31 - (a) Write the complete a decay equation for 249Cf....Ch. 31 - (a) Write the complete decay equation for the...Ch. 31 - (a) Write the complete decay equation for 90Sr,...Ch. 31 - Calculate the energy released in the + decay of...Ch. 31 - (a) Write the complete + decay equation for llC....Ch. 31 - (a) Calculate the energy released in the a decay...Ch. 31 - (a) Write the complete reaction equation for...Ch. 31 - (a) Write the complete reaction equation for...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - Data from the appendices and the periodic table...Ch. 31 - 2H is a loosely hound isotope of hydrogen. Called...Ch. 31 - 56Feis among the most tightly bound of all...Ch. 31 - 209Bi is the heaviest stable nuclide, and its BE/A...Ch. 31 - (a) Calculate BE/A for 235U, the rarer of the two...Ch. 31 - (a) Calculate BE/A for 12C. Stable and relatively...Ch. 31 - The fact that BE/A is greatest for A near 60...Ch. 31 - The purpose of this problem is to show in three...Ch. 31 - Unreasonable Results A particle physicist...Ch. 31 - Derive an approximate relationship between the...Ch. 31 - Integrated Concepts A 2.00T magnetic ?eld is...Ch. 31 - (a) Write the decay equation for the decay of...Ch. 31 - Unreasonable Results The relatively scarce...Ch. 31 - Unreasonable Results A physicist scatters (rays...Ch. 31 - Unreasonable Results A frazzled theoretical...Ch. 31 - Construct Your Own Problem Consider the decay of...Ch. 31 - Prob. 1TPCh. 31 - Prob. 2TPCh. 31 - Prob. 3TPCh. 31 - Prob. 4TPCh. 31 - Prob. 5TPCh. 31 - Prob. 6TPCh. 31 - Prob. 7TPCh. 31 - Prob. 8TPCh. 31 - Prob. 9TPCh. 31 - Prob. 10TPCh. 31 - Prob. 11TPCh. 31 - Prob. 12TP
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