Applied Physics (11th Edition)
11th Edition
ISBN: 9780134159386
Author: Dale Ewen, Neill Schurter, Erik Gundersen
Publisher: PEARSON
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Chapter 23.4, Problem 3P
To determine
Which atom is one electron short of having the
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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 23 Solutions
Applied Physics (11th Edition)
Ch. 23.3 - Prob. 1PCh. 23.3 - Prob. 2PCh. 23.3 - Prob. 3PCh. 23.3 - Prob. 4PCh. 23.3 - Prob. 5PCh. 23.4 - Prob. 1PCh. 23.4 - Prob. 2PCh. 23.4 - Prob. 3PCh. 23.4 - Prob. 4PCh. 23.5 - Prob. 1P
Ch. 23.5 - Prob. 2PCh. 23.5 - Prob. 3PCh. 23.5 - Prob. 4PCh. 23.5 - Prob. 5PCh. 23.5 - Prob. 6PCh. 23.5 - Prob. 7PCh. 23.5 - Prob. 8PCh. 23.5 - Prob. 9PCh. 23.5 - Prob. 10PCh. 23.5 - Prob. 11PCh. 23.5 - Prob. 12PCh. 23.5 - Prob. 13PCh. 23.5 - Prob. 14PCh. 23.6 - Prob. 1PCh. 23.6 - Prob. 2PCh. 23.6 - Prob. 3PCh. 23.6 - Prob. 4PCh. 23.6 - Prob. 5PCh. 23.6 - Estimate the average binding energy per nucleon...Ch. 23.6 - Estimate the average binding energy per nucleon...Ch. 23.6 - Estimate the average binding energy per nucleon...Ch. 23.7 - Prob. 1PCh. 23.7 - Find the half-life of a radioactive sample if its...Ch. 23.7 - Prob. 3PCh. 23.7 - Prob. 4PCh. 23.7 - Find the percent of a sample of C55124s that will...Ch. 23.7 - Prob. 6PCh. 23.7 - Find the remaining quantity of uranium 238 atoms...Ch. 23.7 - Prob. 8PCh. 23.7 - Find the percent of a C614 sample that will decay...Ch. 23.7 - Find the percent of a radioactive sample of...Ch. 23.9 - Prob. 1PCh. 23.9 - Prob. 2PCh. 23.9 - Prob. 3PCh. 23.9 - Prob. 4PCh. 23.9 - Prob. 5PCh. 23.9 - Prob. 6PCh. 23.9 - Prob. 7PCh. 23 - Prob. 1RQCh. 23 - Einstein's equivalence principle relates to a....Ch. 23 - Prob. 3RQCh. 23 - Prob. 4RQCh. 23 - Prob. 5RQCh. 23 - Prob. 6RQCh. 23 - Describe the differences between the electric...Ch. 23 - Prob. 8RQCh. 23 - Prob. 9RQCh. 23 - What is the difference among the following...Ch. 23 - Prob. 11RQCh. 23 - Prob. 12RQCh. 23 - Prob. 13RQCh. 23 - Prob. 14RQCh. 23 - Prob. 15RQCh. 23 - What important discovery was made by Enrico Fermi?Ch. 23 - Prob. 17RQCh. 23 - Prob. 18RQCh. 23 - Prob. 19RQCh. 23 - What fraction of a radioactive sample has not...Ch. 23 - Prob. 21RQCh. 23 - Prob. 22RQCh. 23 - Prob. 1RPCh. 23 - Prob. 2RPCh. 23 - Prob. 3RPCh. 23 - Prob. 4RPCh. 23 - Prob. 5RPCh. 23 - Prob. 6RPCh. 23 - Prob. 7RPCh. 23 - Prob. 8RPCh. 23 - Prob. 9RPCh. 23 - Prob. 10RPCh. 23 - Estimate the average binding energy for R75187e...Ch. 23 - Prob. 12RPCh. 23 - Find the remaining quantity of iodine 131 atoms...Ch. 23 - Find the percent of a strontium 88 sample that...Ch. 23 - Find the percent of an osmium 191 sample that will...Ch. 23 - Prob. 16RPCh. 23 - Prob. 17RPCh. 23 - Prob. 18RPCh. 23 - Prob. 19RPCh. 23 - Prob. 20RPCh. 23 - Prob. 1ACCh. 23 - Prob. 2ACCh. 23 - The binding energy for a H24e nucleus is 28.40...Ch. 23 - Prob. 4ACCh. 23 - Prob. 5AC
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