Download A05715 ANY CALCULATOR Page 1 TURN OVER School of Physics

A05715
ANY CALCULATOR School of Physics and Astronomy
MODULE OUTSIDE THE MAIN DISCIPLINE
03 00680
LC THE COSMIC CONNECTION
SUMMER EXAMINATIONS 2015
Total Time Allowed: 1 hour 30 minutes
Answer Section 1 and two questions from Section 2.
Section 1 counts for 40% of the marks for the examination.
Full marks for this Section may be obtained by correctly answering four
questions. You may attempt more questions, but marks in excess of 40% will
be disregarded.
Section 2 consists of three questions and carries 60% of the marks.
Answer two questions from this Section. If you answer more than two
questions, credit will only be given for the best two answers.
The approximate allocation of marks to each part of a question is shown in [ ].
All symbols have their usual meaning.
Calculators may be used in this examination but must not be used to store text.
Calculators with the ability to store text should have their memories deleted
prior to the start of the examination.
Two tables of constants which may be required to answer some of the
questions are attached to the back of this question paper.
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ANY CALCULATOR SECTION 1
Full marks may be obtained by correctly answering four questions.
You may attempt as many questions as you wish, but any marks in excess of
40% will be disregarded.
1.
Explain briefly why Sunspots are fainter than the surrounding
photosphere.
2.
[10]
What is the Hertzsprung Russell diagram? Describe the position of
a white dwarf star relative to the Main Sequence on such a
diagram. At what stage of stellar evolution does a star become a
[10]
white dwarf?
3.
Use Wien’s law to explain quantitatively in what way the spectrum
of the light from the Sun, with a surface temperature of about
6000K, would differ from that of a B star.
4.
Under what circumstances would the light from stars formed long
ago now be observed at infrared wavelengths?
5.
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[10]
[10]
Compare and contrast images of the Sun taken in (i) visible
radiation; and (ii) X-ray radiation.
[10]
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ANY CALCULATOR 6.
Discuss the properties of Cepheid stars that make them
cosmologically important.
[10]
SECTION 2
Answer two questions from this Section. If you answer more than two
questions, credit will only be given for the best two answers.
7. (a)
Kepler derived his three laws of planetary motion from a study of
Tycho Brahe’s observations of Mars. State Kepler’s three laws and
include a sketch that illustrates their key features.
(b)
[12]
Derive the constant of proportionality in Kepler’s Third Law, by
using expressions for the forces that keep a body in a circular orbit
together with the relationship between the period of a circular orbit,
its radius and the speed of the object.
(c)
[9]
Halley’s comet was last seen from Earth in 1986. The orbit of
Halley’s comet has a semi-major axis of 17.9AU, and a distance of
closest approach to the Sun of 0.59 AU. Use Kepler’s Third Law to
estimate when we can expect to see it again.
[9]
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ANY CALCULATOR Neutron stars are some of the most compact objects in the
8.
Universe.
(a)
Discuss briefly the neutron star stage of stellar evolution.
[12]
(b)
Describe the lighthouse model for a pulsar, and indicate how the
model is consistent with observations.
(c)
[12]
One particular neutron star is observed to have a temperature of
600,000K and a luminosity of 0.046L. Calculate the radius of the
star in kilometres and comment on your answer.
[6]
Discuss each of the following key concepts in the context of
9.
theories of the behaviour of the early Universe:
(a)
The expansion of the Universe;
(b)
The Cosmological Principle;
(c)
The Big Bang;
(d)
The Cosmic Microwave Background; and
(e)
Dark Energy.
(Marks will be divided equally between a brief discussion of the
concept and its relevance to theories of the early Universe.)
[30]
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ANY CALCULATOR Physical Constants and Units
Acceleration due to gravity
g
9.81 m s-2
Gravitational constant
G
6.673  10-11 N m2 kg-2
Avogadro constant
NA
6.022  1023 mol-1
Note: 1 mole = 1 gram molecular-weight
Ice point
Tice
273.15 K
Gas constant
R
8.314 J K-1 mol-1
Boltzmann constant
k, kB
1.381  10-23 J K-1 =0.862  10-4 eVK-1
Stefan constant

5.670  10-8 W m-2 K-4
Rydberg constant
R
1.097  107 m-1
Rhc
13.606 eV
Planck constant
h
6.626  10-34 J s = 4.136  10-15 eV s
h/2

1.055  10-34 J s = 6.582  10-16 eV s
Speed of light in vacuo
c
2.998  108 m s-1
c
197.3 MeV fm
Charge of proton
e
1.602  10-19 C
Mass of electron
me
9.109  10-31 kg
Rest energy of electron
Mass of proton
0.511 MeV
mp
Rest energy of proton
One atomic mass unit
1.673  10-27 kg
938.3 MeV
1.66  10-27 kg
u
Atomic mass unit energy equivalent
931.5 MeV
Electric constant
0
8.854  10-12 F m-1
Magnetic constant
0
4  10-7 H m-1
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ANY CALCULATOR Bohr magneton
B
9.274  10-24 A m2 (J T-1)
Nuclear magneton
N
5.051  10-27 A m2 (J T-1)
Fine-structure constant
 = e2/40  c 7.297  10-3 = 1/137.0
Compton wavelength of electron
c = h/mc
2.426  10-12 m
Bohr radius
ao
5.2918  10-11 m
angstrom

A
10-10 m
torr (mm Hg, 0C)
torr
133.32 Pa (N m-2)
barn
b
10-28 m2
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ANY CALCULATOR Astrophysical Constants
Quantity
Symbol
Value
Astronomical Unit
AU
1.50  1011 m Parsec
pc
3.1  1016 m Tropical year
y
365.2422 mean solar
days Lo∙
Solar luminosity
Absolute bolometric
3.9  1026 W Mbol +4m75
BC
0m08
mv(o)
26m74
magnitude of the Sun
Bolometric correction
for the Sun
Apparent visual magnitude of
the Sun
f
Solar constant
Mo∙
Solar mass
1.37  103 W m 2.0  1030 kg Wien constant
b
2.89  10 m K Hubble constant
HO 75 (km s) Mpc Solar radius
Ro∙
6.96  108 m
Distance of the Sun from
8.7 kpc
galactic centre
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