ISB first semester final 2005

Astrophysics

Atomic and Nuclear Physics

 

Time allowed ........ 2.00 hours

Section A - Multiple choice questions ... (40 marks) Answer all questions

Section B - Astrophysics ... (20 marks) Answer two questions

Section C - Atomic and Nuclear physics ... (20 marks) Answer two questions

 

Section A

Answer all questions

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1 The magnitude scale is a measure of a stars ...

a ... apparent brightness.

b ... real brightness (luminosity).

c ... size (diameter).

d ... astrological importance.

 

2 One parsec is a distance of .......

a ... one second of arc.

b ... one astronomical unit.

c ... one light year.

d ... 3.26 light years.

 

3 A Cepheid variable is ...

a ... a young star on the upper section of the main sequence.

b ... a red giant.

c ... a close orbiting binary system.

d ... an unstable (oscillating) yellow giant star.

 

4 Place in the order of increasing size.

a A neutron star.

b The Sun.

c A planetary nebula.

d A galaxy.

 

5 A brown dwarf is ...

a ... a planet (normally called a gas giant).

b ... a white dwarf in the final stages of cooling.

c ... a star that is too small to become a red dwarf on the main sequence.

d ... a type of red dwarf star that is seen in large numbers in the regions of the galaxy closest to us.

 

6 Kepler's laws of planetary motion were ...

a ... developed in response to Newton's law of universal gravity.

b ... derived from theoretical considerations before Newton published his theory of gravity.

c ... deduced from observations.

d ... based on geometry that is no longer considered appropriate.

 

7 The distance to two stars with parallax angles of 0.1 and 0.2 seconds of arc respectively is....

a ... 3.26 light years and 6.52 light years.

b ... 3.26 light years and 1.62 light years.

c ... 32.6 light years and 65.2 light years.

d ... 32.6 light years and 16.2 light years.

 

8 Which of the following is/are not on the main sequence....

a ... Sirius.

b ... The Sun.

c ... any red dwarf.

d ... any red giant.

 

9 The temperature of the visible surface of the Sun is ~6000°C. The peak emission from the Sun, according to Wein's law, is.in the ....

a ... yellow.

b ... green.

c ... red.

d ... white.

 

10 The absolute magnitude of a star is the apparent brightness if placed at a distance of ...

a ... one astronomical unit.

b ... one light year.

c ... one parsec.

d ... ten parsecs.

 

11 Which of the following completed statements is not correct?

The vertical axis of the Hertzsprung-Russell diagram....

a ... may be marked with kilograms.

b ... may be marked with absolute luminosity.

c ... may be marked with time on the main sequence.

d ... may be marked with stellar magnitude.

 

12 Which of the following completed statements is not correct?

The horizontal axis of the Hertzsprung-Russell diagram....

a ... may be marked with peak black body wavelength.

b ... may be marked with spectral type.

c ... may be marked with surface temperature.

d ... may be marked with stellar magnitude.

 

13 Stars that are nearing the end of their life and have exhausted their nuclear fuel are called white dwarfs because....

a ... they are white.

b ... the ones that are close to us are white.

c ... the first one studied was white.

d ... the bright ones are white.

 

14 The solar wind is.due to ....

a ... storms in the Earth's magnetic field.

b ... coronal mass ejection from the Sun.

c ... sunspots.

d ... the passage of the Earth through the irregular outer atmosphere of the Sun.

 

15 The first serious attempt to account for the motions of the planets in the sky is attributed to....

a ... Newton.

b ... Galileo.

c ... Copernicus.

d ... Ptolemy of Alexandria.

 

16 An astronomical telescope (after Kepler) can be made with a minimum of....

a ... two convex lenses

b ... a concave mirror and a convex lens.

c ... a convex lens and a concave lens.

d ... three convex lenses.

 

17 To find the escape velocity of the Moon it would be sufficient to know....

i ... the radius of the Moon.
ii ... the mass of the Moon.
iii ... the acceleration due to gravity on the surface of the Moon.

b ... i only.

c ... ii only.

d ... i and iii only.

d ... i, ii only.

 

18 The cosmic background is black body radiation at a temperature closest to that of....

a ... liquid helium.

b ... liquid air.

c ... dry ice.

d ... water ice.

 

19 Place the following methods of estimating distance in order. Closest objects first and most distant objects last.

b Parallax

c Cepheid variables

d Super Nova

a Red Shift.

 

20 The units of the Hubble constant are ...

a ... seconds

b ... meters per second

c ... meters per second squared

d ... seconds to the minus one.

 

21 Alpha particles from the decay of Uranium 235 are ...

a ... particles with a short life.

b ... particles with a long range (30 cm +) in air.

c ... particles with a negative charge.

d ... particles with the same initial kinetic energy.

 

22 The atomic mass unit is....

a ... the mass of a proton.

b ... the mass of a helium nucleus.

c ... the mass of a carbon 12 nucleus.

d ... one twelfth of the mass of the carbon 12 nucleus.

 

23 According to the Standard Model, Baryons are ...

a ... combinations of two quarks only.

b ... combinations of three quarks only.

c ... combinations of two or three quarks.

d ... quark-antiquark pairs.

 

24 The Becquerel is a unit of ...

a ... energy.

b ... power.

c ... decay rate.

d ... dose equivalent.

 

25 The binding energy per nucleon is greatest for ...

a ... the helium nucleus.

b ... the carbon 12 nucleus.

c ... the iron nucleus.

d ... the uranium nucleus.

 

26 When, in 1913, Bohr developed a theory to account for the emissions of the excited hydrogen atom he put forward an unlikely condition on the ...

a ... energy of the electron.

b ... orbital angular momentum of the electron.

c ... orbital speed of the electron.

d ... axial spin of the electron.

 

27 The main components of cosmic rays at ground level are....

a ... gamma rays.

b ... alpha particles.

c ... beta particles.

d ... protons.

 

28 The de Broglie wavelength of an electron is inversely proportional to....

a ... the electronic charge.

b ... the velocity of the electron.

c ... the half life of the electron.

d ... the energy of the electron.

 

29 When uranium fissions the products have....

a ... the same mass as the uranium nucleus.

b ... slightly more mass.

c ... slightly less mass.

d ... either one of the above. It depends on what atoms are created.

 

30 The Franck-Hertz demonstration is direct evidence for....

a ... the quantization of charge.

b ... the existence of energy levels in atoms.

c ... the special theory of relativity.

d ... the existence of photons.

 

31 The particles that make up the nucleus are....

a ... leptons.

b ... hadrons.

c ... mesons.

d ... fermions.

 

32 Heavy water is....

a ... water that has a high salt content.

b ... water that is subjected to large centripetal forces in a centrifuge.

c ... ancient water that is melted from the ice caps.

d ... water with a high percentage of deuterium.

 

33 Which of the following completed statements is not correct?

A kaon can be categorized as a....

a ... hadron.

b ... boson.

c ... meson.

d ... lepton.

 

34 The electron is a member of a class of particles called Leptons.

There are....

a ... six known leptons with their antiparticles.

b ... 12 known leptons with their antiparticles.

c ... probably 24 leptons in total with their antiparticles.

d ... probably an unlimited number of leptons.

 

35 Mesons are....

a ... all unstable particles.

b ... mostly unstable particles.

c ... leptons.

d ... fermions.

 

36 The frequency of the shortest wavelength X-rays emitted by a target bombarded with high energy electrons is....

a ... proportional to the atomic number.

b ... proportional to the atomic number squared.

c ... proportional to the reciprocal of the atomic number.

d ... proportional to the reciprocal of the atomic number squared.

 

37 The existence of the neutrino was proposed long before it was discovered. The reason was ....

a ... neutrinos are very rare.

b ... neutrinos are unstable.

c ... neutrinos are invisible.

d ... neutrinos have very little interaction with matter. (The Earth itself is almost perfectly transparent when targeted by neutrinos.)

 

38 The photoelectric effect provided evidence for the existence of....

a ... subatomic particles.

b ... phonons.

c ... electrons.

d ... photons.

 

39 The electron has spin of....

a ... zero

b ... ±1

c .. ±¹/2

d ... ±³/2

 

40 Aluminum components conduct electricity in circuit because....

a ... Aluminum is a metal.

b ... Aluminum is a good conductor.

c ... Aluminum is coated in a layer of oxide.

d ... of the tunnel effect.

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Section B - Astrophysics

Answer two questions only

 

 

Question 1

Part 1

A star has a parallax angle of 0.1 seconds of arc.

a Find (write down) the distance to the star in light years.

[1 mark]

b Why can this method not be used to measure the distance to even the closest galaxies?

[1 mark]

Part 2

Two stars have the same luminosity and different radii. Star A has a radius of 4x10¹⁰ meters and star B has a radius of 1x10¹² meters. Stefan's constant (s) is ... 5.67x10^-8 Wm^-2K^-4.

i Find the ratio of the surface brightness for ..... star A : star B.

Show your working. ............

[4 marks]

ii Find the ratio of surface temperatures for ..... star A/star B

Show your working.

[4 marks]

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Question 2

Part 1

The Sun has a surface temperature of 6000 K.

Assume that the sun is a black body and use Wein's law to find the peak wavelength of the solar output.

[2 marks]

Part 2

The solar constant (energy per second per square meter at the surface of the Earth when the Sun is overhead) is 1000 Watts.

a Find the total energy output of the Sun given that the atmosphere of the Earth reflects 30% of the incident energy and the radius of the Earth's orbit is 1.5x10⁸ meters.

Show your working.

[4 marks]

 

b When one kilogram of matter is converted to energy, 5.61x10³⁵ eV are released. One eV is equivalent to 1.60 x 10^-19 Joules.

Show that the mass-energy conversion constant is 9.0x10¹⁶ J/kg.

[1 mark]

 

c Use the results from a and b to find the rate at which matter is being converted to energy in the Sun, in kilograms per second.

[2 marks]

 

d Explain, in physical terms, how it is possible to estimate the time the Sun will spend on the main sequence. No working is needed - just explain what to do and state clearly what values are required.

[1 mark]

Question 3

Part 1

Explain what is meant by the cosmological red shift and explain how is Hubble's law used to estimate the distance to a faint galaxy?.

[2 marks]

Part 2

A galaxy appears to be receding from our own at 2x10⁷ m/s.

a A spectral line is found to have a wavelength of 2x10^-9meters on Earth (in the UV).

i Find the wavelength of the same line in the spectrum of the receding galaxy.

The wavelength is given by ...

[3 marks]

ii In what region of the spectrum is this line?

[1 mark]

Part 3

Suppose the receding galaxy in Part 2 is at a distance of 10²⁰ meters.

i Find the value of Hubble's constant using this distance and the recession velocity of 2x10⁷ m/s.

[1 mark]

ii Use this value of H to estimate the age of the universe.

[2 marks]

iii Is this age more or less than the current best estimate of the age of the observable universe based on the current best estimate of the value Hubble's constant?

[1 mark]

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Section C - Atomic and Nuclear Physics

Answer two questions only

 

Question 1

Part 1

1 An X-ray tube has a Cesium oxide cathode that is 20 cm from the anode which is a tungsten metal block.

a The anode voltage is +20,000 Volts.

i Write down the energy of electrons as they hit the anode.

[1 mark]

ii Why is the Anode water cooled?

Most of the electron energy (~99%) is converted to heat as electrons impact the anode. The anode becomes extremely hot (red hot) and may melt if not water cooled.

[1 mark]

b The continuous X-ray spectrum is called bremsstrahlung (German word).

i Why is it they called that?

[1 mark]

ii Write down the maximum photon energy of X-ray emissions.

[1 mark]

iii Find the minimum wavelength of X-ray emissions.

[1 mark]

c Find the de Broglie wavelength of the electrons as they hit the tungsten.

[1 mark]

 

Part 2

A photo-tube has a cathode which is exposed to monochromatic light from a filtered mercury arc lamp.

i The stopping voltage for the photo-tube is 2.1 Volts. Write down the maximum energy of emitted electrons in electron Volts.

[1 mark]

ii The work function is 0.8 eV.

i Explain briefly what is meant by the 'work function' and why it is different for different metals.

[1 mark]

 

iii Write down the energy of the incident photons in electron volts and find the wavelength of the incident light.

[2 marks]

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Question 2

Part 1 The diagram shows some of the energy levels of an electron that is bound to a proton to form a hydrogen atom.

The hydrogen spectrum is s series of 'ladders' of wavelengths.

i Describe briefly the connection between the ladders of wavelengths and the energy level diagram.

[2 marks]

 

ii Explain what is meant by the ionization energy of Hydrogen.

[1 mark]

 

Part 2

a A sample of radioactive material has a decay constant of 0.48 s^-1.

i Find the half life of the material.

[2 marks]

ii Find the length of time required for 99% of the material to decay.

[3 marks]

 

b The mass of the products of the radioactive decay are found to be 0.05 % less than the initial mass.

Calculate the energy in Joules released by the decay of 5 grams of the material.

[2 marks]

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Question 3

Part 1

a By equating the kinetic energy of the electron with the energy gained in electron Volts, show that the maximum velocity of an electron in a cathode ray tube with an anode voltage of 3000 V is 3.2x10⁷ m/s ... 10% of the speed of light!

Show your working

[2 marks]

b Remembering the two definitions of electric field strength E....

E = F/q = V/d

... show that if the electron beam is undeflected as it passes through crossed electric and magnetic fields the maximum electron velocity v is given by ... V/Bd where V is the plate voltage and d is the separation.

Show your working

[2 marks]

c Find the electron velocity v in a cathode ray tube where the anode voltage is 3000iV and the magnetic field strength is 2x10^-3 T, with a plate separation of 5x10^-2 m.

Show your working

[2 marks]

Part 2

When an alpha particle approaches a heavy nucleus (gold) on the line of centers, the distance of closest approach gives an upper limit on the size of the nucleus. It is a relatively simple matter to calculate this minimum distance by equating the kinetic energy of the alpha particle with the maximum potential energy in the field of the target nucleus.

PE in an inverse square force field is given by ...

The kinetic energy of the alpha particle is 5.5 MeV.

i Convert the kinetic energy of 5.5 MeV to Joules.

Show your working

[2 marks]

 

ii Find the the distance of closest approach to a gold nucleus (atomic number 79)

Show your working

[2 marks]

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