Synoptic Paper June 2004
Neutrinos: detecting the undetectable
Questions
Problems with beta decay
 Draw and label the paths of an  particle and  particle in a magnetic field (6-8)
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Derive an equation for the radius of curvature of a particle mass m, charge q, moving in a magnetic
field of flux density B such that the particle enters perpendicular to the field (6-8).
Does the magnetic field affect the speed of the  particle or  particle? If so why? If not, why not?
(7)
Why are “rather strong” magnetic fields needed for alpha particles? (8)
Explain the meaning of the term 'spectrum' in line 9.
Show that the speed of a 5.6MeV alpha particle is 1.7x107 m/s. (13)
Using the equation above show that the radius of path of this particle when it is in a field B = 1T,
given q = 2 x 1.6 x 10-19C and mass m = 4 x 1.67 x 10-27 kg is 0.34m.
(Difficult) Why does the conservation of momentum result in nearly all the energy being given to the
alpha particle? Consider the momentum and kinetic energy before and after the disintegration. (1013).
Complete the following equation for the decay of polonium 210 (line 9):
210
84Po
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 He + Pb
Work out the recoil speed of the lead nucleus (12)
Why can a beta particle have a higher speed but rather less kinetic energy than an alpha particle?
(14)
Show that the maximum speed of the beta particle mentioned in line 18 is 6.4x106m/s.
Add another curve to the beta particle energy spectrum to show the energy spectrum for the so-called
‘extra’ particle that Pauli predicted. How are the energies of the extra particle and the beta particle
related?
Complete the following nuclear decay equation for Bismuth – 210:
210
Bi  e +
210
Po
83
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and show how the equation conserves mass, charge, lepton and baryon numbers. Why are antineutrinos produced? (17)
Draw a Feynman diagram to show how the neutron changes into a proton, electron and antineutrino.
Explain why the new particle must be uncharged (27)
What is the “rest energy” of the neutrino? How is it related to its mass? (28)
Why is it difficult to detect particles that are uncharged? (34)
Detecting the neutrino
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In the equation in line 38 show that both lepton number and baryon number are conserved.
In terms of quarks what is happening in this reaction? (38)
In the annihilation of the electron and positron calculate the minimum energy of the gamma photons.
What assumption must you make? (40)
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Why do the photons move in opposite directions? (43, Fig 3)
Estimate the activity of the reactor core (46)
Explain the term 'flux' (46)
How does the photomultiplier tube (48) ‘amplify’ the detection of the gamma photons?
Why did moving the detector 12 metres underground reduce the background count? (55)
Explain the term “signal to noise ratio” (56).
Neutrino astronomy and the solar neutrino problem
 Estimate the power falling on one square metre of the Earth’s surface (62-63)
 The power of the sun is 4 x 1026 J/s. In one second you need 2 x the mass of 1 proton used as fuel.
Show that if there are 2x1038 reactions per second then this requires 6.8 x 1011 kg of hydrogen to be
used each second
 Estimate a typical neutrino energy from Fig 2. Use this to estimate the dose you would receive per
year from a “few thousand” neutrinos (66-67). If the neutrino has a radiation quality factor of 1, is
the phrase “truly negligible” justified? (67).
 The density of tetrachloroethene is 1624kg/m3 and the mass of 1 tetrachloroethene molecule is 2.754
x 10-22g estimate the number of chlorine-37 atoms in the detector. (72)
 Write a nuclear equation to show what happens to chlorine-37 when it absorbs a neutrino (74)
 Estimate the activity of argon 37 atoms shown in line (74)
 We can work out how many neutrinos we would expect from the sun. The distance from the Earth to
the Sun is 4 x 1011 m. Show that the surface area of the sphere of this radius is 2.4 x 1023m2. If the
number of neutrinos/sec = 2 x 1038/sec, show that the number of neutrinos in one m2 is 8.5 x
1014neutrinos/m2/sec. When the flux of neutrinos was 1017 neutrinos/m2/sec there were 3 events per
hour. Use this to show that the number of expected events per hour = 2.6 x 10-3. Then show that the
number of expected neutrinos per month = 18. What fraction of the expected neutrinos has actually
been detected? (83)
Neutrinos, photons and stars
 Explain the term “plasma” (87)
 Estimate typical photon energies for photons in the core and at the surface of the Sun (88-90).
 Draw the first 4 energy levels for hydrogen. If an electron is promoted from the ground state to the
4th level, how many different ways could it return to the ground state? (88)
 Wiens Law states that the peak wavelength emitted from a hot body = 2.898x10-3/T where T is the
absolute temperature. Determine the peak wavelength and hence minimum energy of the photons
(90)
 Compare the distance with the displacement for a molecule going from A to B in fig 4. Does this
agree with the theory given in lines 91-96?
 Estimate the size of the core, assuming neutrinos travel at the speed of light (99)
 Explain lines 100-101 in terms of nuclear binding energy.
 Determine the distance in metres to the supernova (103-104)
‘Oscillating’ neutrinos
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What charge is carried by the up and down quarks referred to in line 110?
A lepton can be defined as a fundamental particle with no ‘strong interactions’ what does this mean?
Show that the mass of an electron is 0.51MeV and hence confirm that the mass of a neutrino is
1/200000 of the mass of an electron (120).
If the neutrinos with mass can oscillate then some ‘restoring force’ may act. Suggest where this
restoring force may come from
Explain how the diagram in fig 6 supports the idea that at night there will be fewer electronneutrinos