QCEVault

Special relativity — Question 181

Original QCE Vault practice · 7 marks

Q181 · Practice questionComplex familiar7 marks

QUESTION 181 (7 marks)

An electron and a positron initially at rest annihilate into two photons travelling in opposite directions with equal energies. Use me=9.1093835×10−31 kgm_e=9.1093835\times10^{-31}\,\mathrm{kg}, c=3.00×108 m s−1c=3.00\times10^8\,\mathrm{m\,s^{-1}}, h=6.626×10−34 J sh=6.626\times10^{-34}\,\mathrm{J\,s} and 1 eV=1.60×10−19 J1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm J.
a)
Determine the energy of each photon in joules and MeV.
[3 marks]
b)
Determine the wavelength of each photon.
[2 marks]
c)
Explain why opposite photon directions are consistent with momentum conservation.
[2 marks]
Question linkSyllabus coverage

Related questions

  1. Q28 · Original practice · 1 mark
    Two laboratories move at constant velocity relative to one another. Each laboratory performs the same mechanics experiment and measures the speed of the same light pulse in vacuum. Which result is consistent with special relativity?
    Special relativity
  2. Q29 · Original practice · 1 mark
    A proper time interval is measured by a clock for which the two events occur
    Special relativity
  3. Q30 · Original practice · 1 mark
    A spacecraft clock measures a proper time interval of 5.0 μs5.0\,\mu\text{s}. The spacecraft moves at 0.80c0.80c relative to Earth. What interval is measured on Earth?
    Special relativity
  4. Q31 · Original practice · 1 mark
    A spacecraft has proper length 12.0 m12.0\,\text{m}. It passes Earth at 0.60c0.60c. What length is measured by Earth observers?
    Special relativity