F7    Problems and Suggestions

  1. Think about how the following energy units must be converted into one another:
    a) J       b) MeV      c) u       d) kg
  2. A common oxygen atom (ie O-16) weighs 15.994915 u. Using the standard values of proton mass, neutron mass and electron mass, calculate the average binding energy of a proton or neutron in the oxygen nucleus and compare your result with the diagram in F3.
  3. A particle of rest mass m collides inelastically with kinetic energy 4 • m • c2 with a resting particle of the same rest mass. Show mathematically that the particles can merge into a single particle and calculate its rest mass.
  4. In a direct collision of an electron with a positron psi particles can be created if the electron and the positron have been accelerated to the point where their masses increase to 3700 times their rest mass.
    a) Determine the required kinetic energy of the electrons in MeV
    b) Determine the rest mass of the resulting psi particle
    c) How heavy would the scrap heap be, if two small cars of rest mass 500 kg collide head on with the same speed as the electron and the positron?
  5. (challenging follow-up to problem 4)
    What energy in MeV must a positron have in order that its collision with a resting electron produces a psi particle? Do not consider the velocity, but rather the energy and momentum and use equation (2) in E5 ! Compare this result with the effort required using a double storage ring as in 4!
  6. Show that you do not obtain the relativistic expression for kinetic energy, if you simply substitute the dynamic mass mv for the variable m in the formula 0.5 • m • v2.
  7. This problem refers to the illustration in F5. The magnetic field perpendicular to the plane of the image has a strength of 0.214 Tesla, and the radii of the two trails at the beginning of their spiral are measured with r1 = 8.31 cm and r2 = 5.17 cm respectively.
    a) Calculate for both the electron and the positron the total energy and hence their mass immediately after their emergence
    b) Determine the kinetic energies and velocities the two particles have after their formation
    c) Determine the minimum energy of the γ-quant that is produced and using Planck’s formula E = h • f also its minimum frequency
    d) For photons E = p • c. Show that only part of the momentum of the quant is given to the two resulting particles and thus another particle must also be at play in this production
  8. An x-ray quantum with an energy of 100 keV collides with an electron at rest and is absorbed by it. What speed does the electron take on?
    a) Solve using the conservation of momentum
    b) What would the electron velocity be, if the total energy of the photon were converted into kinetic energy of the electron?
    c) What percentage of the incidental energy is not converted into kinetic energy of the ? What happens to this part?