Re: Positrons

ram@zedat.fu-berlin.de (Stefan Ram) wrote or quoted:

To get into this mindset just think about how the mass of an atom
of hydrogen is smaller than the mass of the proton and electron
taken in isolation. This would be another example where the
mass of a combined system differs from the sum of the masses of its
components.

  The binding energy of hydrogen is "-13.6 eV".

  It is the sum of the potential energy and the kinetic energy
  of the electron and is part of the mass energy of hydrogen.

  I take this calculation from the World-Wide Web, but might
  have added typos when converting it to plain text:

At the mean radius a_B = 0.528 × 10^{−10} m, the potential energy
of the pair is:

        1    e^2
U = − -----  --- = −4.36 × 10^{−18} J = −27.2 eV.
      4πϵ_o  a_B

The kinetic energy is half this value, and agrees with the classical
result for a particle in uniform circular motion:

mv^2     1     e^2     1          1    e^2
---- = -----  ----- => - mv^2 = -----  ---.
a_B    4πϵ_o  a_B^2    2        8πϵ_o  a_B


So the binding energy is: E = K + U = −13.6 eV.