Problem 4.5: Find the distance of closet approach in Rutherford Scattering

KE alpha= MeV (2 MeV < KE < 10 MeV)

Target: gold | silver | copper

Please wait for the animation to completely load.

For Rutherford scattering, when an alpha particle (z = 2) heads straight for a nucleus (impact parameter, b, equal to zero), the point where the alpha particle gets closest to the nucleus is called the distance of closest approach. You can measure this in the animation above for different values of incident alpha particle kinetic energy and nuclear charge (grid units are in fm, 10−15 m)Restart.

  1. Develop an expression for that as a function of incident kinetic energy of the alpha particle and charge on the nucleus. Verify your relationship with the animation.
  2. How does this distance compare to the size of the nucleus (around 7 fm for gold)? How do these distances compare to the Bohr radius (typical size of an electron orbital)?