A one-electron uranium atom. A neutral uranium atom has 92 electrons surrounding a nucleus containing 92 protons.
(a) Given that the Bohr radius for the lowest energy in hydrogen is a,, = 0.5 A. derive an approximate numerical value on the basis of Newtonian mechanics for the radius of the smallest Bohr orbit about the uranium nucleus.
(b) In a violent nuclear event a uranium nucleus is stripped of all 92 electrons. The resulting bare nucleus captures a single free electron from the surroundings. Given that the ionization energy for hydrogen is 13.6 eV, derive an approximate numerical value for the maximum energy of the photon that can be given off as the uranium nucleus captures this ?rst electron.
(c) Calculate the value of v/c for the ?rst Bohr orbit in U" according to Newtonian mechanics. This will show you that relativistic dynamics should really be used in this problem.