Consider a two-electron atom in which the electrons, orbiting a nucleus of charge +Ze, f...

Consider a two-electron atom in which the electrons, orbiting a nucleus of charge +Ze, follow Bohr-like orbits of the same radius r, with the electrons always on opposite sides of the nucleus. (a) Show that the net force on each electron is toward the nucleus and has magnitude

(b) Use the fact that this is the centripetal force to show that the square of each electron’s orbital speed v is given by

(c) Use the result of part (b) along with Bohr’s rule that the angular momentum of each of the two electrons is L = h in the ground state to show that

(d) Show that the atom’s total energy (kinetic plus potential) is

(e) The energy needed to remove both electrons is just the negative of the energy you found in part (d). Compute the energy needed to remove both electrons in helium, and then repeat for Li⁺. Compare your results with the experimental values of 79.0 eV and 198 eV, respectively.