Consider a helium ion He+.
a) Find the ratio between the ionization energy of the H atomand and the He^+ ion.
b) How does the Bohr radius, we defined for H atom, differ forHe^+ ? Using the Bohr radius of He^+ and the representation of theground state wave function for the H atom, write the ground statewave function for the He^+.
c) Find the average distance of a 1s electron from a nucleus inHe+ ion. How does it compare with the Bohr radius you found in (b)for H atom and He^+ ion?
d) Find the most probable value of r characterizing the distancebetween a 1s electron and the nucleus in the He^+ ion. Compare youranswer with (c) and discuss a physical meaning of obtainedresults.
e) Find the average distance of 2pz electrons from a nucleus inHe+ ion. Compare your results with those for a 1s electron in (c).Are you surprised by the answer?
f) How your answer in (e) would be different, if you find theaverage distance of 2px electrons, instead of pz?
