4.1) What are the formulae for the normalized radial parts of 1s and 2s orbitals of He+, Na10+ and U91+ ions? Which one of them decays fastest with increasing r ?
4.2) From the five solutions for the H - atom for n =3, l = 2 and ml = -2 , -1, 0, 1 and 2 (ie, the 5 d orbitals), construct functions which are real by suitable combinations of the complex components consisting of the
terms.
4.3) Verify that the functons cos and ( 3cos2 -1) satisfy the angular part of the Schrodinger equation for the H- atom.
4.4) Verify that e- / 2 and
e- / 2 (where
= 2Z r/ n a0) satisfy the radial part of the schrodinger equation for the H-atom. Notice that we have used instead of sigma (
) used in Table 4.1.
4.5) What is the asympototic form of the radial part ( for each n ) of the schrodinger equation for large r ?
4.6) For
= e - / 2 . what is the value of energy in the schrodinger equation for the H-atom? Substitute the value of all the constants and obtain the numerical value of this energy.
terms. 
and ( 3cos2
/ 2 and
e-
= 2Z r/ n a0) satisfy the radial part of the schrodinger equation for the H-atom. Notice that we have used 
) used in Table 4.1. 
= e - 
