(a) The nitrogen atom has one electron in each of the 2px,2py and 2pz orbitals. By using the form of the angularwave functions, show that the total electron density,c2(2px) +c2(2py) +c2(2pz), is spherically symmetric(that is, it is independent of the angles u and f). Theneon atom, which has two electrons in each 2porbital, is also spherically symmetric.(b) The same result as in part (a) applies to d orbitals,thus a filled or half-filled subshell of d orbitals isspherically symmetric. Identify the spherically symmetric atoms or ions among the following: F=, Na, Si,S2-, Ar+, Ni, Cu, Mo, Rh, Sb, W, Au.

Give all possible mĮ values for orbitals that have each of the following values: (a) 1 = 3 -1, 0, +1 −2, −1, 0, +1, +2 −3,−2, −1, 0, +1, +2, +3 (b) n = 2 −1, 0, +1 −2,−1, 0, +1, +2 −3, −2, −1, 0, +1, +2, +3 (c) n = 6, 1=1 -1, 0, +1 −2,−1, 0, +1, +2 −3, −2, −1, 0, +1, +2, +3

3.) The experimental electronic configuration of Yb is [Xe]4f¹46s². (a) Is this in line with the theory, e.g. Aufbau principle and atomic structure? (b) If not, which is the expected electronic configuration? (c) Give reasons you think explain this variations (d) State the Aufbau principle

00 P: Pr Figure 2 Figure 2 shows the boundary surface of 2p orbitals of a hydrogenic atom in three dimensions. (i) What are the number 2 and the letter p in the name '2p orbital stand for? 2 (v) Describe how the px, Py and pz orbitals are differentiated and named as such. (vi) Some people say that the non-spherical shapes of the orbitals in Figure 2 can only be obtained by using quantum mechanics. Do you agree? Elaborate. N