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# 22.2.1: i. Review Exercises

## Q1

Draw qualitative shapes of the (1) s, (3) p and (5) d "tangent sphere" atomic orbitals (note that these orbitals represent only the angular portion and do not contain the radial portion of the hydrogen like atomic wavefunctions) Indicate with ± the relative signs of the wavefunctions and the position(s) (if any) of any nodes.

## Q2

Define the symmetry adapted "core" and "valence" orbitals of the following systems:
i. $$NH_3$$ in the $$C_{3v}$$ point group,
ii. $$H_2O$$ in the $$C_{2v}$$ point group,
iii. $$H_2O_2$$ (cis) in the $$C_2$$ point group,
iv. N in $$D_{\infty h}, D_{2h}, C_{2v}$$, and $$C_s$$ point groups,
v. N$${_2} \text{ in } D_{\infty h}\text{, } D_{2h}, C_{2v}$$\text{, and } C_s\) point groups.

## Q3

Plot the radial portions of the 4s, 4p, 4d, and 4f hydrogen like atomic wavefunctions.

## Q4

Plot the radial portions of the 1s, 2s, 2p, 3s, and 3p hydrogen like atomic wavefunctions for the Si atom using screening concepts for any inner electrons.