Problem 1
Distinguish between a vector and a scalar quantity and give examples of each.
Problem 3
Determine the possible values of the quantum numbers \(l\) and \(m_{l}\) corresponding to \(n=4 .\) From your answer, deduce the number of possible \(4 f\) orbitals.
Problem 5
How many orbitals are there in (a) the shell with \(n=3,(\mathrm{b})\) the \(5 f\) sub-shell, (c) the \(2 p\) sub-shell, (d) the \(3 d\) sub-shell and (e) the \(4 d\) sub-shell?
Problem 6
Which atomic orbital has the set of quantum numbers \(n=3, l=0, m_{l}=0 ?\) How do you distinguish between the two electrons that may occupy this orbital?
Problem 7
What do the terms singly degenerate and triply degenerate mean? Give examples of orbitals that are (a) singly and (b) triply degenerate.
Problem 8
How does an increase in nuclear charge affect the (a) energy and (b) the spatial extent of an atomic orbital?
Problem 9
Determine the energy of the levels of the hydrogen atom for \(n=1,2\) and 3.
Problem 11
Sketch an energy level diagram showing the approximate relative energies of the \(1 s, 2 s\) and \(2 p\) atomic orbitals in lithium. How does this diagram differ from a corresponding diagram showing these levels in the hydrogen atom?
Problem 12
For lithium, \(Z=3 .\) Two electrons occupy the \(1 . s\) orbital. Is it energetically better for the third electron to occupy the \(2 s\) or \(2 p\) atomic orbital? Rationalize your choice.
Problem 13
What is the difference between the absolute nuclear charge of an atom and its effective nuclear charge. Are these variable or constant quantities?
