# A. Quantum numbers

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```					A. Quantum numbers.

1.- Determine the number of different allowable sets of quantum numbers that have n = 4.
LIST ALL l VALUES FOR n = 4; FOR EACH l DETERMINE ml; FOR EACH ml there are 2 ms
VALUES ALLOWED FOR A TOTAL OF 32 SETS.

2.- List all the sets of quantum numbers for a 6p electron.
n = 6, l = 1.
WRITE ALL POSSIBLE ml FOR THIS l AND ms FOR EACH ml. TOTAL 6 SETS.

3.- If an electron has n = 3, list the restrictions on its other quantum numbers (i.e. indicate possible
values of l, ml and ms).

l = 0,1 and 2 [0,1,.. (n-1); for each l: ml = [-l, ...-1,0,1...+l]; FOR EACH ml: ms = [± 1/2]

B.- Shape of atomic orbitals.

1.- Draw an electron contour surface of an orbital that corresponds to each of the following sets of
quantum numbers (indicate a coordinate axis)
a) n = 2, l = 1, ml = -1, ms = +1/2 =          2p

b) n = 2, l = 0, ml = 0, ms = -1/2                    =        2s

A. n = 3, l = 2, ml = -2, ms = -1/2                   =         3d

2.- Identify each of the following orbitals and give a valid set of quantum numbers for each (hint: use the
size of the 3s orbital to identify the other three)

3s                       3p                             3d                          3d
n l ml ms                  n l ml ms                           n l ml ms                   n l ml ms
3, 0, 0, -1/2              3 1 -1 1/2                          3 2 -1 1/2                  3 2 0 1/2
C.- Electron configuration
1.- Draw the ground-state orbital energy diagram and write the shorthand configuration for the electrons
in a sulfur atom.
Show the energy level diagram showing the arrangement of 16 electrons of the sulfur atom according to
the four principles to write the ground state electron configurations.

Shorthand notation
1s2, 2s2, 2p6, 3s2, 3p4

2.- Write the electronic configuration (1s2, 2s2, 2p6 …..) of Rhenium (Z = 75)
1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d10, 5p6, 6s2, 4f14, 5d5

3.- What is the ground state configuration of Bismuth? (condensed form). Specify quantum numbers of
any unpaired electrons.
[Xe] 6s2, 4f14, 5d10, 6p3
3 unpaired electrons
n = 6, l = 1, ml = -1, ms = +1/2
n = 6, l = 1, ml = 0, ms = +1/2
n = 6, l = 1, ml = 1, ms = +1/2

4.- None of the following hypothetical configurations describes the ground state of an F atom. For each,
state the reason why it is not correct:

a) 1s2 2s2 2p4
Fluorine has 9 electrons, this configuration is for an 8-electron species.
b) 1s2 2s1 2p6
Violates Aufbau principle
b) 1s3 2s2 2p4
Violates Pauli exclusion principle
d) 1s2 2s2 1p5
The possible numbers l can take are: 0,1,2,,,(n-1)
l = 1 is not a valid solution for n=1
D.- Electron configuration of ions.
1.- What is the ground state electron configuration of Cr3+ cations?
[Ar] 3d3

2.- Which of these species is paramagnetic? Draw orbital energy diagrams to support your answer and
for the paramagnetic species indicate the net spin.
Show the electron configuration of each species.
a) F-          S=0 diamagnetic
b) Zn2+ S=0 diamagnetic
c) Ti          S=1 paramagnetic

E.- Electron Configuration and Periodicity.
1.- Arrange the following atoms in order of increasing size (largest last): Cl, F, P and S.
F<Cl<S<P
2.- As a general trend, the ionization energy of the elements rises from left to right across a period.
However, the measured ionization energy of Nitrogen is 1400 kJ/mol and that of oxygen is 1310
kJ/mol. Suggest a reason for this small decrease.
Show the ground state electron configuration of each using an energy level diagram; electron- electron
repulsion is in place.

3. - Circle the ions that are likely to be formed
Ba2+             Al4+             Tl+             Tl3+          At2-             Se+

F. Write the ground state electron configuration of elements 6-14 using an energy level diagram,
Indicate whether each one is paramagnetic or diamagnetic and write a set of quantum number
for unpaired electrons.

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