Download A. Qualitative Questions

Workshop Tutorials for Physics
Solutions to QR6: Atomic Structure II
A. Qualitative Questions:
1. The periodic table.
a. The elements are ordered according to the number of protons in the nucleus (the atomic number, Z).
The number of protons determines the number of electrons, which determines how an element will
behave chemically.
7
6
b. A row in the periodic table all have their outermost 5
electrons in the same shell, and this shell is the row number,
C
B
N
and they have filled shells at lower energies. For example, Li,
carbon
nitrogen
boron
Be and B have a filled n = 1 shell and partly filled n = 2 shell.
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15
c. A period or column of the periodic table contains elements 13
with the same number of electrons in their outer shell, for
Al
Si
P
example H, Li and Na all have one electron in their outer shell
phosphorus
aluminium
silicon
d. C, Si and Ge have similar chemical properties because they
all have 4 electrons in their outer shell.
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31
33
e. Al, Si and P behave quite differently because they have
Ga
Ge
different numbers of electrons in their outer shell.
As
gallium
germanium
arsenic
2. The exclusion principle.
a. The Pauli exclusion principle says that no two electrons may occupy the same quantum state; in other
words they can’t have the same quantum numbers n, l, ml and ms. (The exclusion principle applies to a
large group of particles, including protons and neutrons, collectively known as fermions).
b. Atoms which have the same number of electrons in their outer shell (described by the n quantum
number) have similar characteristics. For example, the noble gases (down the last column of the periodic
table) have a filled outer shell and are inert, they do not react easily with other atoms. The first row
corresponds to the n =1 shell. The possible l numbers for any shell are 0 to n–1; in this case, for n = 1, the
only possible l number is zero, which is called the s sub-shell. There is only one possible value of ml, and
2 possible values of the spin number, ms. Hence there can be only 2 electrons in the n =1 shell, and only 2
elements in the first row of the periodic table: H with only one outer shell electron and He with a filled
outer shell, which is put at the opposite end of the row above the other elements with filled outer shells. In
the n = 2 shell there are 8 possible combinations of quantum numbers, hence there are eight elements in
the next row. After this it gets a little more complicated as the shells don’t quite fill in order because some
high l sub-shells have higher energy than the low l sub-shells of the next shell.
B. Activity Questions:
1. Periodic table
a. Most common metals, including iron, copper and lead are located around the middle of the periodic
table, four or more rows down, or to the left hand side in rows 2 and 3.
b. The radioactive elements, such as plutonium, uranium and radium are at the bottom end of the
periodic table, with high atomic numbers.
c. Elements in a given column have similar characteristics because they have the same outer electron
configuration, and when atoms interact (at normal energies) it is via their outer shell electrons.
d. The noble gases (the last column) are so inert because they have a complete outer shell of electrons.
This is a very stable configuration, and it is hard for them to either gain or lose electrons, so they do not
associate with other atoms.
e. The elements in the first column are so reactive because they have only a single electron in their outer
shell and a low ionisation energy. This means it is easy for them to form bonds by losing that outer
electron to another atom.
The Workshop Tutorial Project –Solutions to QR6: Atomic Structure II
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2. Molecular models
Atoms with the same number of outer electrons have similar characteristics, and it is also their outer
electron number that determines their bonding behaviour.
C. Quantitative questions:
1. Quantum numbers.
a.
Quantum
Symbol
Possible values
related to:
number
principal
n
1, 2, 3, …
distance from nucleus, energy
orbital
l
0, 1, 2, …, (n-1)
orbital angular momentum
orbital magnetic
ml
orbital angular momentum (z component)
0, 1, 2, …, l
spin magnetic
ms
spin angular momentum (z component)
½
If the quantum number l is 3, then:
b. The principal quantum number must be greater than 3, as l must be less than n. Hence possible values
of n are n = 4, 5, 6, …..
c. The possible values of ml are 0, 1, 2, 3, and the possible values of ms are  ½.
2. The ionisation energies of the elements tend to increase along a given row.
a. The ionization energy is the energy required to separate an electron from the atom, thus ionizing it.
Filled shells are very stable, so it is hard to remove an electron from a filled shell. In general, the closer to
full that a shell is, the harder it is to remove electrons from it. Elements such as lithium and sodium have
only a single electron in their outer shell, and a filled shell at lower energy than this, so they are easily
ionized. Noble gases have a filled outer shell so they have very high ionization energies.
b. For atoms heavier than helium the ionisation energy is much less than you would expect by
considering only the coulomb attraction between the nucleus and the outer shell electron because of
“shielding” due to the other electrons. The attraction to the nucleus is less due to the presence of other
electrons in lower energy states, hence the ionization energy is lower.
c. The nucleus of the lithium atom (Z = 3) would be shielded by two electrons in the n = 1 shell, so the
electron in the n = 2 shell would see an effective nuclear charge of Z’e = 1e.
d. The energy of this outer shell electron would hence be
1 kZe
E= 2 r
2
1
= 2
kZe 2
4 a0 =

Z
4 (13.6 eV) = - ¼ (13.6 eV) = -3.4 eV.
e. In fact, the energy E = 5.39 eV,
E=
 12
kZe 2
4 a0 =

Z
4 (13.6 eV) = -5.39 eV, which we can rearrange to find Z’ :
Z = 4  (-5.39 eV/-13.6eV) = 1.59.
f. Comparing the answers to d and e, we can say that the outer electrons see a reduced nuclear charge
but the nucleus is only partly shielded by the inner electrons.
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The Workshop Tutorial Project –Solutions to QR6: Atomic Structure II