Topic 5_Atomic structure

Topic 5

Atomic Structure

5.0 Atomic Structure

5.1 Atomic orbitals
5.2 Electronic configurations
5.3 Atomic & ionic radii
5.4 Ionization energies
5.5 Electron affinity

5.1 Atomic orbitals

Knowing how electrons are arranged in an atom is
IMPORTANT because that governs how atoms interact with
each others.

An orbital is defined as 3D region/space around the nucleus,
where there is a high probability (>90%) of finding an
electron.

Electrons are treated as a matter as well as waves and are
being located in orbitals

A field of study known as the quantum mechanics is
introduced to solve the problem of finding electrons.

The concept of orbitals is that, not all electrons in an atom
are located as the same distance from nucleus but instead
are all at a certain specified space from nucleus where the
probability of finding electron is the greatest.

Orbitals are described in mathematical terms that is
characterized by the value of four quantum numbers,
designated by {n, l, ml and ms }

indicates the relative size, shape
& orientation in space of the orbital

Quantum Numbers and Atomic Orbitals

An atomic orbital is specified by four quantum numbers.

(i) The principal quantum number (n) is a positive integer.

The value of n indicates the relative size of the orbital and therefore
its relative distance from the nucleus.
n = 1,2,3,4….or K,L,M,N….

* specifies energy / level

(ii) The angular momentum quantum number (l) is an
integer from 0 to (n –1).

The value of l indicates the shape of the orbital.
l = 0, 1, 2, 3…. or s, p, d, f….

Quantum Numbers and Atomic Orbitals

(iii) The magnetic quantum number (ml) is an integer with
values from –l to +l.

The value of ml indicates the spatial orientation of the orbital.
l = 0… ml = 0
l = 1… ml = -1, 0, +1 or px, py, pz
l = 2… ml = -2, -1, 0, +1, +2 or dxy, dyz, dxz, dx2– y2, dz2

(iv) The spin quantum number (ms) represent the spin of e on its

own axis which can be clockwise or anticlockwise

ms = +1/2 or -1/2

Table 8.1 Summary of Quantum Numbers of Electrons in Atoms

Name Symbol Permitted Values Property

principal n positive integers (1, 2, 3, …) orbital energy (size)

angular l integers from 0 to n – 1 orbital shape (The l values
momentum
integers from –l to 0 to +l 0, 1, 2, and 3 correspond to
magnetic ml s, p, d, and f orbitals,
spin ms respectively.)

orbital orientation

+½ or –½ direction of e– spin

*A complete way to describe an orbital in its energy level is by stating the n & l
Example: n=2, l = 0 is 2s



Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals

Name, Symbol

(Property) Allowed Values Quantum Numbers

Principal, n Positive integer 1 2 3

(size, energy) (1, 2, 3, ...)

Angular

momentum, l 0 to n – 1 00 1 0 12

(shape)

00 0

Magnetic, ml -l,…,0,…,+l -1 0 +1 -1 0 +1
(orientation)

-2 -1 0 +1 +2

Sample Problem 7.6 Determining Quantum Numbers for an
Energy Level

PROBLEM: What values of the angular momentum (l) and magnetic

(ml) quantum numbers are allowed for a principal quantum
number (n) of 3? How many orbitals are allowed for n = 3?

PLAN: Values of l are determined from the value for n, since l can take
values from 0 to (n – 1). The values of ml then follow from the
values of l.

SOLUTION: For n = 3, allowed values of l are = 0, 1, and 2

For l = 0, ml = 0 For l = 1, ml = –1, 0, or +1

For l = 2, ml = –2, –1, 0, +1, or +2

There are 9 ml values and therefore 9 orbitals with n = 3.

Sample Problem 7.7 Determining Sublevel Names and Orbital
Quantum Numbers

PROBLEM: Give the name, magnetic quantum numbers, and number
of orbitals for each sublevel with the following quantum
numbers:

(a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3

PLAN: Combine the n value and l designation to name the sublevel.
Knowing l, we can find ml and the number of orbitals.

SOLUTION:
n l sublevel name possible ml values # of orbitals

(a) 3 2 3d –2, –1, 0, 1, 2 5

(b) 2 0 2s 0 1

(c) 5 1 5p –1, 0, 1 3

(d) 4 3 4f –3, –2, –1, 0, 1, 2, 3 7

Sample Problem 7.8 Identifying Incorrect Quantum Numbers

PROBLEM: What is wrong with each of the following quantum numbers
designations and/or sublevel names?

nl ml Name

(a) 1 10 1p

(b) 4 3 +1 4d
(c) 3 1 –2 3p

SOLUTION:

(a) A sublevel with n = 1 can only have l = 0, not l = 1. The only possible
sublevel name is 1s.

(b) A sublevel with l = 3 is an f sublevel, not a d sublevel. The name
should be 4f.

(c) A sublevel with l = 1 can only have ml values of –1, 0, or +1, not –2.

Figure 7.17 The 1s, 2s, and 3s orbitals. All s orbital are
spherically symmetrical
but the size of 2s is
bigger/longer than that
of 1s.

Basically, the relative
energy level of orbitals
depends on the value
of n

The same trend goes
with other type of
orbitals.

▪ As n increase, the
orbital become larger,
and the electron
spends more time
farther from the
nucleus.

▪An increase in n also
means that the
electron has a higher
energy and is
therefore less tightly
bound to the nucleus

Figure 7.18 The 2p orbitals.

Figure 7.19 The 3d orbitals.

Figure 7.19 continued



Figure 7.21 Energy levels of the H atom.

5.2 Electronic configuration

Show how electrons are filled in the orbitals. It describes
the arrangement of electrons in an atom.

To be able to do that, we have to obey the following rules:

(i) The Aufbau Principle : states that electrons in an atom
should be filled into the orbitals in the order of
increasing energy.

Electrons should occupy the orbital with the lowest energy
level first before it enters the higher energy.

Figure 8.5
Order for filling energy sublevels with
electrons.

In general, energies of sublevels increase as
n increases (1 < 2 < 3, etc.)

and as l increases (s < p < d < f).

As n increases, some sublevels overlap.

Aid to memorizing sublevel filling order.

Order of increasing energy of the
orbitals can be simplified by drawing
arrows as shown in the diagram.

The order of the orbitals filled is :
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p
6s 4f 5d 6p 7s 5f 6d 7p

2s2 Number of

electrons in

principal orbital

energy level orbital

(ii) Pauli’s exclusion principle : states that no two
electrons in the same atom can have the same four
quantum numbers. An atomic orbital can hold a
maximum of two electrons and they must have
opposing spins.

Li (Z = 3) 1s22s1

↑↓ ↑

1s 2s n = 2, l = 0, ml = 0, ms= +1/2

n = 1, l = 0, ml = 0, ms= -1/2

n = 1, l = 0, ml = 0, ms= +1/2

None of the e has the same set of four quantum numbers

(iii) Hund’s rule : specifies that when electrons are
added to the orbitals of equivalent energy (degenerate
orbital), each orbital is filled singly with e of the same
spin first before it is paired

N (Z = 7) 1s22s22p3 ↑↓ ↑ ↑ ↑

* The half-filled, 2s 2p
contributes to the
stability of the atom 2px 2py 2pz

O (Z = 8) 1s22s22p4 ↑↓ ↑↓ ↑ ↑

2s 2p

Electron Configurations and Orbital Diagrams

Electron configuration is indicated by a shorthand notation:

nl# # of electrons in the sublevel
as s, p, d, f

At ordinary conditions, e in an atom will occupies the lowest
possible level called the ground state.

When e are excited, they can transfer between shells (they
jump to a higher level) (excited state)

↑↓ or ↑↓

An arrow is used to represent
an electron and its spin.

Sample Problem 8.2 1s22s22p63s23p64s1 Method 1:
[Ar] 4s1 spdf notation
SOLUTION:
(a) For K (Z = 19)

full configuration
condensed configuration

Method 2 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓
Orbital diagram :
1s 2s 3s
2p
↑↓ ↑↓ ↑↓
↑

3p 4s

The anomolous electron configurations of
chromium and copper

Chromium and copper are two elements in the d block that
show irregularities in the electron configuration.

The anomolous configurations are easily on the basis that a
complete-filled or half-filled orbital is exhibits extra stability

24Cr : 1s2 2s2 2p6 3s2 3p6 4s2 3d4 is expected configuration
However to achieve stability, one electron from the 4s orbital occupies
one of the 3d orbitals in order to have half-filled orbital arrangement,
thus the actual configuration is :

1s2 2s2 2p6 3s2 3p6 4s13d5

29Cu : 1s2 2s2 2p6 3s2 3p6 4s2 3d9 is expected configuration

However with 10 electrons filled in 4d make the 4d orbitals
completely filled , which contributes to stability of the atom as
the repulsion between electrons decreases than the partially
filled 4d orbitals, thus the actual configuration is

1s2 2s2 2p6 3s2 3p6 4s1 3d10

Categories of Electrons

Inner (core) electrons are those an atom has in common
with the previous noble gas and any completed transition
series.

Outer electrons are those in the highest energy level
(highest n value).

Valence electrons are those involved in forming compounds.

- For main group elements (s & p block elements), the valence electrons
are the outer electrons.

- For transition elements, the valence electrons include the outer
electrons and any (n -1)d electrons.

Sample Problem 8.2 Determining Electron Configurations

PROBLEM: Using the periodic table on the inside cover of the text (not
Figure 8.10 or Table 8.3), give the full and condensed
electron configurations, partial orbital diagrams showing
valence electrons only, and number of inner electrons for the
following elements:

(a) potassium (b) technetium (c) lead
(Pb; Z = 82)
(K; Z = 19) (Tc; Z = 43)

PLAN: The atomic number gives the number of electrons, and the
periodic table shows the order for filling orbitals. The partial
orbital diagram includes all electrons added after the previous
noble gas except those in filled inner sublevels.

Sample Problem 8.2 1s22s22p63s23p64s1
[Ar] 4s1
SOLUTION:
(a) For K (Z = 19)

full configuration:
condensed configuration:

partial orbital [Ar] ↑
diagram:
4s 3d
4p
18 inner electrons
1 outer electron = 1 valence electron

Sample Problem 8.2 1s22s22p63s23p64s23d104p65s24d5
[Kr]5s24d5
SOLUTION:
(b) For Tc (Z = 43)

full configuration:
condensed configuration:

partial orbital [Kr] ↑↓ ↑ ↑ ↑ ↑ ↑
diagram:
5s 4d
5p
36 inner electrons
7 valence electrons
2 outer electrons

Sample Problem 8.2

SOLUTION:
(a) For Pb (Z = 82)

full configuration 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p2

condensed configuration [Xe] 6s24f145d106p2

partial orbital [Xe] ↑↓ ↑↑
diagram
6s 6p

78 inner electrons
4 valence electrons = 4 outer electrons

Similar electron configurations within groups

The Periodic table are arranged by how electrons within an atom
fill orbitals.

It is broken into blocks according into how electron configurations
of an atom ends.

Valence electron configurations within group are identical and
correlate with similar chemical behaviour.

Block s Block p
Group 1 (alkaline metal except H) : ns1 Group 13 – 18 :
Group 2 (alkaline earth metal) : ns2
ns2np1 - ns2np6

Block d
Group 3 – 12

ns2 (n-1)d1 - ns2 (n-1)d10

Electron Configurations of Cations and Anions
Of Representative Elements

Na: [Ne]3s1 Na+ : [Ne] Atoms lose electrons so that
Ca: [Ar]4s2 cation has a noble-gas outer
Al: [Ne]3s23p1 Ca2+ : [Ar]
Al3+ :[Ne] electron configuration.

H : 1s1 H- :1s2 or [He]

Atoms gain electrons so F : 1s22s22p5 F- :1s22s22p6 or [Ne]
that anion has a noble-gas O : 1s22s22p4 O2- : 1s22s22p6 or [Ne]

outer electron
configuration.

N : 1s22s22p3 N3-: 1s22s22p6 or [Ne]

5.3 Atomic & ionic radii

Defining atomic size.

The size /radius of atom is difficult to be defined exactly
because the electron cloud has no clear boundary.

To solve this, we measure the distance between the 2
nuclei in a molecule.

Defining atomic size.

B. The covalent radius of chlorine.

A. The metallic radius of aluminum.

C. Known covalent radii and distances
between nuclei can be used to find
unknown radii.

Trends in Atomic Size

To be able to interpret the trend, we firstly should know the
factors that determine the size of an atom.

Two factors that contributing to the changes of atomic radius:

• Value of the principal quantum number, n of the
valence electrons

✓The value of n for the valence shell increases
✓ The larger the value of n, the larger the electron cloud.
✓ Therefore, the larger the atoms as we go down a group.

• Effective nuclear charge (Zeff) : is the nuclear charge a
valence electron experiences as a result of shielding
effects due to the presence of other electrons.
The shielding effect is caused by the mutual repulsion
between electrons. This effect occurs between the inner
electrons and valence electrons and causes the
outermost electrons to be less attracted to the nucleus.

Example:
11Na : 1s2 2s2 2p6 3s1

it has a nuclear charge of 11+

The net charge felt by the valence
electrons is:

Zeff = Z – S = 11 – 10 = 1+

Trends in Atomic Size

Atomic size increases as the principal quantum number n
increases.

- As n increases, the probability that the outer electrons will be farther
from the nucleus increases.

Atomic size decreases as the effective nuclear charge Zeff
increases.

- As Zeff increases, the outer electrons are pulled closer to the nucleus.

For main group elements:
- atomic size increases down a group in the periodic table

and decreases across a period.

Figure 8.13

Atomic radii of the main-
group and transition
elements.

Figure 8.14 Periodicity of atomic radius.

Element Na Mg Al Si P S Cl Ar

Proton 11 12 13 14 15 16 17 18
number 1.54 1.36 1.25 1.15 1.1 1.02 0.99 0.94
0.95 0.65 0.50 - 2.12 1.84 1.81 -
Atomic
radii

Ionic
radii

This observation can be explained in the following way:

When across a period, proton number increases and electrons were added

to same n.

This lead to the increase of effective nuclear charge, Zeff. The valence
electron experience a greater attraction, so they are pulled closer to the

nucleus.

This result in a decrease in size of atoms across a period.
Similar trend is observed for +ve or –ve ions.

Sample Problem 8.3 Ranking Elements by Atomic Size

PROBLEM: Using only the periodic table (not Figure 8.15), rank each
set of main-group elements in order of decreasing atomic
size:

(a) Ca, Mg, Sr (b) K, Ga, Ca

(c) Br, Rb, Kr (d) Sr, Ca, Rb

PLAN: Locate each element on the periodic table. Main-group
elements increase in size down a group and decrease in size
across the period.

Sample Problem 8.3

SOLUTION:

(a) Sr > Ca > Mg
Ca, Mg, and Sr are in Group 2. Size increases down the group.

When go down a group, n increases. The greater the n value, the
valence electrons experience less attraction with the nucleus, thus
size become bigger.

(b) K > Ca > Ga
K, Ga, and Ca are all in Period 4. Size decreases across the period.

When across a period, proton number increases and electrons were
added to same n. Hence, Zeff increase. The valence electron
experience greater attraction, so they are pulled closer to the nucleus.

Sample Problem 8.3

SOLUTION:

(c) Rb > Br > Kr

Rb is the largest because it has one more energy level than the other
elements.
Br and Kr are at the same period 4. Kr has greater Zeff than Br and
has stronger attraction between electrons and nucleus, result in
smaller size of Kr than Br.

(d) Rb > Sr > Ca
Ca is the smallest because it has one fewer energy level (lowest n
value).
Rb and Sr are at the same period 54. Sr has greater Zeff than Rb and
has stronger attraction between electrons and nucleus, result in smaller
in size.

Ionic Size vs. Atomic Size

Cations are smaller than their parent atoms while
anions are larger.

Ionic radius increases down a group as n increases.
Cation size decreases as charge increases.

An isoelectronic series is a series of ions that have
the same electron configuration. Within the series, ion
size decreases with increasing nuclear charge.

3– > 2– > 1– > 1+ > 2+ > 3+

ions O2- F- Na+ Mg2+ Al3+ P3- S2- Cl-

Ionic 1.40 1.36 0.95 0.65 0.50 2.12 1.84 1.81
radii

No. of e 10 10 10 10 10 18 18 18

No. of 8 9 11 12 13 15 16 17
proton

There is a decrease of ionic size from O2- to Cl-.

All the ions are isoelectronic. The higher the Z or Zeff, the stronger
attraction between the valence electrons and the nucleus.

1s2 2s2 2p6

Periodic trends in the ionic radius (pg 358)

Size Of Positive Ion
• Size of positive ion is always smaller than the corresponding neutral
atom. Positive ion is formed when an atom loses electrons

Example :

Na Na+
Electron Electron
configuration Configuration
1s22s22p63s1 1s22s22p6
Number of Inner Number of Inner core
core Electron =10 Electron =2
Zeff =11-10=+1 Zeff =11-2=+9

The effective nuclear charge for Na+ is higher so, the attraction between
electron and the nucleus is stronger that makes the size smaller

Size Of Negative Ion
• A negative ion is always larger than the corresponding neutral atom.
• Negative ion is formed when an atom gains electrons.
• The negative ion has more electrons than the neutral atom.
• This will increase the repulsion between electrons and causes the size to

be larger.