L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.1
Part 2: THE ATOMIC STRUCTURE OF ATOMS AND THE PERIODIC TABLE
Chapter 4:
The Electronic Structure of Atoms
4.1 Atomic emission spectra and electronic structure of atoms
I.
Emission Spectrum of Hydrogen and its Characteristic
A spectrum is a display or dispersion f the component of radiation and is obtained by use of
spectrometer.
Electromagetic radiation is a continuous radiation (i.e. containing all wavelengths within a specific
range.) Its spectrum is a continuous spectrum, e.g. Rainbow.
However, the spectrum of elements are discontinuous. The study of the emission spectrum of
hydrogen atom, which consists of discrete lines, gives the insight about the energy levels in an
atom.
A. Production of Hydrogen Spectrum
- When hydrogen is heated to a high temperature or an electric discharge is passed through it at
low pressure, the hydrogen molecules split into atoms and these absorb energy.
- The hydrogen atom is excited as they contain excess energy. Their electrons are promoted from
the ground state (n=1) to high energy level.
- The excited atoms are unstable. When the excited electrons lose energy and fall back to the
ground state, they emit light of various wavelengths, producing the emission spectrum of
hydrogen.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
B.
Ch 4: p.2
Characteristics of Hydrogen Spectrum
Balmer series in the visible spectrum
Interpretation
<1> The emission spectrum consists of coloured bright lines in dark background.
<2> The spectrum of hydrogen consists of several series of discrete lines which converge in
different parts of the electromagnetic spectrum. e.g.
Lyman series in the ultraviolet region.
Balmer series in the visible region.
Paschen series in the infrared region
<3> Within each series, the lines get closer together and converge at shorter wavelengths ( or
higher frequencies). Finally, these lines merge into a continuum of light (line of higher
frequencies). This is the convergence limits.
<4> The wavelengths of the special lines are unique to each element.
<5> The relation between the wavelengths of the lines in spectrum is as follows:
1/ = RH ( 1/n12 – 1/n22 )
where  = wavelength of the spectral line
RH = Ryberg constant, and
n1 and n2 are integers which correspond to different series of lines in the spectrum
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.3
<6> The frequencies of the discrete lines of the various series are found experimentally to obye
the line following relationship:
 = c/= c RH ( 1/n12 – 1/n22 )
Lyman series (ultraviolet region, highest energy ):
1/ = RH ( 1/12 – 1/n22 )
where n2 = 2,3,4,5….
Balmer series (visible region)
1/ = RH ( 1/22 – 1/n22 )
where n2 = 3,4,5,6….
Paschen series (near infrared region)
1/ = RH ( 1/32 – 1/n22 )
where n2 = 4,5,6….
C. The Origin of emission spectrum
The transition of an electron from a higher to a lower energy level emits a discrete amount of
energy in the form of radiation. This produces a line in the atomic spectrum.
II.
Interpretation of the emission spectrum using Planck’s Equation
1.
2.
When a hydrogen atom is excited, the electron temporarily occupies an energy level further
from the nucleus (higher than the ground state).
Energy is then emitted as radiation as electron falls back to lower energy level.
Energy is not released over a continuous wide range of frequencies, but at
unique frequency.
For each electron transition, a quantum of radiation is emitted.
3.
The difference between 2 electronic energy levels can be calculated from Planck’s equation if
the wavelengths of lines are measured.
Einitial - Efinal = h = hc/ * Planck’s equation
where Einitial - Efinal = quantum of energy,
h = the Planck’s constant = 6.624 x 10-34 Js and
 = frequency
4.
5.
6.
Therefore, when an electron falls from a higher energy level(e.g. n=2) to ground state (n=1),
it emits a quantum of energy E in radiation of definite frequency, .
Since E for the change from E2 to E1 is always the same in a given atom, and h is a
constant ,  must be a constant. Therefore, radiation always has the same energy and is
always of the same frequency for this particular electron transition.
As a result, the atomic emission spectra of elements consist of discrete lines, i.e.
discontinuous. They are therefore also called ‘line spectra’.
The discrete lines in the hydrogen emission spectrum are caused by the
transition of electrons from one energy level, with the emission of energy.
These discrete lines confirm the existence of discrete energy levels.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
7.
Ch 4: p.4
The wavelength of each lines in the emission spectrum of atomic hydrogen is given by the
expression.
1/ = RH (1/n12 – 1/n22 )
where  = wavelength of the spectral line
RH = Ryberg constant, and
n1 and n2 are integers which correspond to different series of lines in the spectrum
8.
The Lyman series in the UV region of the emission spectrum is caused by electronic
transition from the various possible energy levels (n=2,3,4…) to the lowest energy level
(n=1).
9.
If the transition are to the Balmer series ( i.e. from the various possible higher energy levels
to n=2) , less energy is released. The radiaion emitted appears in the visible region of the
spectrum and coloured lines are observed.
10. If electronic transitions are from the higher energy levels to n=3, much less energy is released.
The spectral lines in lower energy region (infrared) of the spectrum.
The lines form the Paschen series.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.5
Note: <1> The spectral lines in the atomic spectrum of hydrogen are not equally spaced. Why?
It is because ____________________________________________________________
______________________________________________________________________
______________________________________________________________________
<2> The spectral lines in the atomic spectrum of hydrogen are not of equal intensity. Why?
It is because ____________________________________________________________
______________________________________________________________________
______________________________________________________________________
CONCLUSION
- An electron in an atom does not have a continuous range of energy values. The
electron can only have certain fixed energy values or exist in certain fixed energy
levels. It cannot possess energy of intermediate magnitude.
-
-
When atoms absorb or emit energy, it is the result of electron moving from one
level to another. The amount of energy involved is exactly equal to a photon (a
quantum of energy = h )
Only transitions from one level to another are possible. Transitions of electrons to
intermediate energies are not allowed.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.6
Name: __________________ Class No.:_____
Date:__________
Marks:_________
Exercises:
1. The Lyman series of lines from hydrogen atom have frequencies given by the expression:
 = 3.288 x 1015 ( 1/12 – 1/n2 ) Hz
where n = 2, 3, 4, 5…. 
For the spectral line with n =2 ,
(a) calculate the frequency in hertz and the wavelength in m of the radiation,
(b) calculate the energy of the quanta of this radiation in joules per quantum and per Avorgadro’s
number of quanta.
(c) State what region of electromagnetic radiation this spectral line is in.
Given
c = velocity of light = 3x108 ms-1
h = Planck’s constant = 6.63 x 10-34 Js; Avorgadro’s number = 6.02 x 1023
( 5 marks )
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Name: __________________ Class No.:_____
2.
Ch 4: p.7
Date:__________
Marks:_________
In the atomic spectrum of hydrogen, the frequencies of the first four lines in the Lyman series are
given below:
Transition
Frequency / Hz
n =2 to n = 1
n =3 to n = 1
n =4 to n = 1
n =5 to n = 1
15
15
15
3.157 x 1015
2.466 x 10
2.923 x 10
3.083 x 10
Calculate the frequency of the
(a) first line
(b) last line
in the Balmer series in the atomic spectrum of hydrogen.
Given: c = velocity of light = 3x108 ms-1
h = Planck’s constant = 6.63 x 10-34 Js; Avorgadro’s number = 6.02 x 1023
Rydberg constant = 10967780 m-1
( 4 marks )
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Name: __________________ Class No.:_____
3.
Date:__________
Ch 4: p.8
Marks:_________
All spectral lines in the atomic emission spectrum of hydrogen are related by the formula
1/ = 109680 ( 1/n12 – 1/n22 ) cm-1
where
 = wavelength of the line
n1 and n2 indicates the principal quantum numbers.
(a) 2 hydrogen atomic lines from the Paschen series are measured to be 9140 cm-1 and 7799 cm-1
respectively in an emission. What are the principal quantum numbers associated with these 2
electronic transitions?
(b) Draw an energy level diagram for a hydrogen atom. Indicate on the same diagram the transitions
giving rise to the lines in (a)
( 5 marks )
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.9
IV. Convergence Limits and Ionization
Each series of spectral lines come closer and finally converge to a convergence limits
(continuum line) as frequency increases (wavelength decreases). The spectrum then
becomes continuous.
All electronic energy levels also converge, and come together at the n=  level.
1. Ionization enthalpy is the energy required to remove an electron from the lowest energy level
(ground state, n=1) to the outermost part of the atom (n2 =  )
H(g)  H+(g) + e
2. If sufficient energy is supplied to an atom to promote an electron from one energy level to the
highest possible one and just beyond it, the electron is able to escape. The atom become an ion
3. It is therefore possible to determine the ionization enthalpy of an element from its spectrum.
This can be done if the frequency at which the convergence spectral lines actually come
together is shown.
4. This frequency is known as the ‘convergence limit’
Lyman series represents electrons making transitions to the lowest energy level n=1,
the convergence limits represent the energy required to ionized a hydrogen atom with
its electron in the lowest level. Hence, it may be used to determine the ionization
enthalpy of hydrogen.
V.
Uniqueness of Atomic Emission Spectrum
1. Emission spectra can be obtained from the atoms of all elements. These spectrum consists of
lines basically similar to the hydrogen spectrum but more complex.
2.
The atoms of each element have a unique arrangement of electrons with definite energy
levels.
3.
When an atom is excited, electrons are brought to higher energy levels. As the electrons
return to lower energy levels, the atoms emit radiation of definite wavelengths.
4.
This results in a unique emission spectrum which provide useful information about the atom.
Each element has its own pattern of lines in its emission spectrum.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
4.2
I.
Ch 4: p.10
Prediction of Electronic Structure from Ionization Enthalpy
First Ionization Enthalpy
If an atom absorb energy, its outermost electrons are promoted form the ground state into higher
energy level. If sufficient energy is supplied, an excited electron may reach the energy level of
infinity. This electron is completely detached from the nucleus and the atom becomes an ion on
losing this electron.
The first ionization enthalpy is the minimum enthalpy required to remove one electron
from a gaseous neutral atom and convert it into a positive ion, i.e.
M(g)

M+(g)
+
e
H = first ionization enthalpy
Note:
<1> Subsequently, more electrons may be removed, with corresponding ionization enthalpies.
(2nd, 3rd, and so on)
<2> An element will have as many ionization enthalpies as there are electrons in its atoms.
<3> Ionization enthalpy is the enthalpy change when 1 mole of most loosely held electrons
are removed from one mole of atom / ions to infinity in the gaseous state.
<4> Ionization enthalpy is always positive because
<5>
An high ionization enthalpy means that the electronic structure is not easily disturbed.
As every chemical reaction involves a rearrangement of electronic structures,
atoms or
ions with high ionization enthalpies tend to be chemically stable.
II.
Plots of Successive Ionization Enthalpies for an Element as Evidence of Quantum Shell
The variation in the successive ionization enthalpies for an element indicates the existence of
principal quantum shells.
Consider the plot of successive ionization enthalpies of a potassium atom:
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.11
Evidence:
1. The first ionization of potassium is lowest. The first electron is by far the easiest to remove. It
is farthest from the nucleus.
2. The 2nd ionization enthalpy is much higher than the first. Compare to the first electron the
second is more difficult to remove because much energy is required to remove an electron
from a positive ion than from an atom.
3. The energy required to remove the second to the 9th electron increases steadily but
comparatively slowly.
4. Between the 9th and 10th electrons, there is another very large increase in ionization enthalpy.
5. The energy required to remove the 11th to 17th electron increases steadily but comparatively
6.
7.
slowly.
Between the 17th and 18th electrons, there is another very large increase in ionization
enthalpy.
The last two electrons are very strongly held to the nucleus. The last ionization enthalpies are
extremely high.
Interpretation
1.
2.
3.
Each successive ionization enthalpy is higher than the previous one.
The positive charge (nuclear charge) on an ion increases as more electrons are removed. The
nucleus then exerts a stronger electrostatic attractive force on the subsequent electron to be
removed.
The electrons which are removed later are from lower energy levels and are closer to the
nucleus.
There are sharp and abrupt rises between 1st and 2nd , 9th and 10th ,and 17th and 18th ionization
enthalpies. It can be deduced that
a. the 2nd, 10th and 18th electrons (to be removed) are much closer to the nucleus than are
the 1st, 9th and 17th electrons (to be removed ) respectively.
b. The levels of energy of electrons in a potassium atom can be divided into 4 sets (2,8,8,1).
This arrangement is the electronic configuration of potassium.
Note:
(i)
(ii)
4.
The last number (1) in the sequence (2,8,8,1) refer to the valence electron in the
outer shell of the atom. This is the electron with the lowest ionization enthalpy
and is involved in bonding.
The preceding number (2,8,8) refer to the inner shell electrons. They are
electrons with higher ionization enthalpies and not involved in bonding.
Inner shell electrons partially shield the outer (valence) electrons ( by repulsion between
similar charges) from the attraction of the opposite nuclear charge.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.12
Existence of quantum shells
1.
2.
3.
4.
In a potassium atom, the two electrons in the lowest energy level are closest to the
nucleus. They are most strongly attracted by the positive nucleus electrostatically. These
two electrons are said to occupy the first quantum shell ( n = 1 )
The following 8 electrons occupy the second quantum shell ( n = 2 ) . They have high
energy level than do the first 2 electrons. They are also more further away from the
nucleus.
Another 8 electrons occupy the third quantum shell ( n = 3 ) . They have higher energy
level than do the electrons in both the first and second quantum shells. They are even
more further away from the nucleus.
The last (outermost) electron occupies the fourth quantum shell ( n = 4 ) . It has the
highest energy level and is the most distant from the nucleus.
Electrons move around the nucleus of an atom in definite energy levels. These
energy levels are identified by “ quantum number”.
Increase in quantum number, n , indicates higher energy and consequently
increase in distance from the nucleus.
III.
Plots of First Ionization Enthapies against Atomic Number as Evidence of Subshells
The variation in the ionization enthalpies against atomic number indicate the existence of
subshells.
Consider the pattern of first ionization enthalpies of the first 20 elements:
Atomic number
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.13
Evidience
1.
Across a period (i.e. from Li to Ne or Na to Ar ), the ionization enthalpy generally
increase with atomic number.
Reason:
2.
a.
There are regular discontinuities across each period:
Across Period 1 ( from H to He ), a peak occurs in He ( a noble gas).
Reason:
b.
Across Period 2 ( from Li to Ne ),
(i)
A peak occurs in Ne ( a noble gas)
(ii)
Intermediate peaks occur in Be (Group II) and N (Group V)
Reason:
(iii) I
A deep tough occurs in Li (group I),
Reason:
(iv) Intermediate troughs occur in B (Group III) and O (Group VI).
c.
Across Period 3 (from Na to Ar ), a peak occurs in Ar ( a noble gas ). Intermediate peaks
occur in Mg (Group II) and P (Group V). A deep trough occurs in Na (Group I ) ,
whereas intermediate troughs occur in Al (Group III) and S (Group VI).
A pattern of “ 2-3-3” is observed across Periods 2 and 3.
Interpretation
1.
As the effective nuclear charge increases across a period, the attraction between the valence
electron and the nucleus increases. More energy is required to overcome this attractive force,
resulting in an increase in ionization enthalpy.
2.
The second quantum shell ( Accommodating a maximum of 8 electrons) is split into 2
subshells, a electrons occupy the 2s subshell whereas 6 electrons occupy the 2p subhsell. The
2s and 2p subshells have different energy levels.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
IV.
Ch 4: p.14
Shells, Subshells, Orbitals and Subdivision of Electron Energies
-
The electrons are distributed in a atom as shells having different energy levels and principal
quantum numbers.
-
Each shell (e.g. n = 2, 3, …. ) is split into subshells (e.g. s, p, d, f).
-
Each subshell is further split into orbitals (e.g. px , py , pz ). Each orbital can accommodate no
more than 2 electrons.
An orbital is a volume of space within which the probability of finding an electron is
very high (95%).
A shell in a given atom is the collection of all the orbitals of the same principal
energy level. The orbitals have the same value of quantum number, n.
e.g. the n = 3 shell of all atoms contain one 3s orbital, three 3p orbitals and five 3d
orbitals.
A subshell in a given atom refers to the collection of all orbitals with the same
principal quantum number which have the same energy level.
Therefore, the 3px , 3py , and 3pz orbitals, which have the same energy level, are
collectively referred to as 3p subshells.
-
The number of orbitals in each subshell is summarized as follows:
Subshell
No. of orbitals
s
1
p
3
d
5
f
7
The orbital within the same subshell have the same energy level.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
-
Ch 4: p.15
The table below summarizes the division of electrons in an atom.
Shell
Principal quantum no. (n)
Subshell
Orbitals
Max.No. of electrons
K
1
One (1s)
One orbital
1s
2
L
2
Two subshells
2s, 2p
Four orbitals
2s, 2px, 2py, 2pz
8
M
3
Three subshells
3s, 3p, 3d
Nine orbitals
3s, 3px, 3py, 3pz
and five 3d orbitals
18
-
The arrangement of energy level sub-levels in an atom is shown below:
-
In the same quantum shell (i.e. same principal quantum number n), energy of
subshells in the order s < p < d < f. The distance of the subshell from the
nucleus also follows this order.
-
4s < 3d in energy and the orbitals of n = 4 overlap those with n=3
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.16
4.3
Bohr’s Atomic Models and its Limitation
Bohr suggested that an atom is made of a small heavy positively charged nucleus with
elelctrons arranged outside the nucleus in different shells. The shells nearer to the nucleus
have lower energy contents and shells further away from the nucleus have higher energy
contents.
However, there are several Limitations.
1. it cannot explain the more complicated spectral lines observed in spectra other than
hydrogen.
2. there is no experimental evidence that proved electrons are moving around the nucleus
of an atom in fixed orbits.
4.4
Atomic Orbitals
I.
Wave Nature of Electrons
That a beam of electrons can be diffracted shows that moving electrons have wave
like properties.
-
By considering that electromagnetic radiation could have both a wave and particle nature,
scientist viewed that the electron as a standing wave which colud be fitted into an orbit. An
equation could be written for the electron:
 = h / mv
where  = wavelength of the electron
m = mass of electron
v = velocity of electron
Only an integral number of wavelengths were permitted in an orbit.
-
The wave-like properties of the electron were confirmed experimentally that a beam of
electrons, like a beam of light could be diffracted through a crystal and through metal foil.
Other evidence supported both the wave and particle nature of electron. This evidence is
summarized in the following table:
Evidence
Wave theory
Particles theory
Diffraction

X
Reflection


Refraction


Interference

X

Photoelectric effect e.g. solar
cell
-

In view of the wave-like properties, it is impossible to predict the exact position of an electron
at a given time.
The location of an electron can only be described in terms of probability of finding it
in a certain position at any time.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
II.
Ch 4: p.17
Atomic Orbital
An atomic orbital can be visualized as a volume of space within which there is a high
probability (say 95 % ) of finding an electron.
The density of the electron charge cloud in 1s orbital is show below:
-
-
The 1s orbital is spherical in shape.
The variation of electron density is exactly the same in any direction from the nucleus. In other
words, the probability of finding an electron at a distance r from the nucleus is the same from
any direction.
The maximum probability of finding an electron is at a distance of 0.053 nm from the nucleus.
This distance is referred to as the Bohr’s radius.
The electron density is zero at the nucleus and at infinite distance from the nucleus.
As the distance form the nucleus increases , the probability of find an electron increases to a
maximum at Bohr’s radius and then declines to almost zero.
The 1s orbital is depicted as a spherical charge cloud, a distribution of
electrical charge of varying density in wave manner around the nucleus.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.18
III. Shapes of s and p Orbitals
- The charge cloud representing an atomic orbital has indistinct and fuzzy edges.
- In diagrammatic expression of an atomic orbital
The boundary surface of an atomic orbital is drawn such that the chance of finding a
particular electron within this region is 95 %.
A. s-orbital
- The s orbital is spherically symmetrical about the nucleus. Therefore, the charge cloud, being
non-directional is not concentrated in any direction.
-
All electrons in the s-orbital exist somewhere with the sphere with the atomic nucleus as
center.
s-orbital
B.
p-orbital
There are three 2p orbitals. They are all dumb-bell in shape. They are directional and situated
along three coordinate axes (x, y and z), which are mutually perpendicular as shown below:
-
There is zero probability of finding a p electron at the nucleus.
The 2px , 2py and 2pz orbitals are perpendicular to one another .
The three 2p orbitals have the same energy level (i.e. being degenerate) and are collectively
referred to as the 2p subshell.
L.S.T. Leung Chik Wai Memorial School
F6 Chemistry
The Electronic Structure of Atoms
Ch 4: p.19
IV. The Designation, Number and Relative Energies of s, p and d Orbitals
1. There are four types of orbitals in the quantum shells: s, p, d and f. Each orbital may
hold a maximum of 2 electrons.
2. The number preceding the type of orbital denotes the quantum shell in which the orbitals
are placed.
3. The number of electrons allowed in each principal quantum shell is as follows:
1s2 = 2
2s2 2p6 = 8
3s2 3p6 3d10 = 18
4s2 4p6 4d10 4f14
= 32
4.
5.
6.
The superscripts above indicate the maximum no. of electrons allowed in the orbitals of
that shell.
All orbitals in a given subshell are of the same energy and are said to be degenerate.
For orbitals defined by the same quantum number, s-orbital is the one of lowest energy.
This is followed by p, d, f orbitals representively, which has increasing energy.