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Chapter 7
Spectroscopy is the study of the interaction
between radiation (electromagnetic
radiation, or light, as well as particle
radiation) and matter.
Spectrometry is the measurement of these
interactions and an instrument which
performs such measurements is a
spectrometer or spectrograph.
A plot of the interaction is referred to as a
The spectrum of colors emitted by atoms
that have been heated to high
temperatures is called an atomic emission
Light is electromagnetic radiation, a wave
of electric and magnetic field that travels
at the speed of light(3.00х108m/s).
Light waves travel at a constant speed.
Because of this there is a one to one
relationship between light's wavelength
and its frequency. If waves are short, there
must be more of them in a set amount of
time to travel the same distance in that
time (the same speed).
The unit of frequency is Hertz(Hz)
The intensity of the light is proportional to the
square of the amplitude of the wave.
 The distance between adjacent peaks gives its
 λ=c/ν
Our eyes detect electromagnetic radiation with
wavelengths from 700nm(red light) to
400nm(violet light). The electromagnetic radiation
in this range is called as visible light.
 Ultraviolet radiation(UV) has a frequency higher
than that of violet light; its wavelength is less than
about 400nm.
 Infrared radiation(IR) has a frequency lower than
that of red light ;its wavelength is greater than
about 800nm.
 Microwaves, used in radars and microwave
ovens, have wavelengths in the millimeter to
centimeter range.
What is the wave length of orange light of
frequency 4.8х1014Hz?
Electromagnetic radiation is a stream of many packets of
electromagnetic energy. These packets are called as
The photon is the elementary particle responsible for
electromagnetic phenomena.
The photon travels (in vacuum) at the speed of light, c.
Energy is transferred in discrete amounts called as
quantum(plural quanta)
Like all quanta, the photon has both wave and particle
properties (“wave particle duality “).
The more intense the light the greater the number of photons
passing a given point each second.
The relation between the energy , E of a photon and the
frequency ν, of the radiation as E=hν where h is Plank’s
constant, with a value of 6.63х10-34 J.s
What is the energy in kilojoules per mole
of photons of amber light of frequency
5.2х1014 Hz?
A student’s favorite radio station
broadcasts a signal at a frequency of
91.5MHz. What is the energy of the
photon’s broadcast?
Page 314
7.12,7.14 and 7.18
The Lyman series is the wavelengths in the
ultraviolet (UV) spectrum of the hydrogen
atom, resulting from electrons dropping from
higher energy levels into the n = 1 orbit.
The Balmer series is the wavelengths in
the visible light spectrum of the hydrogen
atom, resulting from electrons falling from
higher energy levels into the n = 2 orbit.
The Paschen series is the wavelengths
in the infrared spectrum of the hydrogen
atom, resulting from electrons falling from
higher energy levels into the n = 3 orbit.
Rydberg formula for hydrogen
λvac is the wavelength of the light emitted in
vacuum, RH is the Rydberg constant for
The Bohr model of the hydrogen
atom where negatively charged
electrons confined to atomic shells
encircle a small positively charged
atomic nucleus, and that an
electron jump between orbits must
be accompanied by an emitted or
absorbed amount of
electromagnetic energy hν. The
orbits that the electrons travel in are
shown as grey circles; their radius
increases n2, where n is the
principal quantum number. The
3→2 transition depicted here
produces the first line of the Balmer
series, and for hydrogen (Z = 1)
results in a photon of wavelength
656 nm (red).
Louis-Victor formulated the de Broglie
hypothesis, claiming that all matter, not just
light, has a wave-like nature; he related
wavelength (denoted as λ ),
and momentum (denoted as p):
This is a generalization of Einstein's equation
above, since the momentum of a photon is
given by p=E/c and the wavelength by λ=c/f,
where c is the speed of light in vacuum.
Calculate the wavelength of a marble of
mass 5.00 g traveling at 1.00m/s.
Our current model of a hydrogen atom was
proposed by the Austrian scientist Erwin
Schrodinger. He devised an equation
(Schrodinger’s Equation)that enabled him to
calculate the shape of the wave associated
with any particle.
Quantum theory is based on Schrodinger's
equation; Hψ=Eψ in which electrons are
considered as wave-like particles whose
"waviness" is mathematically represented by
a set of wave functions ψ, obtained by
solving Schrodinger's equation.
The wave function for an electron is so
important that it is given a special name an
atomic orbital. Atomic orbitals have
characterestic energy and shapes. The
different shapes are identified by different
An s orbital is a spherical cloud that becomes
less dense as the distance from the nucleus
increases. p-orbital is a cloud with two lobes
on opposite sides of the nucleus. The lobes
are separated by a nodal plane. The d and f
orbital have complicated shapes.
As for p-orbital the
opposite shades of color
denote opposite signs of
The location of an electron
is best described as a cloud
of probable locations.
Page 314
Each orbital has a characteristic energy. When
Schrodinger solved his equation, he found that the
allowed energies of the electron in a hydrogen atom
are given by the expression E=-hRH /n² n=1,2…
RH, is called as the Rydberg’s constant. The
experimental value of Rydberg’s
constant=3.29х1015 Hz
Whenever the atom emits a photon of radiation, the
energy emitted is equal to the difference in two of
the allowed energy levels. Each transition
corresponds to a line in the spectrum of atomic
Calculate the wavelength of a photon emitted by
a hydrogen atom when an electron makes a
transition from an orbital with n=3 to one with
Schrodinger found that each atomic orbital is
identified by three numbers called quantum
numbers. The quantum number n is called the
principal quantum number. The orbital angular
momentum quantum number, l, specifies the
shape of the orbital. The magnetic quantum
number,ml specifies the individual orbital of a
particular shape.
An orbital is specified
by three quantum
numbers; orbitals are
organized into shells
and subshells.
An electron has the
property of spin ; the
spin is described by
the quantum number
ms which may have
one of the two values.
Calculate the total number of orbitals in a shell
with n=6.
In a many-electron atom, because of the effects
of penetration and shielding, s-electrons have a
lower energy than p-electrons of the same shell;
the order of increasing orbital energies within a
given shell is s<p<d<f.
No more than two electrons may occupy any
given orbital. When two electrons do occupy
one orbital, their spins must be paired.
If more than one orbital in a subshell is
available, electrons will fill empty orbitals before
pairing in one of them.
The ground state electron configuration of an
atom of an element with atomic number Z is
predicted by adding Z electrons to available
orbitals so as to obtain the lowest total energy.
Predict the ground state electron configuration
of a sulfur atom and draw the box diagram.
 Predict the ground state electron configuration
of a magnesium atom.
To predict the electron configuration of a cation ,
remove outermost electrons in the order np,
 For an anion, add electrons until the next noble
gas configuration has been reached.
Page 315
Atomic radius: The atomic radius is defined as
half the distance between the centers of
neighboring atoms.
Atomic radii generally increase down a group
and decrease from left to right.
The ionic radius of an element is its share of
the distance between neighboring ions in an
ionic solid.
Ionic radii generally increase down a group
and decrease from left to right across a
period. Cations are smaller than their parent
atoms and anions are larger.
Arrange each pair of ions in order of increasing
ionic radius:(a)Mg2+ and Ca2+
 (b)O2- and F
The ionization energy of an element is the
energy needed to remove an electron from an
atom of the element in the gas phase.
 For the first ionization energy we start with a
neutral atom.
For the first ionization energy,I1, we start with the
neutral atom, for example, for copper,
Cu(g)Cu+(g) +e-(g)
I1 =(energy of Cu+ +e-)-(energy of Cu)
The experimental value for copper is
785kJ/mol.The second ionization energy I2 is
the energy required to remove an electron from
a singly charged gas phase cation. For copper
Cu+(g) Cu2+(g) + e-(g)
I2=(energy of Cu2+ +e-)-(energy of Cu+)For
copper I2 =1958kJ/mol
The second ionization energy is always greater
than the first because once the first electron is
pulled off, you are now trying to remove the
second electron from a positively charge ion.
Because of the electrostatic attraction between
+ and -, it is more difficult to pull an electron
away from a positively charge ion than a neutral
The first ionization energy is highest for
elements close to helium and is lowest for
elements close to cesium. Second ionization
energies are higher than first ionization energies
(of the same element). An ionization energy is
very high if the electron is to be expelled from a
closed shell.
The electron affinity is a measure of the energy
change when an electron is added to a neutral
atom to form a negative ion. For example, when a
neutral chlorine atom in the gaseous form picks
up an electron to form a Cl- ion, it releases an
energy of 349 kJ/mol or 3.6 eV/atom.
 An electron affinity of -349 kJ/mol and this large
number indicates that it forms a stable negative
 Small numbers indicate that a less stable
negative ion is formed. Groups VIA and VIIA in the
periodic table have the largest electron affinities.
Elements with the highest electron affinities are
those close to oxygen, fluorine, and chlorine.
Group 17 atoms can acquire one electron with a
release of energy and group 16 atoms can
accept two electrons with chemically attainable
energies. The halogens typically form X- ions
and group 16 elements form X2- ions.
 On moving diagonally across the periodic table, the
elements show certain similarities in their properties
which are quite prominent in some cases as shown
below. This is called a diagonal relationship.
A Diagonal Relationship is said to exist between certain pairs of
diagonally adjacent elements in the second and third periods of the
periodic table. These pairs (Li & Mg, Be & Al, B & Si etc.) exhibit
similar properties; for example, Boron and Silicon are both
semiconductors form halides that are hydrolysed in water and have
acidic oxides.
Such a relationship occurs because crossing and descending the
periodic table have opposing effects.
On crossing a period of the periodic table, the size of the atoms
decreases, and on descending a group the size of the atoms
increases. Similarly, on moving along the period the elements
become progressively more covalent, less reducing and more
electronegative whereas on descending the group the elements
become more ionic, more basic and less electronegative.
Thus, on both descending a group and crossing by one
element the changes cancel each other out, and
elements with similar properties which have similar
chemistry are often found - the atomic size,
electronegativity, properties of compounds (and so forth)
of the diagonal members are similar.
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