Unit II - Structure of Atom
A. Modern Atomic Theory
1. All matter is made up of very tiny particles called atoms
2. Atoms of the same element are chemically alike
3. Individual atoms of an element may not all have the same
mass. However, the atoms of an element have a definite
average mass that is characteristic of the element
4. Atoms of different elements have different average masses
5. Atoms are not subdivided, created, or destroyed in
Sizes of Atoms
A. Atomic radius
1. 40 to 270 Pico meters (pm)
1pm = 10-12m
2. Most of the atomic radius is due to the electron cloud
B. Nuclear radius
1. 0.001 pm
2. density is 2x108 metric tons/cm3
1metric ton = 1000kg
“An insight into the structure of atom was obtained
from the experiments on electrical discharge
through gases i.e., through discharge tube
Structure of the Nuclear Atom
Discovery of Electron
In 1830, Michael Faraday showed that if electricity is passed through a
solution of an electrolyte, chemical reactions occurred at the
electrodes, which resulted in the liberation and deposition of matter at
the electrodes. He formulated certain laws. These results suggested the
particulate nature of electricity.
As we know “Like charges repel each other and unlike charges attract
In mid 1850s many scientists mainly Faraday began to study
electrical discharge in partially evacuated tubes, known as cathode ray
discharge tubes. It is depicted Fig. A cathode ray tube is made of glass
containing two thin pieces of metal, called electrodes, sealed in it. The
electrical discharge through the gases could be observed only at very
low pressures and at very high voltages. The pressure of different gases
could be adjusted by evacuation. When sufficiently high voltage is
applied across the electrodes, current starts flowing through a stream
of particles moving in the tube from the negative electrode (cathode) to
the positive electrode (anode).
These were called cathode rays or cathode ray particles. The flow of
current from cathode to anode was further checked by making a hole in
the anode and coating the tube behind anode with phosphorescent
material zinc sulphide. When these rays, after passing through anode,
strike the zinc sulphide coating, a bright spot on the coating is
developed (same thing happens in a television set)
Rutherford alpha ray scattering
Almost all the particles
pass through the metal and are
Some of these particles
are deflected at small angles.
Very few of these
particles are deflected through as
much as 90o or even larger
1. Joseph John Thomson (1897)
The characteristic properties of cathode rays:
(i) The cathode rays start from cathode and move towards the anode.
(ii) These rays themselves are not visible but their behaviour can be
observed with the help of certain kind of materials.
(iii) In the absence of electrical or magnetic field, these rays travel in
straight lines. (As they cast shadow if we place an opaque object in their
(iv) In the presence of electrical field, they move towards +ve electrode,
suggesting that the cathode rays consist of negatively charged particles,
(v) The characteristics of cathode rays (electrons) do not depend upon the
material of electrodes and the nature of the gas present in the cathode
Thus, we can conclude that electrons are basic constituent of all the
Fig: Cathode ray discharge tube
Cathode ray tubes are in most televisions and computer monitors.
Cathode ray tubes with a fluorescent screen at one end would glow.
Thomson measured the deflection of the beam - Magnet deflected in one
direction and plate attracted the beam - therefore, negative particles
Calculate the ratio: Charge vs. Mass
Fig: Cathode ray discharge tube
experiment in presence of magnetic
Regardless of the type of gas or metal used in cathode-ray tube - the
ratio of charge to mass remained the same. Therefore, the particles in
the cathode-ray tube were identical to one another.
Electron, symbol is e- with a negative one charge.
Thomson also observed in cathode-ray tube, when he used Hydrogen gas and
high voltage with low pressure - he noticed that two beams (one negative) and
another beam moving in the opposite direction - toward the cathode - a positive
Thomson found that the deflection of the beam varied with different gases.
Hydrogen ions had the greatest deflection - therefore the smallest mass.
A Proton is a positively charged particle found in all atoms and each proton
possess a plus one charge.
DISCOVERY OF PROTON:
POSITIVE RAYS OR CANAL RAYS
Atoms are electrically neutral. Hence after the discovery of the negatively
charged constituent (electron) of an atom, attempts were made to discover the
positively charged counterpart of electrons. By using a discharge tube containing
Fig: Cathode ray discharge tube
experiment in presence of electric field
a perforated cathode. Goldstein (1886) found that some rays passed through
these holes in a direction opposite to that of the cathode rays.
These are called the positive rays or canal rays. J.J. Thomson (1910) measured
their charge by mass ratio from which he was able to deduce that these contain
positive ions. Their properties are:
They are positively charged.
The positive charge is either equal to or whole number multiple of the charge
on an electron.
When hydrogen gas was filled in the discharge tube the positive charge on the
positive rays was equal to the negative charge on an electron, and the mass was
less than the hydrogen atom.
Fig: Cathode ray discharge tube
experiment with perforated cathode
Unlike cathode rays the properties of positive rays are characteristics of the gas
in the tube.
The deflection of positive rays under the influence of an electric or magnetic
field is smaller than that of the cathode rays for the same strength of field. This
shows that the positive rays have a greater mass than that of electrons.
The mass of the positive rays depends on the atomic weights or molecular
weights of the gases in the discharge tube. The charge/mass ratio also varies
because the change in positive charge on the rays. It may be either equal to or
integral multiple of the charge on an electron.
The lightest of all particles identified in positive rays from different elements
was one with a mass very slightly less than that of hydrogen atom (or nearly
equal to H-atom). The lightest positively charged particle is called a proton (P or
P+). Positive rays are atomic or molecular resides from which some electrons
have been removed. The removed electrons constitute the cathode rays and the
positive residues form the positive or canal rays.
In 1932 Discovery of Neutrons by James Chadwick (1891 - 1974)
In 1932, James Chadwick bombarded beryllium (Be) with alpha
particles. He allowed the radiation emitted by beryllium to incident on a paraffin
wax. It was found that protons were shot out form the paraffin wax. People
began to look for what was in the "beryllium radiations".
The radiation consisted of neutral particles of mass approximately equal to that
of proton. This neutral particle was named neutron.
J.J.Thomson’s plum pudding model:
Thomson suggested a model of the atom called the
Plum Pudding model.
● Its name is supposed to make you think of a lump of
stuff with little pieces floating inside it.
● this model of the atom is that small negatively
charged electrons are floating around inside a lump of
positively charged material.
Drawbacks of this model
1. It could not explain the stability of atom.
2. It could not give the theoretical explanations of a no. of
Rutherford Nuclear Model:
On the basis of the scattering experiment, Rutherford described the structure of
the atom as follows:
1. An atom consists of a positively charged nucleus and is surrounded by
electrons that revolve around it. The nucleus' positive charge is due to
the presence of protons.
2. Electrons and neutrons are held together by columbic force of
3. The nucleus' effective volume is found to be extremely small as
compared to the effective volume of the atom. The nucleus occupied a
volume of about 10-12 times the volume of the atom.
4. The atom's entire mass is concentrated only at the nucleus.
5. As each atom is found to be electrically neutral, the number of protons
in the nucleus of an atom is exactly equal to that of the electrons in it.
J.J.Thomson’s plum pudding model
Rutherford's model suffered some drawbacks, as
1. It could not explain the stability of an atom in-spite of the revolving
electrons around the nucleus.
2. The electrons revolving around should emit radiation and subsequently
lose energy. The loss of energy should slow down the electrons, which
should gradually move towards the nucleus in a spiral path and then fall
into the nucleus. This should result in the collapse of the atom and
make it unstable, which is found to be untrue.
Millikan's Oil Drop Experiment:
In this experiment a charged oil drop was suspended vertically between the two
electrodes. Then the electric field is applied to such an extent that the free fall of
the oil drop, under the influence of gravitational pull, was stopped. With the
known electric field and other parameters Millikan was succeeded to calculate
the charge on the drop. He published his findings in 1913 and was awarded
Nobel Prize for physics in 1923 for his work on finding the charge of the electron.
With the known electric field applied and other parameters it is easy to
calculate the charge on the oil drop. The Millikan using this apparatus
was able to find the electron charge as precious as 1.5924 × 10−19 C,
which is within 1% accuracy range of the modern corrected value of the
electron (1.6 x 10-19 C).
Postulates of Niels Bohr Atomic Theory
The important postulates in his theory are,
Electrons revolve round the nucleus with definite velocities in
concentric circular orbits situated at definite distances from the
nucleus. The energy of an electron in a certain orbit remains constant.
As long as it remains in that orbit, it neither emits nor absorbs energy.
These are termed stationary states or main energy states.
Bohr proposed that the angular momentum of an electron is quantized.
Thus, the motion of an electron is restricted to those orbits where its
angular momentum is an integral multiple of h/2π where h is Planck’s
Thus we have the relationship mvr = nh/2π where m is mass of
electron, v is velocity of electron of said orbit, r is radius of that orbit, n
is a simple integer.
The stationary states or allowed energy levels are only those where n =
1, 2, 3 … This is called Bohr quantum condition.
The energy of an electron changes only when it moves from one orbit
to another. An electronic transition from an inner orbit to outer orbit
involves absorption of energy. Similarly, when an electron jumps from
an outer orbit to inner orbit it releases energy, which is equal to the
difference between the two energy levels.
The energy thus released in the form of a radiation of a certain
frequency appears in the form a line in the atomic spectrum. If the
energy of an electron in the outer orbit (n2) is E2 and energy of electron
in the inner orbit (n1) is E1 then E2 - E1 = ΔE = hν.
The value of n could be small integers 1, 2, 3 and these correspond to
the first, second, third, and so on. Quantum states are shells for the
electron; n is termed as principal quantum number.
Based on the Bohr Theory, he calculated the radii of the various orbits
and the energies associated with the electrons present in those shells.
Millikan’s oil drop experiment
Bohr Model of Hydrogen
Bohr used the concept of quantization of energy and laws of classical physics. He
gave many mathematical expressions like radius of orbits, velocity and energy of
electrons. These expressions satisfactorily explain the spectrum of hydrogen.
Let’s calculate all these expressions to explain the spectrum of hydrogen (1H1).
1. Radius of nth orbit:
According to bohr model, the attraction force between
electron and nucleus is balanced by centrifugal force of
electron which is due to motion of electron and tend to take
electron away from nucleus.
Atomic number of atom = Z
Charge on electron = e
Charge on nucleus = Z e
Radius of nth orbit = r n
The electrostatic force of attraction = Z e 2 /r n 2 -------------- (1)
The centripetal force = mV 2 / r
Since both forces balanced each other. Hence from equation 1
Ze 2 /rn 2 = mV 2/ r
V2 = Ze 2 /rn m
Form Bohr postulate mVrn = h /2π
or m2V2rn2 = h 2/4π 2
Plug the value of V2 from equation (3)
m2 * Ze 2 rnm * rn2 = h 2/4π 2
m x Ze2 x rn = n 2 h 2/ 4π 2
rn = n 2 h 2 /mZe 24π 2
h = 6.62 x 10-27 erg.sec
π = 3.142
m = 9.109 x 10-28gm
e = 4.803 x 10-10esu
h 2/me 2 4π 2 = 0.529 Å
Plug value of constants in (4)
rn = n 2 /Z x 0.529Å
Since the atomic number for hydrogen is one, so, the radius of nth orbit of
hydrogen will be r1= n 2 * 0.529 Å.
Since the value of Z is constant for an atom, r n α n 2 , so radius increases
with increasing the value of n.
If the value of n is constant , rn α 1 /Z
Hence, radius of a particular orbit decreases with increasing the atomic
2. Calculation of the velocity of electron in Bohr orbit
From Bohr postulate
/rn 2 = mV 2 /r
V = Ze
x 2.188 x 108 cm/sec
for hydrogen atom, Z = 1
Since rn = n 2 h 2 /mZe 2 4π 2
Hence V2 = Z 2 e 4 4π 2 /n 2 h 2
V = Ze 2 2π /nh
Plug all constants (e, r, h, π) values in equation (5)
x 2.188 x 108 cm/sec
for hydrogen atom, Z = 1
Hence V = 2.188 x 108 /n cm.sec-1
3. Energy of electron in nth orbit
According to Bohr atomic model, the maximum energy value of electron at
infinite is zero because of negligible attraction force between electron and
nucleus at infinite distance.
Hence, as electron comes closer to nucleus, the energy becomes negative.
Hence V = 2.188 x 108 /n cm.sec-1
Energy of electron is the sum of its potential energy because the electron lies in
the field of the positive nucleus and kinetic energy which is due to motion of
electron. The potential energy of electron is negative and equals to –Ze 2 /r ,
while the kinetic energy is positive and equals to 1/ 2 mv 2.
Hence the total energy of electron
En = –Ze 2/ r + 1 /2 mv 2
Since mv2 = Ze 2 / rn
Hence En = −1/ 2 Ze 2 ×mZe 2 4π 2 /n 2 h2
travel in wide range of
wavelengths. Lower the
wave length higher will be
En = −Z 2/ n 2 x 13.60
En = −Z 2 / n 2 x 2.179
En = - 1/2Ze 2 /rn
We know that
rn = n 2 h2 /mZe 24π 2
So En = 1/ 2 Ze2 * mZe 2 4π 2 /n 2 h 2
= −Z 2 /n 2 * 2π 2 me 2/ h 2
Since 2π 2 me 2 /h 2 is a constant value, which is equals to 13.60 ev/atom.
So En = −Z 2/ n 2
x 13.60 ev/atom
En = −Z 2 / n 2 x 2.179 erg/atom
En = −Z 2/ n 2 x 313.6 KCal/mol
En = −Z 2/n 2 x 21.79 x 10-19 J/atom
For hydrogen Z = 1 so for
So En = - 1 /n 2 x 13.60 eV/atom
According to Rutherford model of atom the electrons revolve round the nucleus
containing protons and neutrons. Bohr improved upon Rutherford theory by
suggesting the fixed orbits for the movement of electrons. The subsequent
improvements fixed the movement of electrons in limited number in orbits and
are called orbitals with different energy potential.
The farther the electron is in the orbit from the nucleus and lesser the number in
an orbital, the electron can be removed easily. The energy that is required to
excite an electron from normal position is called ionization energy.
By absorbing energy from outside source the electron gets excited from the
designated position in the orbit. The energy it absorbs to reach the excited state
is given back when it reaches the normal position in the atom. This emitted
energy is recorded on spectrometer.
En = −Z 2/ n 2 x 313.6
En = −Z 2/n 2 x 21.79 x 10-19
For hydrogen Z = 1 so for
So En = - 1 /n 2 x 13.60
The equipment that records the wavelengths is called the spectrometer. In the
visible range, it is a well-known fact that the white light is a combination of 7
colours VIBGYOR, and white light is spread over a range of 3,800Å - 7600Å.
A spectrum is an assembly of energy levels in the form of radiations emitted by
an atom in its excited state. Every atom gives discontinuous line spectra. Each
line in the spectra corresponds to a specific wavelength and it is unique to a
given element. No two elements give same pattern of lines in their spectra.
White light is a combination of 7 colours
White light is spread over a range of
3,800Å - 7600Å.
Spectroscopy is the branch of physical chemistry which involves the observation
and interpretation of radiation emitted and absorbed by atoms and molecules
and used to identify their structures. When a monochromatic light passes
through the prism, the electromagnetic radiation gets separated in a different
number of colors. This image of color is called as spectrum. The spectrum
obtained from white light shows seven different colors and this is also called as
simple spectrum. Each color in spectrum is associated with a certain wave
In 1864, Maxwell explained the term electromagnetic radiation. According to
Maxwell, theory of radiation, the alternating current of high frequency emitted
radiant energy. This radiant energy travels in space with the velocity of light.
These radiations are the form of energy emitted and absorbed by charged
particles. It can exhibit wave-like behaviour with both electric and magnetic field
components which oscillate in phase perpendicular to each other and
perpendicular to the direction of energy and wave propagation.
The energy of electromagnetic radiation is
E = hc /λ
h = Plank’s constant
c = velocity of light
λ = wave length of light
Atomic Spectra Definition
Each element can produce a unique set of spectral lines which will be quite
different from any other atom. Due to this property, any two elements can be
identified on the basis of their line spectrum. The spectrum from the radiation
emitted by an atom is known as atomic spectrum. According to Bohr’s atomic
model, there are certain energy levels in an atom, where electrons revolve
around positively charged nucleus.
When an atom gets excited, it emits light of certain wavelengths which
correspond to different colors. This emitted light can be observed as a series of
color lines with dark spaces in between. This image of series of color lines is
known as a line or atomic spectra.
Each energy level is associated with a certain amount of energy. For the
transition of electron form lower energy level to higher energy level it absorbs
some amount of energy. The transition of electron from higher level to lower
level emits some amount of energy in the form of radiation.
The energy of
electromagnetic radiation is
E = hc /λ
h = Planck’s constant
c = velocity of light
λ = wave length of light
The energy level is associated with different energy values. Hence each
transition involves a different amount of energy and emits a certain amount of
energy. Excitation is the process of an electron in an atom absorbing a photon
and after absorbing a photon the electron, atom is said to be in an excited state.
Since electron in excited state is not stable, it radiates some amount of energy in
the form of radiation and back to ground state. A photon emitted or absorbed is
equal to the difference E2 - E1 between the energy levels is released or absorbed
in the process. The relation between frequency and energy change of the
spectral line is called as Bohr's frequency.
E2 – E1 =hυ
An electron located in the lowest energy level (n=1) is the closest to the nucleus.
As well as electron occupying its lowest energy level is known to be in the
ground state. The energy of an electron in a certain energy level is given by,
En = - RH/n2
Where RH = Rydberg constant
n = Energy level of the electron
The energy of photon involve in transition of electron in two level is equals to,
When an atom gets excited, it emits
light of certain wavelengths which
correspond to different colors. This
emitted light can be observed as a
series of color lines with dark spaces in
between. This image of series of color
lines is known as a line or atomic
The energy of an electron in
a certain energy level is
En = - RH/n2
Where RH = Rydberg
n = Energy level of the
Ephoton = RH (1/ni2 – 1/nf2)
Where ni = Initial energy level of the electron
nf = final energy level of the electron
Since energy is directly proportional to the frequency of the photon emitted,
νphoton = (Ei - Ef)/h
Where Ei = Initial energy of the electron
Ef = Final energy of the electron.
Atomic spectroscopy involves the interaction of light with gaseous atoms. A
device converts a sample into a gaseous atoms and is called as atom cell. There
are three basic types of atomic spectroscopy.
1. Atomic emission
2. Atomic absorption
3. Atomic fluorescence
The energy of photon
involve in transition of
electron in two level is
Ephoton = RH (1/ni2 – 1/nf2)
Where ni = Initial energy
level of the electron
nf = final energy level of the
Atomic Line Spectra
Spectrometers or spectroscopes are instruments which record the emitted
radiations in their wavelengths. These recordings are done in bands which are a
range of wavelengths. More sensitive spectroscopes to record a particular
wavelength are used for the sensitive studies like atomic radiations. Such
recordings are done as lines on a graph. Each line is a specific wavelength.
This is called Atomic Line Spectrum.
With a prism we can spread out the light from a bulb to give a continuous
spectrum that is a spectrum containing light of all wavelength, like that of a
rainbow. The light emitted by a heated gas, however yields different results,
rather than a continuous spectrum with all colours or specific wavelength of
light. When a light from a hydrogen gas discharge tube is separated into its
components by a prism, it gives a spectrum of lines, each line corresponding to
the light of a given wavelength.
The relation between
frequency and energy
change of the spectral line
is called as Bohr's
E2 – E1 =hυ
Atomic Emission Spectrum
When we provide some amount of energy to a substance, its atoms get excited
and transit to higher energy level. This excited state of atoms is not a stable
condition, hence atoms emit some photon of energy and drop to the lower
energy level. Each photon corresponds to a particular wavelength and energy. If
many electrons emit the same wavelength of photons it will form a spike in the
spectrum at that particular wavelength and form a banding pattern.
For example, in emission spectrum of hydrogen the Hydrogen atoms present
inside the lamp are excited by using an electric current. The emitted light then
passed through a prism to get spectrum. If there are n energy levels in hydrogen
atom, we can predict the frequencies of the spectral lines of Hydrogen using an
equation discovered by Johann Balmer.
ν = 3.2881 x 1015s-1 (1/22 - 1/n2)
Where n must be a number greater than 2. This is because Balmer’s formula only
applies to visible light and some longer wavelengths of ultraviolet. Hence by
using Rydberg’s equation, we can calculate the wave number of different
In spontaneous emission, the electron “spontaneously", i.e., without any
outside influence, transit from a higher energy level to a lower one. While in
case of Stimulated emission, an electron is induced for the transition from a
higher energy level to a lower one in the presence of electromagnetic radiation
at the frequency of the transition. Hence this type of atomic emission is also
termed as induced emission.
Photo electric effect is an effect caused by the electromagnetic radiation on the
surface of metals. If a radiation of sufficient energy is made to fall on the surface
of a metal, the surface electrons absorb some energy and get excited. These
excited electrons return to their normal state by releasing the same amount of
energy that it absorbed while getting excited.
Each electron in an atom has a definite minimum energy required to get excited,
which is called the threshold energy or work function or ionization energy. The
energy of an electromagnetic radiation is measured in its wavelengths.
Spectrometer is an instrument that can record these wavelengths.
Atomic Absorption Spectrum
As the name suggests the atomic absorption spectra are the spectral reading
obtained when the electromagnetic radiations are absorbed by the atoms. These
spectra are used for the study of certain atomic reaction where the process
require some energy to activate an atom.
The transition of an electron form lower energy level to higher energy level takes
place by the absorption of photons of certain energy. The magnitude of
absorbed energy must be equal to the difference between those two energy
Î.E = E2-E1
Where; E1= energy of lower energy level
E2= Higher energy level
When a beam of white light is passed through the given sample solution, the
sample atoms absorb some of the light and their electrons get excited.
Since the electrons only absorb certain frequencies of photon, there are some
black bands in continuous spectrum of white light. This type of spectrum is
called as atomic absorption spectrum.
A range of wavelength radiations of known wavelengths are passed through the
medium under examination and the wavelengths that pass through are
recorded. The missing wavelength lines give the value of the absorbed radiation
for the required excitement. Since the study is with absorption it is called Atomic
Types of Atomic Spectrum
Atomic absorption and emission spectrum can be of two types,
1. Atomic continuous spectrum
2. Atomic discontinuous spectrum
Atomic continuous spectrum
If there is no boundary between the spectrum lines in a spectrum, it is called as
continuous spectrum. When a white light passes through a prism, it divides into
a seven colour spectrum. Each colour corresponds to a certain frequency and
wave length. There is no separation line between all these seven colours. Hence
it not possible to decide the end line of one colour and starting line of another
colour. Such type of spectrum is known as atomic continuous spectrum.
Atomic discontinuous spectrum
This type of spectrum is divided in certain number of segments. They can be of
1. Atomic line spectrum
There are many lines associated with a certain value of wave length and wave
number. Generally line spectrum are obtained from atoms in gaseous or vapor
state. Since each electron can show various transitions between different energy
levels, hence there are many lines for one electron system. For example, line
spectrum of hydrogen atom. If the line spectrum is absorption spectrum, black
lines observed on a bright surface, while emission line spectrum shows bright
lines on a dark surface.
2. Atomic band spectrum
Such type of atomic spectrum is given by the substance if it is present in a liquid
state while in a solution; such spectrums are given off if the substance is present
in its molecular state. Hence, they are also called as molecular spectrum. In this
type of spectrum a group of bands are observed for certain frequency and wave
Atomic absorption and emission
spectrum can be of two types,
1. Atomic continuous spectrum
2. Atomic discontinuous spectrum
Atomic Spectra of Hydrogen Atom
Hydrogen is the simplest element with its atom having only one electron. Hence,
the atomic spectrum of hydrogen has played a significant role in the
development of atomic structure. In the emission spectrum of hydrogen, when
an electric discharge is passed through hydrogen gas, the molecules of hydrogen
break into atoms. The hydrogen atoms get energized and go into an excited
state. The excited atoms then return to the ground state by emitting light.
Hydrogen atoms emit bluish light. On passing this light through a prism, a
discontinuous line spectrum consisting of several sharp lines is obtained. This is
the line spectrum of hydrogen.
Electromagnetic radiations are emitted when an electric discharge is passed
through a discharge tube filled with hydrogen gas at a very low pressure. These
emitted radiations produce various lines in the emission spectrum. The spectra
obtained by recording various electromagnetic radiations emitted by hydrogen
are called the Atomic spectra of hydrogen. Different series of lines are recorded
by different scientists and they are named after their discoverers.
J.J.Balmer first discovered the spectral series of hydrogen and named it as
Balmer series. This series is in visible region of the spectrum and consists of a
number of lines named as I 1, I2, I3, etc., at different wavelengths. Balmer showed
that if spectral lines are expressed in wave numbers (1/ƛ) then all the visible
lines of hydrogen spectrum can be fitted in the formula
1/ƛ cm-1 = R [ 1/22 - 1/n2 ]
where n is an integer equal to or greater than 3.
Rydberg later gave a more general equation 1/ƛ = ῦ cm-1 = R [ 1/n12 - 1/n22 ]
where for Balmer's spectral lines n1 is 2 and n2 = 3, 4,5, etc., to âˆž. R is called
Rydberg constant and has a value 197,677 per centi meter.
Four sharp coloured lines were observed in the visible region of this spectrum by
Balmer, in the ultra violet region by Lyman, in the infrared region by Paschen,
Brackett and Pfund. These series of lines are named after these scientists who
discovered them. Balmer expressed these lines in terms of inverse of their
wavelength ( ) by a mathematical relation, which was later modified by
where 'RH' is the Rydberg's constant and 'n1', 'n2' are integers with values equal
to or greater than 3 and 'l' is the wavelength.
Later on Lymann found hydrogen series starting at UV range and the value of n 1
= 1 and n2 = 2, 3, 4........
And Paschen found another series in Infra-red range with value of n1 = 3 and
n2 = 4, 5, 6........
Bracket series are also in Infra-red range and has values of n1 = 4 and
n2 = 5, 6, 7......
Pfund series are the next in IR range and it has the values of n1 = 5 and
n2 = 6, 7, 8 ...
The Photoelectric Effect
There are three ways in which electrons eject out of a material. They are
(i) Thermionic emission
(ii) Field emission
(iii) Photo electric emission
In all the above cases, energy is given to the material but in different forms. If
given in the form of heat it is called as Thermionic emission, if in the form of
electrical energy, it is field emission and if in the form of light (photons), then it
is photoelectric effect.
What is photoelectric effect?
When light of sufficiently small wavelength is incident on a metal surface,
electrons are ejected from the metal. This phenomenon is called as
'photoelectric effect' and the ejected electrons are called as 'photoelectrons'. A
systematic study of this effect can be done using the following experiment.
Two metal plates are sealed in a vacuum tube. If light of reasonably short
wavelength is made to fall on the plate (emitter). If a high potential, difference is
applied to the plates, making the emitter negative and the collector positive a
photocurrent is registered in the ammeter connected in series in the circuit as
long as the emitter is irradiated with light.
Let us increase the potential difference between the plates continuously. We
find that the photocurrent also increases but reaches a saturation. This shows
that the number of electrons attracted by the collector is becoming more
because of higher potential difference. After a certain potential, the number of
electrons reaching the collector remains the same irrespective of the attracting
potential. This must be due to the fact that the number of electrons ejected out
remains the same and all the ejected electrons are attracted by the collector
thereby producing a 'saturation region'.
The adjacent graph (V-I) shows the above observation. Now if the potential
difference between the plates is made zero still there is a photocurrent, as
shown by the intercept on the y-axis.
If the potential of the collector is made negative with respect to the cathode.
Even then, a photocurrent is registered and if the negative potential is
increased, the photocurrent decreases. For some negative potential of the
collector, the photocurrent becomes zero and it is called as 'stopping potential'.
The above can be explained as follows. When the collector potential is negative,
the electrons are repelled by the anode. Some electrons go back to the anode.
Some of them with high kinetic energy are still able to reach the anode (collector).
As the negative potential increase, less and less electrons reach the
collector and finally when none can reach the photocurrent becomes zero.
The stopping potential is related to the maximum kinetic energy of the ejected
electrons. The fastest photoelectron as it reaches the anode has kinetic energy
[K.Emax - eV0]
where K.Emax - energy of the electron when it leaves the emitter.
eV0 - increase in the potential energy of the electron
as it moves from emitter to collector.
If the intensity of the light increases the photocurrent also increases
proportionally but the stopping potential remains the same. This is depicted in
At the same time, if we decrease the intensity of light the amount of the
photocurrent decreases but for even the weakest signal 'photoelectric
phenomenon' takes place.
(K.E)max + (f) = hu
Einstein's photoelectric equation
Where f= work function of the surface
If classical theory is true, the lesser the intensity the energy imparted to the
electron must be less and hence there should have been a 'threshold intensity'
below which there is no photoelectric effect. But this is not true.
Instead, it was found that the frequency of the light is the key parameter. When
the frequency of light is increased, the stopping potential also increases and
there lies a threshold frequency below which there is no photoelectric effect.
The correct explanation for photoelectric effect was given by Albert Einstein in
1905. Einstein postulated that a beam of light consisted of small bundles of
energy called as photons. The energy 'E' of the photon is proportional to the
frequency ''u". Mathematically expressed as
E = hu
where 'h' is Planck's constant. The value of 'h' is 6.626 x 10-34 Js. When a photon
collides with an electron, it may transfer its energy to the electron. This transfer
is an "all or none" process, the electron getting all the photon's energy or none
at all. The energy received by the electrons helps it to escape from the surface of
the metal and to do this the electron loses an amount of energy called as the
work function of the surface of the metal (f). Therefore, if the energy received
by the electron from photon is hu [equation (2)] and uses an energy (f) (work
function of the surface) to escape the surface then the remaining is in the form
of kinetic energy.
(K.E)max + (f) = hu ..... (3).
this is called as Einstein's photoelectric equation.
But the stopping potential V0 provides a direct measurement of the maximum
kinetic energy with which electrons leave the cathode.
We can write it as
eV0 = hu – f
Equation (3) can be written as eV0 = hu – f
The graph shows the variation of stopping potential with frequency in
accordance to the above equation.
The above experimental study can be summarized as follows:
Before that, let us recollect some of the parameters and their symbols.
V0 - Stopping potential
u0 - Threshold potential
f - Work function
h - Planck's constant
ϑ - Frequency of the incident light
e - Electronic charge
(i) The metal emits electrons when light of sufficiently small wavelength falls on
it and the emission is instantaneous.
(ii) There exists a threshold frequency g0 for a given metal, below which there is
no photoelectric effect.
(iii) The photocurrent can be made zero by applying a negative potential to the
collector and the minimum negative potential to produce zero photocurrent is
called as stopping potential
(iv) The stopping potential depends on the frequency of the light falling on the
metal and not on the intensity of light.
(v) The photocurrent increases with the intensity of the incident light.
Millikan made the first accurate measurement of cut-off voltage for sodium
metal by using monochromatic light of known frequencies.
QUANTUM MECHANICAL MODEL OF ATOM
The atomic model which is based on the particle and wave nature of the
electron is known as wave or quantum mechanical model of the atom. This was
developed by Erwin Schrodinger in 1926. This model describes the electron as a
three dimensional wave in the electronic field of positively charged nucleus.
Schrodinger derived an equation which describes wave motion of an electron.
The differential equation is
∂2ψ /∂x2 + ∂2ψ/∂y2 + ∂2ψ/∂z2 + 8π2m/h2 ( E - v ) ψ = o
where x, y, z are certain coordinates of the electron, m = mass of the
electron E = total energy of the electron. V = potential energy of the electron;
h = Planck’s constant and ψ (psi) = wave function of the electron.
Significance of ψ: The wave function may be regarded as the amplitude function
expressed in terms of coordinates x, y and z. The wave function may have
positive or negative values depending upon the value of coordinates. The main
aim of Schrodinger equation is to give solution for probability approach. When
the equation is solved, it is observed that for some regions of space the value
of ψ is negative. But the probability must be always positive and cannot be
negative, it is thus, proper to use ψ2 in favour of ψ.
Where nth frequency of the wave
and ‘h’ is is Planck’s constant
Significance of ψ2: ψ2 is a probability factor. It describes the probability of
finding an electron within a small space. The space in which there is maximum
probability of finding an electron is termed as orbital. The important point of the
solution of the wave equation is that it provides a set of numbers called
quantum numbers which describe energies of the electron in atoms, information
about the shapes and orientations of the most probable distribution of electrons
Where x, y, z are certain coordinates of
m = mass of the electron
E = total energy of the electron.
V = potential energy of the electron;
h = Planck’s constant and
ψ (psi) = wave function of the electron.
∂2ψ /∂x2 + ∂2ψ/∂y2 +
8π2m/h2 ( E - v ) ψ = o
Nodal Points and Planes:
The point where there is zero probability of finding the electron is called nodal
point. There are two types of nodes: Radial nodes and angular nodes. The
former is concerned with distance from the nucleus while latter is concerned
The point where there is zero
probability of finding the electron is
called nodal point.
No. of radial nodes = n – l – 1
No. of angular nodes = l
No. of radial nodes = n – l – 1
No. of angular nodes = l
Total number of nodes = n – 1
Nodal planes are the planes of zero probability of finding the electron. The
number of such planes is also equal to l.
Total number of nodes = n – 1
DUAL CHARACTER (PARTICLE AND WAVE
CHARACTER OF MATTER AND RADIATION)
In case of light some phenomenon like diffraction and interference can be
explained on the basis of its wave character. However, the certain other
phenomenon such as black body radiation and photoelectric effect can be
explained only on the basis of its particle nature. Thus, light is said to have a dual
character. Such studies on light were made by Einstein in 1905.
Louis de Broglie, in 1924 extended the idea of photons to material particles such
as electron and he proposed that matter also has a dual character-as wave and
Derivation of de-Broglie Equation:
The wavelength of the wave associated with any material particle was calculated
by analogy with photon. In case of photon, if it is assumed to have wave
character, its energy is given by
E = hυ
(According to the Planck’s quantum theory)
Nodal planes are the planes of zero
probability of finding the electron.
The number of such planes is also
equal to l.
If the photon is supposed to have particle character, its energy is given by
E = mc2
(according to Einstein’s equation)
where ‘m’ is the mass of photon, ‘c’ is the velocity of light.
λ = h/mv
By equating (i) and (ii)
Where mv = p, momentum of the
hv = mc2
But v = c/λ
-De- Broglie’s hypothesis
h c/λ = mc2
(or) λ = h /mc
The above equation is applicable to material particle if the mass and velocity of
photon is replaced by the mass and velocity of material particle. Thus for any
material particle like electron.
λ = h/mv or λ = where mv = p is the momentum of the particle.
HEISENBERG’S UNCERTAINTY PRINCIPLE
All moving objects that we see around us e.g., a car, a ball thrown in the air etc.,
move along definite paths. Hence their position and velocity can be measured
accurately at any instant of time. Is it possible for subatomic particle also?
As a consequence of dual nature of matter, Heisenberg, in 1927
gave a principle about the uncertainties in simultaneous
measurement of position and momentum (mass x velocity) of
This Principle States:
“It is impossible to measure simultaneously the position and
momentum of a small microscopic moving particle with
absolute accuracy or certainty” i.e., if an attempt is made to
measure any one of these two quantities with higher accuracy,
the other becomes less accurate.
The product of the uncertainty in position ( x) and the uncertainty in the
momentum ( p = m. v where m is the mass of the particle and v is the
uncertainty in velocity) is equal to or greater than h/4π where h is the Planck’s
Thus, the mathematical expression for the Heisenberg’s uncertainty principle is
simply written as
p > h/4π
“It is impossible to measure
simultaneously the position and
momentum of a small microscopic
moving particle with absolute accuracy
Explanation of Heisenberg’s uncertainty principle
Suppose we attempt to measure both the position and momentum of an
electron, to pinpoint the position of the electron we have to use light so that the
photon of light strikes the electron and the reflected photon is seen in the
microscope. As a result of the hitting, the position as well as the velocity of the
electron are disturbed. The accuracy with which the position of the particle can
be measured depends upon the wavelength of the light used. The uncertainty in
position is ±λ. The shorter the wavelength, the greater is the accuracy. But
shorter wavelength means higher frequency and hence higher energy. This high
energy photon on striking the electron changes its speed as well as direction. But
this is not true for macroscopic moving particle. Hence Heisenberg’s uncertainty
principle is not applicable to macroscopic particles.
An atom contains large number of shells and subshells. These are distinguished
from one another on the basis of their size, shape and orientation (direction) in
space. The parameters are expressed in terms of different numbers
called quantum numbers.
Quantum numbers may be defined as a set of four numbers with the help of
which we can get complete information about all the electrons in an atom. It
tells us the address of the electron i.e., location, energy, the type of orbital
occupied and orientation of that orbital.
Principal quantum number (n): It tells the main shell in which the electron
resides, the approximate distance of the electron from the nucleus and energy of
that particular electron. It also tells the maximum number of electrons that a
shell can accommodate is 2n2, where n is the principal quantum number.
Azimuthal or angular momentum quantum number (l): This represents the
number of subshells present in the main shell. These subsidiary orbits within a
shell will be denoted as 0, 1, 2, 3, 4, or s, p, d, f… This tells the shape of the
subshells. The orbital angular momentum of the electron is given as √l (l +1)
h/2π or √l (l+1) h for a particular value of ‘n’ (where h = h/2π). For a given value
of n values of possible l vary from 0 to n – 1.
The magnetic quantum number (m): An electron due to its angular motion
around the nucleus generates an electric field. This electric field is expected to
produce a magnetic field. Under the influence of external magnetic field, the
electrons of a subshell can orient themselves in certain preferred regions of
space around the nucleus called orbitals. The magnetic quantum number
determines the number of preferred orientations of the electron present in a
subshell. The values allowed depends on the value of l, the angular momentum
quantum number, m can assume all integral values between –l to +l including
zero. Thus m can be –1, 0, +1 for l = 1.Total values of m associated with a
particular value of l is given by 2l+ 1.
The spin quantum number (s): Just like earth which not only revolves around the
sun but also spins about its own axis, an electron in an atom not only revolves
around the nucleus but also spins about its own axis. Since an electron can spin
either in clockwise direction or in anticlockwise direction, therefore, for any
particular value of magnetic quantum number, spin quantum number can have
two values, i.e., +1/2 and –1/2 or these are represented by two arrows pointing
in the opposite directions, i.e., ↑ and ↓. When an electron goes to a vacant
orbital, it can have a clockwise or anti clockwise spin i.e., +1/2 or –1/2. This
quantum number helps to explain the magnetic properties of the substances.
The maximum number of
electrons that a shell can
accommodate = 2n2
Where n is the principal quantum
For a given value of n values of
possible l vary from 0 to n – 1.
Total values of m associated
with a particular value of l is
given by 2l+ 1 values i.e. from –
l to +l including zero.
Spin quantum number can
have a clockwise or anti
clockwise spin i.e.,
+1/2 or –1/2
SHAPES AND SIZE OF ORBITALS
An orbital is the region of space around the nucleus within which the probability
of finding an electron of given energy is maximum (90–95%). The shape of this
region (electron cloud) gives the shape of the orbital. It is basically determined
by the azimuthal quantum number l, while the orientation of orbital depends on
the magnetic quantum number (m). Let us now see the shapes of orbitals in the
S–orbital: These orbitals are spherical and symmetrical about the nucleus. The
probability of finding the electron is maximum near the nucleus and keeps on
decreasing as the distance from the nucleus increases. There is vacant space
between two successive s–orbitals known as radial node. But there is no radial
node for 1s orbital since it is starting from the nucleus.
The size of the orbital depends upon the value of principal quantum number (n).
Greater the value of n, larger is the size of the orbital. Therefore,
2s–orbital is larger than 1s orbital but both of them are non-directional and
spherically symmetrical in shape.
s- orbital – spherical shape
p- Orbital – dumb bell shape
d- orbital – double dumb bell shape
f- orbital – complex shape
The probability of finding the p–electron is maximum in two lobes on the
opposite sides of the nucleus. This gives rise to a dumb–bell shape for the p–
orbital. For p–orbital l = 1. Hence, m = –1, 0, +1. Thus, p–orbital have three
different orientations. These are designated as px, py & pz depending upon
whether the density of electron is maximum along the x y and z axis
respectively. As they are not spherically symmetrical, they have directional
character. The two lobes of p–orbitals are separated by a nodal plane, where the
probability of finding electron is zero.
The three p-orbitals belonging to a particular energy shell have equal energies
and are called degenerate orbitals.
d–orbital (l = 2):
For d–orbitals, l = 2. Hence m = –2,–1, 0, +1, +2. Thus there are 5d orbitals. They
have relatively complex geometry. Out of the five orbitals, the three (d xy, dyz, dzx)
project in between the axis and the other two dz2 and dz2-y2 lie along the axis.
FILLING OF ELECTRONS IN VARIOUS
The atom is built up by filling electrons in various orbitals according to the
Aufbau Principle: This principle states that the electrons are added one by one
to the various orbitals in order of their increasing energy starting with the orbital
of lowest energy. The increasing order of energy of various orbital is
How to remember such a big sequence? To make it simple we are giving you the
method to write the increasing order of the orbitals. Starting from the top, the
direction of the arrow gives the order of filling of orbitals.
Alternatively, the order of increasing energies of the various orbitals can be
calculated on the basis of (n + l ) rule.
The energy of an orbital depends upon the sum of values of the principal
quantum number (n) and the azimuthal quantum number (l). This is called (n +l)
rule. According to this rule,
“In neutral isolated atom, the lower the value of (n + l) for an orbital, lower is
its energy. However, if the two different types of orbitals have the same value
of (n +l), the orbitals with lower value of n has lower energy’’.
Spins of an electron
Pauli’s Exclusion Principle
No two electrons in an atom can have identical quantum numbers. This is an
example of a general principle which applies not only to electrons but also to
other particles of half-integer spin. It does not apply to particles of integer spin.
When filling sublevels other than s, electrons are placed in individual orbitals
before they are paired up.
Electronic Configuration of Elements:
Definition: A statement describing the populations of electronic energy
sublevels of an atom. See the chart of electronic configurations to get the
notation for all of the elements.
Examples: The electronic configuration of the lithium atom is 1s22s1, which
indicates there are two electrons in the 1s sublevel and one electron in the 2s
Anomalous electronic configurations:
1. Half-filled and completely filled degenerate orbitals give greater stability to
Chromium (Z = 24) and copper (Z = 29) have anomalous electronic
configuration due to this reason.
Electronic configuration of chromium atom is 1s22s22p63s23p63d54s1 or [Ar]
3d54s1 but not 1s22s22p63s23p63d44s2.
Electronic configuration of copper atom is 1s22s22p63s23p63d104s1 or [Ar]
4s13d10 but not 1s22s22p63s23p63d94s2.
Stability of atoms:
Theory of exchange forces will explain why Cr has (Ar) 3d5 4s1 but not (Ar)
According to this theory, greater the number of unpaired electrons, greater
is the number of possible exchange pairs of electrons and more is the
exchange energy released and the atom is more stable.
For Cr → (Ar) 3d5 4s1, the possible number of exchange pairs = 15.
If energy released for each exchange pair is k, the total exchange energy is
For Cr → (Ar) 3d4 4s2, the possible number of exchange pairs = 10 and total
exchange energy is only 10k.
Therefore Cr → (Ar) 3d5 4s1 is more stable than Cr: (Ar) 3d4 4s2