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Objectives

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After studying this unit you will be
able to
• know about the discovery of
electron, proton and neutron and
their characteristics;
• describe Thomson, Rutherford
and Bohr atomic models;
• understand the important
features of the quantum
mechanical model of atom;
• understand nature of
electromagnetic radiation and
Planck’s quantum theory;
• explain the photoelectric effect
and describe features of atomic
spectra;
• state the de Broglie relation and
Heisenberg uncertainty principle;
• define an atomic orbital in terms
of quantum numbers;
• state aufbau principle, Pauli
exclusion principle and Hund’s
rule of maximum multiplicity; and
• write the electronic configurations
of atoms.

The rich diversity of chemical behaviour of different elements
can be traced to the differences in the internal structure of
atoms of these elements.

The existence of atoms has been proposed since the time
of early Indian and Greek philosophers (400 B.C.) who
were of the view that atoms are the fundamental building
blocks of matter. According to them, the continued
subdivisions of matter would ultimately yield atoms which
would not be further divisible. The word ‘atom’ has been
derived from the Greek word ‘a-tomio’ which means
‘uncut-able’ or ‘non-divisible’. These earlier ideas were
mere speculations and there was no way to test them
experimentally. These ideas remained dormant for a very
long time and were revived again by scientists in the
nineteenth century.
The atomic theory of matter was first proposed on a
firm scientific basis by John Dalton, a British school
teacher in 1808. His theory, called Dalton’s atomic
theory, regarded the atom as the ultimate particle of
matter (Unit 1). Dalton’s atomic theory was able to explain
the law of conservation of mass, law of constant
composition and law of multiple proportion very
successfully. However, it failed to explain the results of
many experiments, for example, it was known that
substances like glass or ebonite when rubbed with silk
or fur get electrically charged.
In this unit we start with the experimental
observations made by scientists towards the end of
nineteenth and beginning of twentieth century. These
established that atoms are made of sub-atomic particles,
i.e., electrons, protons and neutrons — a concept very
different from that of Dalton.

2.1 DISCOVERY OF SUB-ATOMIC
PARTICLES
An insight into the structure of atom was
obtained from the experiments on electrical
discharge through gases. Before we discuss
these results we need to keep in mind a basic
rule regarding the behaviour of charged
particles : “Like charges repel each other and
unlike charges attract each other”.

2.1.1 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 which
you will study in class XII. These results
suggested the particulate nature of
electricity.
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
in Fig. 2.1. 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 of the
glass tubes. 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 is developed
on the coating [Fig. 2.1(b)].

The results of these experiments are
summarised below.
(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
(fluorescent or phosphorescent) which
glow when hit by them. Television picture
tubes are cathode ray tubes and
television pictures result due to
fluorescence on the television screen
coated with certain fluorescent or
phosphorescent materials.
(iii) In the absence of electrical or magnetic
field, these rays travel in straight lines
(Fig. 2.2).
(iv) In the presence of electrical or magnetic
field, the behaviour of cathode rays are
similar to that expected from negatively
charged particles, suggesting that the
cathode rays consist of negatively
charged particles, called electrons.
(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 ray tube.
Thus, we can conclude that electrons are
basic constituent of all the atoms.

2.1.2 Charge to Mass Ratio of Electron
In 1897, British physicist J.J. Thomson
measured the ratio of electrical charge (e) to
the mass of electron (me
) by using cathode ray
tube and applying electrical and magnetic field
perpendicular to each other as well as to the
path of electrons (Fig. 2.2). When only electric
field is applied, the electrons deviate from their
path and hit the cathode ray tube at point A
(Fig. 2.2). Similarly when only magnetic field
is applied, electron strikes the cathode ray tube
at point C. By carefully balancing the electrical
and magnetic field strength, it is possible to
bring back the electron to the path which is
followed in the absence of electric or magnetic
field and they hit the screen at point B.
Thomson argued that the amount of deviation
of the particles from their path in the presence
of electrical or magnetic field depends upon:
(i) the magnitude of the negative charge on
the particle, greater the magnitude of the
charge on the particle, greater is the
interaction with the electric or magnetic
field and thus greater is the deflection.
(ii) the mass of the particle — lighter the
particle, greater the deflection.

(iii) the strength of the electrical or magnetic
field — the deflection of electrons from its
original path increases with the increase
in the voltage across the electrodes, or the
strength of the magnetic field.
By carrying out accurate measurements on
the amount of deflections observed by the
electrons on the electric field strength or
magnetic field strength, Thomson was able to
determine the value of e/me
as:

Where me
is the mass of the electron in kg and
e is the magnitude of the charge on the electron
in coulomb (C). Since electrons are negatively
charged, the charge on electron is –e.

2.1.3 Charge on the Electron
R.A. Millikan (1868-1953) devised a method
known as oil drop experiment (1906-14), to
determine the charge on the electrons. He found
the charge on the electron to be
– 1.6 × 10–19 C. The present accepted value of
electrical charge is – 1.602176 × 10–19 C. The
mass of the electron (me
) was determined by
combining these results with Thomson’s value
of e/me
ratio.

2.1.4 Discovery of Protons and Neutrons
Electrical discharge carried out in the modified
cathode ray tube led to the discovery of canal
rays carrying positively charged particles. The
characteristics of these positively charged
particles are listed below.
(i) Unlike cathode rays, mass of positively
charged particles depends upon the
nature of gas present in the cathode ray
tube. These are simply the positively
charged gaseous ions.
(ii) The charge to mass ratio of the particles
depends on the gas from which these
originate.
(iii) Some of the positively charged particles
carry a multiple of the fundamental unit
of electrical charge.
(iv) The behaviour of these particles in the
magnetic or electrical field is opposite to
that observed for electron or cathode
rays.
The smallest and lightest positive ion was
obtained from hydrogen and was called
proton. This positively charged particle was
characterised in 1919. Later, a need was felt
for the presence of electrically neutral particle
as one of the constituent of atom. These
particles were discovered by Chadwick (1932)
by bombarding a thin sheet of beryllium by
α-particles. When electrically neutral particles
having a mass slightly greater than that of
protons were emitted. He named these
particles as neutrons. The important
properties of all these fundamental particles
are given in Table 2.1.

2.2 ATOMIC MODELS
Observations obtained from the experiments
mentioned in the previous sections have
suggested that Dalton’s indivisible atom is
composed of sub-atomic particles carrying
positive and negative charges. The major
problems before the scientists after the
discovery of sub-atomic particles were:
• to account for the stability of atom,
• to compare the behaviour of elements in
terms of both physical and chemical
properties,

Millikan’s Oil Drop Method
In this method, oil droplets in the form of
mist, produced by the atomiser, were allowed
to enter through a tiny hole in the upper plate
of electrical condenser. The downward motion
of these droplets was viewed through the
telescope, equipped with a micrometer eye
piece. By measuring the rate of fall of these
droplets, Millikan was able to measure the
mass of oil droplets. The air inside the
chamber was ionized by passing a beam of
X-rays through it. The electrical charge on
these oil droplets was acquired by collisions
with gaseous ions. The fall of these charged
oil droplets can be retarded, accelerated or
made stationary depending upon the charge
on the droplets and the polarity and strength
of the voltage applied to the plate. By carefully
measuring the effects of electrical field
strength on the motion of oil droplets,
Millikan concluded that the magnitude of
electrical charge, q, on the droplets is always
an integral multiple of the electrical charge,
e, that is, q = n e, where n = 1, 2, 3… .

• to explain the formation of different kinds
of molecules by the combination of different
atoms and,
• to understand the origin and nature of the
characteristics of electromagnetic radiation
absorbed or emitted by atoms.

Different atomic models were proposed to
explain the distributions of these charged
particles in an atom. Although some of these
models were not able to explain the stability of
atoms, two of these models, one proposed by
J.J. Thomson and the other proposed by
Ernest Rutherford are discussed below.

2.2.1 Thomson Model of Atom
J. J. Thomson, in 1898, proposed that an atom
possesses a spherical shape (radius
approximately 10–10 m) in which the positive
charge is uniformly distributed. The electrons
are embedded into it in such a manner as to
give the most stable electrostatic arrangement
(Fig. 2.4). Many different names are given to
this model, for example, plum pudding, raisin
pudding or watermelon. This model can be

visualised as a pudding or watermelon of
positive charge with plums or seeds (electrons)
embedded into it. An important feature of this
model is that the mass of the atom is assumed
to be uniformly distributed over the atom.
Although this model was able to explain the
overall neutrality of the atom, but was not
consistent with the results of later experiments.
Thomson was awarded Nobel Prize for physics
in 1906, for his theoretical and experimental
investigations on the conduction of electricity
by gases.

 

In the later half of the nineteenth century
different kinds of rays were discovered,
besides those mentioned earlier. Wilhalm
Röentgen (1845-1923) in 1895 showed
that when electrons strike a material in
the cathode ray tubes, produce rays
which can cause fluorescence in the
fluorescent materials placed outside the
cathode ray tubes. Since Röentgen did not
know the nature of the radiation, he
named them X-rays and the name is still
carried on. It was noticed that X-rays are
produced effectively when electrons strike
the dense metal anode, called targets.
These are not deflected by the electric and
magnetic fields and have a very high
penetrating power through the matter
and that is the reason that these rays are
used to study the interior of the objects.
These rays are of very short wavelengths
(∼0.1 nm) and possess electro-magnetic
character (Section 2.3.1).
Henri Becqueral (1852-1908)
observed that there are certain elements
which emit radiation on their own and
named this phenomenon as
radioactivity and the elements known
as radioactive elements. This field was
developed by Marie Curie, Piere Curie,
Rutherford and Fredrick Soddy. It was
observed that three kinds of rays i.e., α,
β- and γ-rays are emitted. Rutherford
found that α-rays consists of high energy
particles carrying two units of positive
charge and four unit of atomic mass. He
concluded that α- particles are helium

nuclei as when α- particles combined with
two electrons yielded helium gas. β-rays
are negatively charged particles similar to
electrons. The γ-rays are high energy
radiations like X-rays, are neutral in
nature and do not consist of particles. As
regards penetrating power, α-particles are
the least, followed by β-rays (100 times
that of α–particles) and γ-rays (1000 times
of that α-particles).

2.2.2 Rutherford’s Nuclear Model of Atom
Rutherford and his students (Hans Geiger and
Ernest Marsden) bombarded very thin gold foil
with α–particles. Rutherford’s famous
α–particle scattering experiment is

represented in Fig. 2.5. A stream of high energy
α–particles from a radioactive source was
directed at a thin foil (thickness ∼ 100 nm) of
gold metal. The thin gold foil had a circular
fluorescent zinc sulphide screen around it.
Whenever α–particles struck the screen, a tiny
flash of light was produced at that point.
The results of scattering experiment were
quite unexpected. According to Thomson
model of atom, the mass of each gold atom in
the foil should have been spread evenly over
the entire atom, and α– particles had enough
energy to pass directly through such a uniform
distribution of mass. It was expected that the
particles would slow down and change
directions only by a small angles as they passed
through the foil. It was observed that:
(i) most of the α–particles passed through
the gold foil undeflected.
(ii) a small fraction of the α–particles was
deflected by small angles.
(iii) a very few α–particles (∼1 in 20,000)
bounced back, that is, were deflected by
nearly 180°
.
On the basis of the observations,
Rutherford drew the following conclusions
regarding the structure of atom:
(i) Most of the space in the atom is empty as
most of the α–particles passed through
the foil undeflected.
(ii) A few positively charged α–particles were
deflected. The deflection must be due to
enormous repulsive force showing that
the positive charge of the atom is not
spread throughout the atom as Thomson
had presumed. The positive charge has
to be concentrated in a very small volume
that repelled and deflected the positively
charged α–particles.
(iii) Calculations by Rutherford showed that
the volume occupied by the nucleus is
negligibly small as compared to the total
volume of the atom. The radius of the
atom is about 10–10 m, while that of
nucleus is 10–15 m. One can appreciate
this difference in size by realising that if

a cricket ball represents a nucleus, then
the radius of atom would be about 5 km.
On the basis of above observations and
conclusions, Rutherford proposed the nuclear
model of atom. According to this model:
(i) The positive charge and most of the mass
of the atom was densely concentrated in
extremely small region. This very small
portion of the atom was called nucleus
by Rutherford.
(ii) The nucleus is surrounded by electrons
that move around the nucleus with a very
high speed in circular paths called orbits.
Thus, Rutherford’s model of atom
resembles the solar system in which the
nucleus plays the role of sun and the
electrons that of revolving planets.
(iii) Electrons and the nucleus are held
together by electrostatic forces of
attraction.

2.2.3 Atomic Number and Mass Number
The presence of positive charge on the
nucleus is due to the protons in the nucleus.
As established earlier, the charge on the
proton is equal but opposite to that of
electron. The number of protons present in
the nucleus is equal to atomic number (Z ).
For example, the number of protons in the
hydrogen nucleus is 1, in sodium atom it is
11, therefore their atomic numbers are 1 and
11 respectively. In order to keep the electrical
neutrality, the number of electrons in an
atom is equal to the number of protons
(atomic number, Z ). For example, number of
electrons in hydrogen atom and sodium atom
are 1 and 11 respectively.

While the positive charge of the nucleus
is due to protons, the mass of the nucleus,
due to protons and neutrons. As discussed
earlier protons and neutrons present in the
nucleus are collectively known as nucleons.

The total number of nucleons is termed as
mass number (A) of the atom.

2.2.4 Isobars and Isotopes
The composition of any atom can be
represented by using the normal element
symbol (X) with super-script on the left hand
side as the atomic mass number (A) and
subscript (Z) on the left hand side as the atomic
number (i.e., A
Z
X).
Isobars are the atoms with same mass
number but different atomic number for
example, 6
14C and 7
14N. On the other hand, atoms
with identical atomic number but different
atomic mass number are known as Isotopes.
In other words (according to equation 2.4), it
is evident that difference between the isotopes
is due to the presence of different number of
neutrons present in the nucleus. For example,
considering of hydrogen atom again, 99.985%
of hydrogen atoms contain only one proton.
This isotope is called protium (1
1H). Rest of the
percentage of hydrogen atom contains two other
isotopes, the one containing 1 proton and 1
neutron is called deuterium (
1
2
D, 0.015%)
and the other one possessing 1 proton and 2
neutrons is called tritium (
1
3
T ). The latter
isotope is found in trace amounts on the earth.
Other examples of commonly occuring
isotopes are: carbon atoms containing 6, 7 and
8 neutrons besides 6 protons ( 6
12
6
13
6
14 C, C, C );
chlorine atoms containing 18 and 20 neutrons
besides 17 protons ( 17
35
17
37 Cl, Cl ).
Lastly an important point to mention
regarding isotopes is that chemical properties
of atoms are controlled by the number of
electrons, which are determined by the
number of protons in the nucleus. Number of
neutrons present in the nucleus have very little
effect on the chemical properties of an element.
Therefore, all the isotopes of a given element
show same chemical behaviour.

2.2.5 Drawbacks of Rutherford Model
As you have learnt above, Rutherford nuclear
model of an atom is like a small scale solar
system with the nucleus playing the role of the

massive sun and the electrons being similar
to the lighter planets. When classical
mechanics* is applied to the solar system, it
shows that the planets describe well-defined
orbits around the sun. The gravitational force
between the planets is given by the expression

is the distance of separation of the masses and
G is the gravitational constant. The theory can
also calculate precisely the planetary orbits and
these are in agreement with the experimental
measurements.

The similarity between the solar system
and nuclear model suggests that electrons
should move around the nucleus in well
defined orbits. Further, the coulomb force
(kq1
q2
/r
2
where q1
and q2
are the charges, r is
the distance of separation of the charges and
k is the proportionality constant) between
electron and the nucleus is mathematically
similar to the gravitational force. However,
when a body is moving in an orbit, it
undergoes acceleration even if it is moving with
a constant speed in an orbit because of
changing direction. So an electron in the
nuclear model describing planet like orbits is
under acceleration. According to the
electromagnetic theory of Maxwell, charged
particles when accelerated should emit
electromagnetic radiation (This feature does
not exist for planets since they are uncharged).
Therefore, an electron in an orbit will emit
radiation, the energy carried by radiation
comes from electronic motion. The orbit will
thus continue to shrink. Calculations show
that it should take an electron only 10–8 s to
spiral into the nucleus. But this does not
happen. Thus, the Rutherford model
cannot explain the stability of an atom.
If the motion of an electron is described on the
basis of the classical mechanics and
electromagnetic theory, you may ask that
since the motion of electrons in orbits is
leading to the instability of the atom, then
why not consider electrons as stationary

around the nucleus. If the electrons were
stationary, electrostatic attraction between
the dense nucleus and the electrons would
pull the electrons toward the nucleus to form
a miniature version of Thomson’s model
of atom.
Another serious drawback of the
Rutherford model is that it says nothing about
distribution of the electrons around the
nucleus and the energies of these electrons.

Classical mechanics is a theoretical science based on Newton’s laws of motion. It specifies the laws of motion of
macroscopic objects.

2.3 DEVELOPMENTS LEADING TO THE
BOHR’S MODEL OF ATOM
Historically, results observed from the studies
of interactions of radiations with matter have
provided immense information regarding the
structure of atoms and molecules. Neils Bohr
utilised these results to improve upon the
model proposed by Rutherford. Two
developments played a major role in the
formulation of Bohr’s model of atom. These
were:
(i) Dual character of the electromagnetic
radiation which means that radiations
possess both wave like and particle like
properties, and
(ii) Experimental results regarding atomic
spectra.
First, we will discuss about the duel nature
of electromagnetic radiations. Experimental
results regarding atomic spectra will be
discussed in Section 2.4.

2.3.1 Wave Nature of Electromagnetic
Radiation
In the mid-nineteenth century, physicists
actively studied absorption and emission of
radiation by heated objects. These are called
thermal radiations. They tried to find out of
what the thermal radiation is made. It is now
a well-known fact that thermal radiations
consist of electromagnetic waves of various
frequencies or wavelengths. It is based on a
number of modern concepts, which were
unknown in the mid-nineteenth century. First
active study of thermal radiation laws occured
in the 1850’s and the theory of electromagnetic
waves and the emission of such waves by
accelerating charged particles was developed

in the early 1870’s by James Clerk Maxwell,
which was experimentally confirmed later by
Heinrich Hertz. Here, we will learn some facts
about electromagnetic radiations.
James Maxwell (1870) was the first to give
a comprehensive explanation about the
interaction between the charged bodies and
the behaviour of electrical and magnetic fields
on macroscopic level. He suggested that when
electrically charged particle moves under
accelaration, alternating electrical and
magnetic fields are produced and transmitted.
These fields are transmitted in the forms of
waves called electromagnetic waves or
electromagnetic radiation.
Light is the form of radiation known from
early days and speculation about its nature
dates back to remote ancient times. In earlier
days (Newton) light was supposed to be made
of particles (corpuscules). It was only in the
19th century when wave nature of light was
established.
Maxwell was again the first to reveal that
light waves are associated with oscillating
electric and magnetic character (Fig. 2.6).

Although electromagnetic wave motion is
complex in nature, we will consider here only
a few simple properties.
(i) The oscillating electric and magnetic fields
produced by oscillating charged particles

are perpendicular to each other and both
are perpendicular to the direction of
propagation of the wave. Simplified
picture of electromagnetic wave is shown
in Fig. 2.6.
(ii) Unlike sound waves or waves produced
in water, electromagnetic waves do not
require medium and can move in
vacuum.
(iii) It is now well established that there are
many types of electromagnetic radiations,
which differ from one another in
wavelength (or frequency). These
constitute what is called electromagnetic
spectrum (Fig. 2.7). Different regions of
the spectrum are identified by different
names. Some examples are: radio
frequency region around 106 Hz, used for
broadcasting; microwave region around
1010 Hz used for radar; infrared region
around 1013 Hz used for heating;
ultraviolet region around 1016Hz a
component of sun’s radiation. The small
portion around 1015 Hz, is what is
ordinarily called visible light. It is only
this part which our eyes can see (or
detect). Special instruments are required
to detect non-visible radiation.
Fig. 2.7 (a) The spectrum of electromagnetic radiation. (b) Visible spectrum. The visible region is only
a small part of the entire spectrum.
(iv) Different kinds of units are used to
represent electromagnetic radiation.
These radiations are characterised by the
properties, namely, frequency (ν ) and
wavelength (λ).
The SI unit for frequency (ν) is hertz
(Hz, s–1), after Heinrich Hertz. It is defined as
the number of waves that pass a given point
in one second.
Wavelength should have the units of length
and as you know that the SI units of length is
meter (m). Since electromagnetic radiation
consists of different kinds of waves of much
smaller wavelengths, smaller units are used.
Fig.2.7 shows various types of electro-
magnetic radiations which differ from one
another in wavelengths and frequencies.
In vaccum all types of electromagnetic
radiations, regardless of wavelength, travel at
the same speed, i.e., 3.0 × 108
m s–1 (2.997925
× 108
m s–1, to be precise). This is called speed
of light and is given the symbol ‘c‘. The
frequency (ν ), wavelength (λ) and velocity of light
(c) are related by the equation (2.5).

The other commonly used quantity
specially in spectroscopy, is the wavenumber
( ). It is defined as the number of wavelengths
per unit length. Its units are reciprocal of
wavelength unit, i.e., m–1. However commonly
used unit is cm–1 (not SI unit).

2.3.2 Particle Nature of Electromagnetic
Radiation: Planck’s Quantum
Theory
Some of the experimental phenomenon such
as diffraction* and interference** can be
explained by the wave nature of the
electromagnetic radiation. However, following
are some of the observations which could not
be explained with the help of even the
electromagentic theory of 19th century
physics (known as classical physics):
(i) the nature of emission of radiation from
hot bodies (black -body radiation)
(ii) ejection of electrons from metal surface
when radiation strikes it (photoelectric
effect)
(iii) variation of heat capacity of solids as a
function of temperature

(iv) Line spectra of atoms with special
reference to hydrogen.
These phenomena indicate that the system
can take energy only in discrete amounts. All
possible energies cannot be taken up or
radiated.
It is noteworthy that the first concrete
explanation for the phenomenon of the black
body radiation mentioned above was given by
Max Planck in 1900. Let us first try to
understand this phenomenon, which is given
below:
Hot objects emit electromagnetic radiations
over a wide range of wavelengths. At high
temperatures, an appreciable proportion of
radiation is in the visible region of the
spectrum. As the temperature is raised, a
higher proportion of short wavelength (blue
light) is generated. For example, when an iron
rod is heated in a furnace, it first turns to dull
red and then progressively becomes more and
more red as the temperature increases. As this
is heated further, the radiation emitted becomes
white and then becomes blue as the
temperature becomes very high. This means
that red radiation is most intense at a particular
temperature and the blue radiation is more
intense at another temperature. This means
intensities of radiations of different wavelengths
emitted by hot body depend upon its
temperature. By late 1850’s it was known that
objects made of different material and kept at
different temperatures emit different amount of
radiation. Also, when the surface of an object is
irradiated with light (electromagnetic radiation),
a part of radiant energy is generally reflected
as such, a part is absorbed and a part of it is
transmitted. The reason for incomplete
absorption is that ordinary objects are as a rule
imperfect absorbers of radiation. An ideal body,
which emits and absorbs radiations of all
frequencies uniformly, is called a black body
and the radiation emitted by such a body is
called black body radiation. In practice, no
such body exists. Carbon black approximates
fairly closely to black body. A good physical
approximation to a black body is a cavity with
a tiny hole, which has no other opening. Any
ray entering the hole will be reflected by the
cavity walls and will be eventually absorbed by
the walls. A black body is also a perfect radiator
of radiant energy. Furthermore, a black body
is in thermal equilibrium with its surroundings.
It radiates same amount of energy per unit area
as it absorbs from its surrounding in any given
time. The amount of light emitted (intensity of
radiation) from a black body and its spectral
distribution depends only on its temperature.
At a given temperature, intensity of radiation
emitted increases with the increase of
wavelength, reaches a maximum value at a
given wavelength and then starts decreasing
with further increase of wavelength, as shown
in Fig. 2.8. Also, as the temperature increases,
maxima of the curve shifts to short wavelength.
Several attempts were made to predict the
intensity of radiation as a function of
wavelength.
But the results of the above experiment
could not be explained satisfactorily on the
basis of the wave theory of light. Max Planck

arrived at a satisfactory relationship by
making an assumption that absorption and
emmission of radiation arises from oscillator
i.e., atoms in the wall of black body. Their
frequency of oscillation is changed by
interaction with oscilators of electromagnetic
radiation. Planck assumed that radiation
could be sub-divided into discrete chunks of
energy. He suggested that atoms and
molecules could emit or absorb energy only
in discrete quantities and not in a continuous
manner. He gave the name quantum to the
smallest quantity of energy that can be
emitted or absorbed in the form of
electromagnetic radiation. The energy (E ) of a
quantum of radiation is proportional
to its frequency (ν ) and is expressed by
equation (2.6).

The proportionality constant, ‘h’ is known
as Planck’s constant and has the value
6.626×10–34 J s.
With this theory, Planck was able to explain
the distribution of intensity in the radiation
from black body as a function of frequency or
wavelength at different temperatures.
Quantisation has been compared to
standing on a staircase. A person can stand
on any step of a staircase, but it is not possible
for him/her to stand in between the two steps.
The energy can take any one of the values from
the following set, but cannot take on any
values between them.
E = 0, hυ, 2hυ, 3hυ….nhυ…..

 

Max Planck
(1858 – 1947)
Max Planck, a German physicist,
received his Ph.D in theoretical
physics from the University of
Munich in 1879. In 1888, he was
appointed Director of the Institute
of Theoretical Physics at the
University of Berlin. Planck was awarded the Nobel
Prize in Physics in 1918 for his quantum theory.
Planck also made significant contributions in
thermodynamics and other areas of physics.

Diffraction is the bending of wave around an obstacle.
** Interference is the combination of two waves of the same or different frequencies to give a wave whose distribution at
each point in space is the algebraic or vector sum of disturbances at that point resulting from each interfering wave.