UNIT 1 OLD QUANTUM THEORY
Structure
Introduction
Objectives
li;,:overy of Sub-atomic Particles
Earlier Atom Models
Light as clectromagnetic Wave
Failures of Classical Physics
Black Body Radiation 1'
Heat Capacity Variation
Photoelectric Effect
Atomic Spectra
Planck's Quantum Theory, Black Body ~ d i a t i o n.
and Heat Capacity Variation
Einstein's Theory of Photoelectric Effect
Bohr Atom Model
Calculation of Radius of Orbits
Energy of an Electron in an Orbit
Atomic Spectra and Bohr's Theory
Critical Analysis of Bohr's Theory
Refinements in the Atomic Spectra The61-y
Summary
Terminal Questions
Answers
1.1 INTRODUCTION
The ideas of classical mechanics developed by Galileo, Kepler and Newton, when
applied to atomic and molecular systems were found to be inadequate. Need was felt
for a theory to describe, correlate and predict the behaviour of the sub-atomic
particles. The quantum theory, proposed by Max Planck and applied by Einstein and
Bohr to explain different aspects of behaviour of matter, is an important milestone
in the formulation of the modern concept of atom.
In this unit, we will study how black body radiation, heat capacity variation,
photoelectric effect and atomic spectra of hydrogen can be explained on the basis of
theories proposed by Max Planck, Einstein and Bohr. They based their theories on
the postulate that all interactions between matter and radiation occur in terms of
definite packets of energy, known as quanta. Their ideas, when extended further, led
to the evolution of wave mechanics, which shows the dual nature of matter and energy.
Objectives
After studying this unit, you should be able to :
describe the discovery of electron, proton and neutron,
explain the atom models of Thomson and Rutherford,
list the wave parameters of light,
describe the shortcomings of classical physics,
state Planck's theory and explain its application to black body radiation and heat
capacity variation,
define photoelectric effect and explain it in the light of Einstein's theory,
list Bohr's postulates and derive an expression useful in calculating the radius of
the hydrogen atom,
explain the atomic spectra of hydrogen in the light of Bohr's theory,
analyse critically the advantages and limitations of Bohr's theory, and
state the refinements in the atomic spectra theory.
1.2 DISCOVERY OF SUB-ATOMIC PARTICLES
The atomic theory of the Greek philosophers, Leucippus and Democretus (400 B.C.)
held that continued subdivision of matter would ultimately yield atoms which would
,1 Structure of Matter not be further divided. The word 'atom' is derived from the Greek word, aromos,
which means "uncut" or indivisible. Dalton (1808) based his atomic theory on the
Cathode rays are a stream ot
ideas of Democretus and was able to explain the laws of chemical combination.
negatively charged pudticks.
known as electrons. Toward the end of nineteenth century, it began to appear that the atom itself might
Mass of the electron
be composed of even smaller particles. This discovery was brought about by
= 9.109 x l w 3 ' kg experiments with electricity.
Charge of the electron Attempts to pass a high voltage electric current through gases under reduced pressure
= - 1.602 X 10--'' c
led to Julius Plucker's discovery (1859) of cathode rays, Fig. 1.1. The cathode rays
The unit for charge of the eluctron stream from the negative electrode, which is called the cathode. These rays consist
is coulomb, C. of negatively charged particles which travel in straight lines. The cathode rays give
off flashes of light, when they strike a screen coated with substances like zinc
sulphide. The picture tubes in television sets and computer monitors, function on this
principle.
Fig. 1.1: Deflection of cathode rays towards a positive plate in an
electrostatic field proving their negative charge.
The particles in cathode rays were later called electrons, as suggested by Stoney. The
determination of charge to mass ratio of electrons by Thomson (1897) confirmed the
fact that the electrons, which originate from the metal of which the cathode is
constituted, are the same no matter what metal is employed as the cathode. In other
words, electrons are fundamental particles of all types of matter.
If one or more electrons are removed from a neutral atom or molecule, the residual
entity is positively charged. During the formation of cathode rays in an electric
discharge tube, one or more electrons are removed from each of the atoms, and the
positive particles so produced, move toward the negative electrode. If this electrode
has holes in it, the positve ions pass through them, as shown in Fig. 1.2.
Cathode rays
/
Anode (f17mzm &'el Positive rays
I
Cathode
T o vacuum
(-1
Fig. 1.2: Positive rays.
Charge of the proton is equal in These streams of positive ions, called positive rays, were first observed by Goldstein
magnitude but opposite in sign to (1886). The charge t o mass ratios of positive ions depend on the nature of gases taken
that of the electron. in the discharge tube. For example, charge to mass ratios for the positive rays
obtained from hydrogen and neon are not the same. You can compare this fact with
the earlier statement that the charge to mass ratio value of electrons is the same
irrespective of the nature of gases kept in the discharge tube.
The positive particles produced, when hydrogen is taken in the discharge tube, are
called protons in accordance with the suggestio of Rutherford (1920). In Greek
P
'protes' means first. The protons, like electrons afe assumed to be constituents of all
atoms. The proton has positive charge, although equal in magnitude to that of the
electron.
, Old Quantum Theory
In the same year, Rutherford suggested that there might exist particles which he
called neutrons, having a mass equivalent to aproton but without charge. Chadwick
(1932) discovered neutrons during his experiments on the bombardment of beryllium
by a - particles. The properties ofelectron, proton and neutron are summarised in a - particles are helium nuclei rr
Table 1.1. Although other sub-atomic pafiicles have also oeen identified, atomic helium atoms which have lost
their electr0ns.
struciure is adequately explained on the basis of the n"mber of electrons, protons
and neutrons in an atom.
TaMe 1.1: Sub-atomic Particles
Particle Masdkg ChargeIC
Electron 9.109 x - 1.602 x
Proton 1.673 x + 1.602 x 1VIY
Neutron 1.675 x
Along with discoveries of sub-atomic particles, various theories were put forward to
explain the structure of the atom.
As mentioned in the last section, Dalton proposed a theory that atom is indivisible.
But the discovery of sub-atomic particles like electron, led to a revision of this theory.
Thomson (1904) proposed a model for the atomic structure, known as "plum
pudding" model, which is pictorially described in Fig. 1.3. He considered an atom to
be a uniform sphere of positive electricity of about lo4 cm radius, with the electrons
embedded in such a way as to give the most stable electrostatic arrangement.
This model was not able to explain the observation of Geiger and Marsden (1909)
regarding-the scattering of the a-particles directed towards thin gold foil. Some were Fin. 1.3: Th~bmwn's.*plum
deflected from their straight-line path arid a few recoiled back toward their source pudding" model for the atoni.
(Fig. 1.4). A uniform sphere of positive charge, would mean only a gradu;~ldcflcction
of the a-particle. but not scattering as it progressed thro~rgl~the for1
N~~~~~ Atoms in meal foil
Scattered and panicles lhnmson compsred atom to a
pudding With partially drid .
$rapes in it.
Rutherford. on 0bSelVing the
recoil of some a - particles h m
- thth gold foil. exclaimed "It was
quite the most incredible event
that has ever happened to me in
* my life. It was almost as if you
fired a 15 inch shell into a p i m of
tissue paper and it came back and
hit you".
If a nucleus of an atom were'the
slze of a tennis ball, the atom
(a) w u l d have a diameter of over
Defluxion one mtle.
Fig. I . : C;c-igrr -
and Manden's tr plrrlirie cxprirnmt: (h)
-
(h) Ikflcction of rx prticles by nuclei of m&l toll. Curved lines show the path or a -rapd c l l c d ,
rLllcrrtmkht~~teUcpOlnCt~nn~dcMcC
t
Rutherford (1911), on the basis of the a-ray scattering experiment, suggested that
positive charge and mass of the atom are concentrated iri a space which is very much
smaller than that occupied by the atom as a whole. He suggested an atomic model,
known as auclear model whicn consisted of a nucleus at the centre and negative
particles surrounding it. The nucleus accounted for mass and positive charge. To
support the fact that the electrons did not fall into a nucleus as a result of electrostatic
attraction, Rutherford found it necessary to postulate rapid rotation of the electrons
a h <the nucleus just as planets go round the sun. This analogy is misleading since
according to classical electromagnetic theory, an electron in orbit is subject 30
continual acceleration towards the centre and the accelerated electric charge must
emit radiation. The consequent loss of energy, should bring the electron down in a Ernest RuUmlord
spiral path to the nucleus - that is the collapse of the atom. 1811-1937 7
Structure
Introduction
Objectives
li;,:overy of Sub-atomic Particles
Earlier Atom Models
Light as clectromagnetic Wave
Failures of Classical Physics
Black Body Radiation 1'
Heat Capacity Variation
Photoelectric Effect
Atomic Spectra
Planck's Quantum Theory, Black Body ~ d i a t i o n.
and Heat Capacity Variation
Einstein's Theory of Photoelectric Effect
Bohr Atom Model
Calculation of Radius of Orbits
Energy of an Electron in an Orbit
Atomic Spectra and Bohr's Theory
Critical Analysis of Bohr's Theory
Refinements in the Atomic Spectra The61-y
Summary
Terminal Questions
Answers
1.1 INTRODUCTION
The ideas of classical mechanics developed by Galileo, Kepler and Newton, when
applied to atomic and molecular systems were found to be inadequate. Need was felt
for a theory to describe, correlate and predict the behaviour of the sub-atomic
particles. The quantum theory, proposed by Max Planck and applied by Einstein and
Bohr to explain different aspects of behaviour of matter, is an important milestone
in the formulation of the modern concept of atom.
In this unit, we will study how black body radiation, heat capacity variation,
photoelectric effect and atomic spectra of hydrogen can be explained on the basis of
theories proposed by Max Planck, Einstein and Bohr. They based their theories on
the postulate that all interactions between matter and radiation occur in terms of
definite packets of energy, known as quanta. Their ideas, when extended further, led
to the evolution of wave mechanics, which shows the dual nature of matter and energy.
Objectives
After studying this unit, you should be able to :
describe the discovery of electron, proton and neutron,
explain the atom models of Thomson and Rutherford,
list the wave parameters of light,
describe the shortcomings of classical physics,
state Planck's theory and explain its application to black body radiation and heat
capacity variation,
define photoelectric effect and explain it in the light of Einstein's theory,
list Bohr's postulates and derive an expression useful in calculating the radius of
the hydrogen atom,
explain the atomic spectra of hydrogen in the light of Bohr's theory,
analyse critically the advantages and limitations of Bohr's theory, and
state the refinements in the atomic spectra theory.
1.2 DISCOVERY OF SUB-ATOMIC PARTICLES
The atomic theory of the Greek philosophers, Leucippus and Democretus (400 B.C.)
held that continued subdivision of matter would ultimately yield atoms which would
,1 Structure of Matter not be further divided. The word 'atom' is derived from the Greek word, aromos,
which means "uncut" or indivisible. Dalton (1808) based his atomic theory on the
Cathode rays are a stream ot
ideas of Democretus and was able to explain the laws of chemical combination.
negatively charged pudticks.
known as electrons. Toward the end of nineteenth century, it began to appear that the atom itself might
Mass of the electron
be composed of even smaller particles. This discovery was brought about by
= 9.109 x l w 3 ' kg experiments with electricity.
Charge of the electron Attempts to pass a high voltage electric current through gases under reduced pressure
= - 1.602 X 10--'' c
led to Julius Plucker's discovery (1859) of cathode rays, Fig. 1.1. The cathode rays
The unit for charge of the eluctron stream from the negative electrode, which is called the cathode. These rays consist
is coulomb, C. of negatively charged particles which travel in straight lines. The cathode rays give
off flashes of light, when they strike a screen coated with substances like zinc
sulphide. The picture tubes in television sets and computer monitors, function on this
principle.
Fig. 1.1: Deflection of cathode rays towards a positive plate in an
electrostatic field proving their negative charge.
The particles in cathode rays were later called electrons, as suggested by Stoney. The
determination of charge to mass ratio of electrons by Thomson (1897) confirmed the
fact that the electrons, which originate from the metal of which the cathode is
constituted, are the same no matter what metal is employed as the cathode. In other
words, electrons are fundamental particles of all types of matter.
If one or more electrons are removed from a neutral atom or molecule, the residual
entity is positively charged. During the formation of cathode rays in an electric
discharge tube, one or more electrons are removed from each of the atoms, and the
positive particles so produced, move toward the negative electrode. If this electrode
has holes in it, the positve ions pass through them, as shown in Fig. 1.2.
Cathode rays
/
Anode (f17mzm &'el Positive rays
I
Cathode
T o vacuum
(-1
Fig. 1.2: Positive rays.
Charge of the proton is equal in These streams of positive ions, called positive rays, were first observed by Goldstein
magnitude but opposite in sign to (1886). The charge t o mass ratios of positive ions depend on the nature of gases taken
that of the electron. in the discharge tube. For example, charge to mass ratios for the positive rays
obtained from hydrogen and neon are not the same. You can compare this fact with
the earlier statement that the charge to mass ratio value of electrons is the same
irrespective of the nature of gases kept in the discharge tube.
The positive particles produced, when hydrogen is taken in the discharge tube, are
called protons in accordance with the suggestio of Rutherford (1920). In Greek
P
'protes' means first. The protons, like electrons afe assumed to be constituents of all
atoms. The proton has positive charge, although equal in magnitude to that of the
electron.
, Old Quantum Theory
In the same year, Rutherford suggested that there might exist particles which he
called neutrons, having a mass equivalent to aproton but without charge. Chadwick
(1932) discovered neutrons during his experiments on the bombardment of beryllium
by a - particles. The properties ofelectron, proton and neutron are summarised in a - particles are helium nuclei rr
Table 1.1. Although other sub-atomic pafiicles have also oeen identified, atomic helium atoms which have lost
their electr0ns.
struciure is adequately explained on the basis of the n"mber of electrons, protons
and neutrons in an atom.
TaMe 1.1: Sub-atomic Particles
Particle Masdkg ChargeIC
Electron 9.109 x - 1.602 x
Proton 1.673 x + 1.602 x 1VIY
Neutron 1.675 x
Along with discoveries of sub-atomic particles, various theories were put forward to
explain the structure of the atom.
As mentioned in the last section, Dalton proposed a theory that atom is indivisible.
But the discovery of sub-atomic particles like electron, led to a revision of this theory.
Thomson (1904) proposed a model for the atomic structure, known as "plum
pudding" model, which is pictorially described in Fig. 1.3. He considered an atom to
be a uniform sphere of positive electricity of about lo4 cm radius, with the electrons
embedded in such a way as to give the most stable electrostatic arrangement.
This model was not able to explain the observation of Geiger and Marsden (1909)
regarding-the scattering of the a-particles directed towards thin gold foil. Some were Fin. 1.3: Th~bmwn's.*plum
deflected from their straight-line path arid a few recoiled back toward their source pudding" model for the atoni.
(Fig. 1.4). A uniform sphere of positive charge, would mean only a gradu;~ldcflcction
of the a-particle. but not scattering as it progressed thro~rgl~the for1
N~~~~~ Atoms in meal foil
Scattered and panicles lhnmson compsred atom to a
pudding With partially drid .
$rapes in it.
Rutherford. on 0bSelVing the
recoil of some a - particles h m
- thth gold foil. exclaimed "It was
quite the most incredible event
that has ever happened to me in
* my life. It was almost as if you
fired a 15 inch shell into a p i m of
tissue paper and it came back and
hit you".
If a nucleus of an atom were'the
slze of a tennis ball, the atom
(a) w u l d have a diameter of over
Defluxion one mtle.
Fig. I . : C;c-igrr -
and Manden's tr plrrlirie cxprirnmt: (h)
-
(h) Ikflcction of rx prticles by nuclei of m&l toll. Curved lines show the path or a -rapd c l l c d ,
rLllcrrtmkht~~teUcpOlnCt~nn~dcMcC
t
Rutherford (1911), on the basis of the a-ray scattering experiment, suggested that
positive charge and mass of the atom are concentrated iri a space which is very much
smaller than that occupied by the atom as a whole. He suggested an atomic model,
known as auclear model whicn consisted of a nucleus at the centre and negative
particles surrounding it. The nucleus accounted for mass and positive charge. To
support the fact that the electrons did not fall into a nucleus as a result of electrostatic
attraction, Rutherford found it necessary to postulate rapid rotation of the electrons
a h <the nucleus just as planets go round the sun. This analogy is misleading since
according to classical electromagnetic theory, an electron in orbit is subject 30
continual acceleration towards the centre and the accelerated electric charge must
emit radiation. The consequent loss of energy, should bring the electron down in a Ernest RuUmlord
spiral path to the nucleus - that is the collapse of the atom. 1811-1937 7
