Download 2.1 Historical Development

ATOMIC STRUCTURE
2.1 Historical Development
Based upon the information gathered in the form of laws of chemical combination and other
known properties of matter, John Dalton (1809) regarded the atom as a hard, dense and smallest
indivisible particle of matter. However, the emission of negatively and positively charged
particles from radioactive elements as well as from gases, on the passage of electricity through
them at very low pressures convinced the scientists that atom is not indivisible but consists of
much smaller fundamental particles. Thus, if electric discharge from a high potential source is
passed through a discharge tube evacuated to pressures around 0.01mm or less, rays are emitted
from the cathode. These are called cathode rays.
(a). These rays travel in straight lines at right angles to the cathode surface.
(b).They produce mechanical motion in a small paddle wheel placed in their path indicating that
they are material particles.
(c). These particles are deflected from their path by electric and magnetic fields showing that
they are electrically charged. The direction of deflection indicates that they are negatively
charged. The negatively charged material particles which constitute the cathode rays are called
electrons
With the discovery of electrons from the discharge tube experiments, J.J Thomson suggested a
model called plum – pudding model in which the electrons were assumed to be embedded in a
ball of positive charge. He determined the ratio e/m of electron by subjecting the beam of
electrons produced in a discharge tube to magnetic as well as electric fields and he was awarded
the physics Nobel Prize in 1906. e /m of electron = 1.75875 x 1011C Kg-1
Robert Milliken determined the charge on electron by using his famous oil drop technique and
was awarded the physics Nobel Prize in 1923. He found charge of an electron is 1.6022 x 10-19
Coulomb
Since e = 1.6022 x 10-19 C and e/m = 1.75875 x 1011C Kg
e
e/m
= mass of electron =
1.6022 x 10-19 C
= 9.1091 x 10-31kg
1.75875 x 1011C Kg
This is called the rest mass of the electron, i.e the mass which it possesses when it is moving
with a velocity much smaller than that of light.
On the atomic mass scale, the rest mass of electron = 0.0005486amu
1amu =
1
12
x (12/6.023 x 1023 )g = 1.66 x 10-24 g = 1.66 x 10-27 Kg
9.1091 x 10-31 Kg = 9.1091 x 10-31 / 1.66 x 10-27 amu = 0.0005487amu
Careful experiments with discharge tubes containing perforated cathode reveal the emission of
another type of radiations which start from the side of the anode and pass through the holes of
the cathode. These radiations which carry positive charge are called positive rays or anode rays.
The positive particles are in fact, the positive residues of the gas left when one or more electrons
are knocked out of the atoms of the gas. The smallest positive particle given out by the lightest
element hydrogen is called the proton. It is another fundamental particle whose charge has been
found to be equal in magnitude but opposite in sign to that of electron. Its mass is 1.6726 x 10-27
Kg or 1.00722 amu
2.2
The Rutherford Scattering Experiments (1911)
Ernest Rutherford directed a narrow beam of alpha particles obtained from polonium at an
extremely thin sheet of a metal like silver and gold. After passing through the metal sheet, the
alpha particles were made to strike a fluorescent screen. Rutherford`s observations were
1. Most of the alpha particles passed through the metallic sheet without suffering any
change in their path showing that the atom consists predominantly of empty space.
2. An extremely small number of alpha particles get deflected through wider angles or even
backwards showing the presence of a heavy positively charged body in each atom and
that the volume of this body is only a minute fraction of the total volume of the atom.
Chadwick discovered, in 1932, that when beryllium or boron is bombarded by alpha
particle, new particles which carry no charge but have mass almost equal to that of a
proton, are emitted. These particles are called neutrons. Chadwick won the physics
Nobel prize in 1935 for the discovery of neutron. Neutron mass = 1.6749 x 10 -27Kg or
1.00866 amu
Mass of a proton is almost the same as the mass of a neutron and it is taken as unit mass.
Mass of an electron is only 1/1836 the mass of a proton. Protons and neutrons are
together known as nucleons. Very approximately the radius of an atomic nucleus is only
10-15m compared with 10-10m for the atom as a whole.
2.3 The Rutherford Atomic Model
Based on his scattering experiments, combined with the discovery of neutron, Rutherford
suggested the following model of the atom.
1. An atom consists of a minute positively charged body, located at its centre, called the
nucleus. The nucleus, though small, contains all the protons and neutrons. Since the
mass of an atom is entirely due to the presence of protons and neutrons, it is evident
that almost the entire mass of an atom resides in the nucleus.
2. An atom also consists of a sufficient number of extremely small negatively charged
electrons distributed around the nucleus to balance the positive charge on the nucleus.
So Rutherford proposed that the electrons are revolving round the nucleus at
extremely high speeds at great distances from the nucleus. The centrifugal force
arising from this motion balances the force of electrostatic attraction. The electrons,
therefore, do not fall into the nucleus.
2.4 Objection to the Rutherford model
It was pointed out by Niels Bohr that Rutherford`s atom should be highly unstable.
J.C Maxwell had shown a few years earlier that whenever an electric charge is
subjected to acceleration, it emits radiation and loses energy. Bohr argued, therefore
that if an electron (a charged particle) moves round the nucleus in an orbit, as in
Rutherford`s model, it should be subjected to acceleration due to continuous change
in its direction of motion. The electron should, therefore, continuously emit radiation
and lose energy. As a result, its orbit should become smaller and smaller and finally it
should drop into the nucleus. This, however, does not happen.
Bohr solved this problem on the basis of the quantum theory of radiation put forth by
the German physicist Max Planck in 1900 to explain the observed distribution of
energy in the spectrum of the heat radiations emitted by a black body.
The energy density, i.e, the amount of energy radiated per unit volume, by a black
body depends upon the temperature at which the body is keeping. The correlation
between energy density and wave length at different temperatures is depicted in
Fig.2.1. These curves have the following characteristics:
Fig.2.1. Emission of radiation from a black body at different temperatures.
1. For each temperature , there is a particular wave length at which the energy
radiated is the maximum
2. The position of the maximum shifts towards lower wave lengths with increase in
temperature.
3. The higher the temperature, the more pronounced is the maximum.
These curves are usually referred to as the black body radiation curves. A black
body is defined as an object that absorbs all the radiations falling on it and emit all
the absorbed radiations also.
2.5 Classical mechanics: Its Success and Failure
Classical mechanics, as formulated by Newton in the 17th century and further
developed in the 18th and 19th centuries, could adequately describe the motion of
macroscopic bodies. However, it could not explain the nature of the radiation emitted
by hot bodies, i.e, the black body radiations, the heat capacities of solids and the
spectra of atoms and molecules. All the observations indicated that the system can
take up energy not continuously but only in discrete amounts (quanta).
2.6 Planck`s Quantum Theory of Radiation
Max Planck explained the distribution of energy radiated by a black body as follows
1. Radiant energy is not emitted or absorbed continuously but discontinuously in the
form of tiny bundles of energy called quanta.
2. Each quantum is associated with a definite amount of energy E which is
proportional to the frequency(ν) of radiation ie E α ν or E = hν where h is a
fundamental constant known as Planck`s constant. The numerical value of h is
6.626 x 10 -34 Js
3. A body can emit or absorb energy only in whole number multiples of quantum ie
E = nhν where n = 1,2,3…. This means that a body can emit or absorb energy
equal to 1hν, 2hν, 3hν,……. Energy in fractions of a quantum ie 0.7hν, 1.2hν,
3.6hν etc can not be lost or absorbed. This is known as quantization energy.
Max Planck is known as father of quantum theory and he was awarded Nobel
Prize in physics in 1918.
Based on this theory, Planck obtained the following expression for energy density
of black body radiation.
ρ(λ,T) = 8пhc / λ5 exp (hc /λkT) – 1
where h- Planck`s constant, c – velocity of light, λ- wave length of radiation
coming from black body, k- Boltzmann constant, T temperature in absolute scale.
2.7 Photoelectric Effect and Particle like Properties of Radiation
Sri J.J Thomson, in some of his famous experiments observed that when light of a
certain frequency strikes the surface of a metal, electrons are ejected from the metal.
The phenomenon of ejection of electrons from the surface of a metal when light of
a suitable frequency strikes on it is known as photoelectric effect. The ejected
electrons are called photoelectrons.
It may be noted that only a few metals show this effect under the action of visible
light but many more show it under the action of more energetic ultraviolet light.
Cesium which amongst the alkali metals has the lowest ionization energy is also the
metal from which electrons are ejected more easily. This metal is, therefore, used
largely in photoelectric cells.
According to classical theory,
1. The intensity of radiation is proportional to the square of the amplitude of the
electric field
2. As the intensity increases, the amplitude of the oscillating electric field is also
increasing
3. The electrons at the surface of the metal should oscillate along with the field and
so, as the intensity increases, the electrons oscillate more violently and eventually
breakaway from the surface with a kinetic energy that depends on the intensity of
the field.
This nice classical explanation is in complete disagreement with the experimental
observations. Experimentally the kinetic energy of the ejected electrons is
independent of the intensity of the incident radiation. Furthermore the classical
theory predicts that the photoelectric effect should occur for any frequency of
light as long as the intensity is sufficiently high. The experimental fact, however
is that there is a minimum frequency, threshold frequency (ν0), characteristic of
the metallic surface, below which no electrons are ejected, whatever be the
intensity of radiation. Above ν0 the kinetic energy of the ejected electrons varies
linearly with the frequency ν
To explain these results, Einstein used Planck`s quantum theory. When light is
absorbed by a metal, the total energy of the photon hν is given to a single electron
within the metal. If this quantity of energy is sufficiently large, the electron may
penetrate the potential barrier at the surface of the metal and still retain some
energy as kinetic energy. The kinetic energy retained by the electron depends on
the frequency of the photon that ejected it.
hν = ∅ + KE
Where ∅ is called the work function of the metal. The minimum frequency that
will eject an electron is just the frequency required to overcome the work function
of the metal, ie the threshold frequency,ν0
Then hν0 = ∅
The number of electrons ejected depends on the number of incident photons and
therefore the intensity of light.
Problem
The work function for Na metal is 2.92 x 10-19 J. Calculate the threshold
frequency for Na.
∅ = hν0
ν0 = 2.92 x 10-19 J / 6.626 x 10-34Js
= 4.40 x 1014 Hz