physics

1. UNIT 7
MODERN PHYSICS
BY GK BASAK

2. • The first model of atom was proposed by J. J. Thomson in
1898. According to this model, the positive charge of the atom
is uniformly distributed throughout the volume of the atom
and the negatively charged electrons are embedded in it like
seeds in a watermelon. This model was picturesquely called
plum pudding model of the atom.
• Ernst Rutherford (1871–1937), a former research student of J.
J. Thomson, was engaged in experiments on α-particles
emitted by some radioactive elements. In 1906, he proposed
a classic experiment of scattering of these α-particles by
atoms to investigate the atomic structure.
• According to this the entire positive charge and most of the
mass of the atom is concentrated in a small volume called the
nucleus with electrons revolving around the nucleus just as
planets revolve around the sun.

4. volume. Rutherford scattering therefore, is a powerful way to determine an upper limit to the
size of the nucleus.

5. • POSTULATES OF BOHR THEORY
• The model of the atom proposed by Rutherford assumes that the atom,consisting
of a central nucleus and revolving electron is stable much like sun-planet system
which the model imitates. However, there are some fundamental differences
between the two situations. While the planetary system is held by gravitational
force, the nucleus-electron system being charged objects, interact by Coulomb’s
Law of force. We know that an object which moves in a circle is being constantly
accelerated – the acceleration being centripetal in nature. According to classical
electromagnetic theory, an accelerating charged particle emits radiation in the form of
electromagnetic waves. The energy of an accelerating electron should therefore,
continuously decrease. The electron would spiral inward and eventually fall into the
nucleus (Fig. 12.7). Thus, such an atom can not be stable. Further, according to the
classical electromagnetic theory, the frequency of the electromagnetic waves emitted
by the revolving electrons is equal to the frequency of revolution.

6. • Bohr combined classical and early quantum concepts and gave his theory in the
form of three postulates. These are :
(i) Bohr’s first postulate was that an electron in an atom could revolve in certain
stable orbits without the emission of radiant energy, contrary to the predictions of
electromagnetic theory. According to this postulate, each atom has certain
definite stable states in which it can exist, and each possible state has definite
total energy. These are called the stationary states of the atom.
(ii) Bohr’s second postulate defines these stable orbits. This postulate states that the
electron revolves around the nucleus only in those orbits for which the angular
momentum is some integral multiple of h/2π where h is the Planck’s constant (= 6.6 ×
10–34 J s). Thus the angular momentum (L) of the orbiting electron is quantised. That
is L = nh/2π
(iii) Bohr’s third postulate incorporated into atomic theory the early quantum concepts
that had been developed by Planck and Einstein. It states that an electron might make
a transition from one of its specified non-radiating orbits to another of lower energy.
When it does so, a photon is emitted having energy equal to the energy difference
between the initial and final states. The frequency of the emitted photon is then given
by hν = – where and are the energies of the initial and final states and > .

7. • Bohr’s second postulate about the angular momentum of the electron the
quantisation condition – is used. The angular momentum L is given by L =
mvr ,Bohr’s second postulate of quantisation says that the allowed values
of angular momentum are integral multiples of h/2π. = m = where n is an
integer, is the radius of nth possible orbit and is the speed of moving
electron in the nth orbit.

8. • Different orbits in which electrons revolve are known as stationary states
or energy levels. These stationary states/ energy level for an electron are
numbered as n = 1, 2, 3……….. These integers are also known as the
principal quantum numbers.
• Energy levels: The energy of an atom is the least (largest
negative value) when its electron is revolving in an orbit
closest to the nucleus i.e., the one for which n = 1. For n = 2,
3, ... the absolute value of the energy E is smaller, hence the
energy is progressively larger in the outer orbits. The lowest
state of the atom, called the ground state, is that of the
lowest energy, with the electron revolving in the orbit of
smallest radius, the Bohr radius, a0. The energy of this state (n
= 1), E1 is –13.6 eV. Therefore, the minimum energy required
to free the electron from the ground state of the hydrogen
atom is 13.6 eV. It is called the ionisation energy of the
hydrogen atom.

10. • The key difference between excitation and ionization potential is that excitation
potential is the energy required to jump from one energy level to other while
ionization potential is the energy required to remove an electron from an atom.
Note: an electron is removed from the atom and there is no attraction
with the nucleus when it is removed.

12. • What are X-Rays?
We can define X-Rays or X-radiation as a form of electromagnetic radiation. They
are powerful waves of electromagnetic energy. Most of them have a wavelength
ranging from 0.01 to 10 nanometres, corresponding to frequencies in the range
30 petahertz to 30 exahertz and energies in the range 100 eV to 100 keV.
• Who invented the X-Ray?
German physicist Wilhelm Röntgen is typically credited for the discovery of X-
Rays in 1895 because he was the first to comprehensively study them, though he
is not thought to be the first to have seen and perceived their effects.

13. • How do X-Rays work?
They are produced when high-velocity electrons collide with the metal
plates, thereby giving the energy as the X-Rays and themselves absorbed by
the metal plate.
• The X-Ray beam travels through the air and comes in contact with the
body tissues, and produces an image on a metal film.
• Soft tissue like organs and skin, cannot absorb the high-energy rays, and
the beam passes through them.
• Dense materials inside our bodies, like bones, absorb the radiation.

14. • Properties of X-Rays
The X-Rays properties are given below:
• They have a shorter wavelength of the
electromagnetic spectrum.
• Requires high voltage to produce X-Rays.
• They are used to capture the human skeleton defects.
• They travel in a straight line and do not carry an electric
charge with them.
• They are capable of travelling in a vacuum.

15. • X-Rays Uses
Since the discovery of X-radiation, they are used in various fields and for various purposes.
Some key uses of X-Ray are given below.
• Medical Science
• Security
• Astronomy
• Industry
• Restoration
• Medical Use:
They are used for medical purposes to detect the breakage in human bones.
• Security:
They are used as a scanner to scan the luggage of passengers in airports, rail terminals,
and other places.
• Astronomy:
It is emitted by celestial objects and are studied to understand the environment.
• Industrial Purpose:
It is widely used to detect the defects in the welds.
• Restoration:
They are used to restoring old paintings.

16. Soft x ray having energy around 1.24 KeV, hard x rays having energy
around 1.24 MeV.

17. COOLIDGE X-RAY TUBE
• The Coolidge Tube, first produced in 1913 by W. Coolidge. The Coolidge tube was the first type of practical x-
ray tube to employ the principle of thermionic emission.
• A tungsten filament is used as the tube cathode, and during operation is heated to incandescence by passing
a current through it. This causes the filament to emit electrons at a rate dependent on the temperature of
the filament. The electrons are then accelerated towards the tube anode by the strong tube voltage. Upon
hitting the anode, the electrons are decelerated very rapidly, and shed their excess kinetic energy mostly as
heat, and partly as x-ray radiation. To prevent the electron beam from dispersing due to repulsive forces
between the electrons, the cathode filament is surrounded by a metal focusing cup at a high negative
potential, that has the effect of converging the beam to a relatively small focal area on the anode. X-ray
tubes previous to the Coolidge tube (known as Gas Tubes), relied for their electron source, on the tube
voltage being strong enough to 'pull' electrons from the cathode. These were accelerated towards the
anode, and collided with residual gas molecules purposefully left in the tube, ionizing the molecules and
causing the ejection of more electrons. In this way, the required electron beam was built up with a kind of
'avalanche effect'. However, the number of electrons in a beam produced this way, and their energy upon
collision with the anode, were both dependent on the gas pressure within the tube, which was rarely stable,
and difficult to control. In addition, the number of electrons produced in this way, was, by today's standards
extremely small, and hence the intensity of the produced x-rays very low, leading to very long exposure
times.
• The Coolidge tube, using as it did thermionic emission to obtain a source of electrons, removed the
dependency on residual gas for the number and energy of the electrons in the electron beam (an indeed in
Coolidge tubes, almost all gas is removed). In fact, as the number of electrons produced depended on the
current applied across the cathode filament, and the energy of the electrons on the tube voltage, the
Coolidge tube made it possible to easily and independently vary the number of electrons (and hence the
intensity of x-rays produced), and their energy (and hence the frequency of produced x-rays). Also,
thermionic emission allowed a much higher bound on the numbers of electrons produced, and hence lead to
a drastic reduction in exposure times.

19. • Continuous X-rays
• Bremsstrahlung (Braking Radiation) transitions create the phenomenon of
continuous x-rays whereas regular characteristic x-rays are created by
inner shell transitions. Bremsstrahlung (sudden deflection or slowing
down of charged particles) mechanism can be viewed when a target made
of metal suffers electron bombardment. The atoms of the metal target
scatter the electrons, whose change in acceleration causes a phenomenon
of radiation in them.

20. • What Are Continuous X – Rays?
• Just like the phenomenon of visible light, continuous X-ray spectra also contains photons
ranging through a lot of wavelengths. As we all are well aware by now, the production of
X-rays happens when the target which is made up of an element with a high atomic
number is hit by electrons travelling at a high velocity. Most of the energy applied is
wasted by being converted into heat energy in the target material’s system. X-rays that
have continuously unstable wavelengths are produced due to the loss of energy that the
few electrons who were moving fast enough (and penetrated to the interior sections of
the atoms of the material being targeted) suffer. The attractive pulling forces applied by
the nucleus of the target element causes a deceleration of these fast-moving electrons, in
turn, decreasing their energy continuously. A varying frequency of X-rays is emitted
continuously due to the retardation of the speed of electrons. The X – rays consist of a
continuous range of frequencies up to a maximum frequency fmax or minimum wavelength
λmin. This is called continuous X – rays. The minimum wavelength depends on the anode
voltage. If V is the potential difference between the anode and the cathode.
• eV = hfmax = hc / λmin
• The minimum wavelength of the given radiation is,
• λmin = hc /eV
Where the Planck’s constant is h, the velocity of light is c and the charge of the electron is e.
Substituting the known values in the above equation, we get
λmin = 12400/V A0

21. • Characteristic X-ray - Characteristic radiation is a sort of
energy emission that is important in the creation of X-
rays. When a fast-moving electron collides with a K-shell
electron, the electron in the K-shell is ejected (if the
incident electron's energy is larger than the K-shell
electron's binding energy), leaving a 'hole' behind. An
outer shell electron fills this hole (from the L-shell, M-
shell, and so on) with the emission of a single X-ray
photon with an energy level equal to the energy level
difference between the outer and inner shell electrons
engaged in the transition.