3. Construction
and Theory
The GM counter consists of a hollow metallic chamber as shown in the figure
that acts as a cathode.
A thin wire anode is also placed along its axis.
The chamber has a sealed window, through which the radiation enters the
chamber.
The chamber is filled with an inert gas at low pressure.
There is a counter connected to this system to measure the radiation.
Geiger-Müller tubes need a high voltage to operate. The tube consists of a
chamber containing two electrodes and a potential difference of several hundred
volts. The chamber is filled with a gas at a low pressure. A charged particle
passing through the gas causes excited and ionized molecules along its path. A
neutral molecule being ionized results in a positive ion and a free, negatively
charged electron: an ion pair. Due to the high voltage, there is a strong electric
field accelerating the positive ions towards the cathode and the electrons
towards the anode. Free electrons close to the anode gain sufficient energy to
ionize more gas molecules due to a stronger electric field. This creates a large
number of electron avalanche, meaning the tube can produce a significant
output pulse from a single original ionizing event. This phenomenon is called
Townsend avalanche.
4. Advantages Disadvantages
GM counter can count alpha particles,
beta particles, gamma particles, and
cosmic rays as well.
They have high sensitivity.
In this case power supply required not to
be with precise regulation because the
pulse height is constant almost
throughout the range.
As the output pulse is very high, hence
amplification required is more subtle.
GM counter can not measure energy due
to a lack of differentiating abilities.
GM counters cannot differentiate
between the type of radiation.
GM counters are less efficient due to its
large paralysis time limits, and also due
to large dead-time.
Quenching agents used in GM counters
often decompose, which leads to the
reduction in a lifetime.
Advantages and Disadvantages
5. Important
Definitions
Townsend Avalanche- The Townsend discharge or Townsend avalanche is a gas
ionization process where free electrons are accelerated by an electric field, collide with gas
molecules, and consequently free additional electrons. Those electrons are in turn accelerated
and free additional electrons.
Dead Time- After a count has been recorded, it takes the positive ion some time to reach
the cathode and reset the counter to its initial stage. During this time the counter cannot
detect anymore radiation.
Spurious Counts- When positive ions strike the cathode, secondary electrons are given
off from the surface. These electrons could be accelerated to give additional spurious counts
Quenching-In GM counter the phenomenon of quenching is to save the counter from
spurious counts. When first pulse is detected by hitting the electrons to the anode, it emits
secondary electrons. These secondary electrons may generate false counts. The quenching gas
will slow these electrons and make the detector ready for next pulse.
Internal quenching- a small amount of gas is added into the GM counter is called internal
quenching.
External quenching- a large negative voltage is applied to the anode instantly after recording
the output pulse. This minimizes the electrical field below the critical value for ionization by
collision.
7. Construction
The experimental set up consists of probe arrangement,
sample , oven 0-200°C, constant current generator , oven
power supply and digital panel meter(measuring voltage
and current). Four probe apparatus is one of the standard
and most widely used apparatus for the measurement of
resistivity of semiconductors. This method is used when
the sample is in the form of a thin wafer, such as a thin
semiconductor material deposited on a substrate. The
sample is millimeter in size and having a thickness “w”. It
consists of four probe arranged linearly in a straight line at
equal distance S from each other. A constant current is
passed through the two probes and the potential drop V
across the middle two probes is measured. An oven is
provided with a heater to heat the sample so that behaviour
of the sample is studied with increase in temperature.
8. Theory
The function, f(w/S) is a divisor for computing
resistivity which depends on the value of w and
S
We assume that the size of the metal tip is
infinitesimal and sample thickness is greater
than the distance between the probes,
Where V – the potential difference between
inner probes in volts.
I – Current through the outer pair of probes in
ampere.
S – Spacing between the probes in meter.
Total electrical conductivity of a semiconductor
is the sum of the conductivities of the valence
band and conduction band carriers. Resistivity
is the reciprocal of conductivity and its
temperature dependence is given by
Where Eg – band gap of the material
T – Temperature in kelvin
K – Boltzmann constant, K – 8.6x10-5 eV/K
The resistivity of a semiconductor rises
exponentially on decreasing the temperature.
9. Laser Diffraction
When a light of wavelength λ is incident normally on a narrow slit of width b, the resultant intensity
of the transmitted light is given by,
where, θ being the angle of diffraction. The diffraction pattern consists of a principal maximum for β
= 0, where all the secondary wavelets arrive in phase, and several secondary maxima of
diminishing intensity with equally spaced points of zero intensity at β = mπ. The positions of the
minima of a single-slit diffraction pattern are,
mλ = b sin θ, m = ±1, ±2, ±3, . . . .
mλ = b sin θ, m = ±1,±2,±3……..
If θ is small i.e. the slit to screen distance D is large compared to the distance xm between two m-th
order minima (on either side of principal maximum).
The above equation can be used to determine the wavelength of the monochromatic light source,
laser in present case, by measuring b, D and xm for various m. The positions of the minima can
be obtained by averaging the two extremities of the zero intensity region
10. CRO
The CRO stands for a cathode ray oscilloscope. It is typically
divided into four sections which are display, vertical controllers,
horizontal controllers, and Triggers. Most of the oscilloscopes
are used the probes and they are used for the input of any
instrument. We can analyze the waveform by plotting amplitude
along with the x-axis and y-axis. The applications of CRO are
mainly involved in the radio, TV receivers, also in laboratory
work involving research and design. it is used to obtain
waveforms when the different input signals are given. In the
early days, it is called as an Oscillograph. The oscilloscope
observes the changes in the electrical signals over time, thus the
voltage and time describe a shape and it is continuously
graphed beside a scale. By seeing the waveform, we can analyze
some properties like amplitude, frequency, rise time, distortion,
time interval, and etc.
11. B-H Curve
Hysteresis, in general, is defined as the lag in a variable property of a system with respect to the
effect producing it as this effect varies. In ferromagnetic materials the magnetic flux density B lags
behind the changing external Magnetizing field Intensity H. Hysteresis curve is drawn by plotting the
graph of B-field vs H (or M-H) by taking the material through a complete cycle of H values.
Retentivity - A measure of the residual flux density corresponding to the saturation of a magnetic
material. It is a material's ability to retain a certain amount of residual magnetic field when the
magnetizing force is removed after achieving saturation (The value of B at point E on the hysteresis
curve).
Residual Magnetism or Residual Flux - The magnetic flux density B that remains in a material when
the magnetizing field intensity H is zero. Residual magnetism and retentivity are same only when the
material is magnetized to the saturation point. However, it may be lower than the retentivity value
otherwise.
Retentivity - A measure of the residual flux density corresponding to the saturation of a magnetic
material. It is a material's ability to retain a certain amount of residual magnetic field when the
magnetizing force is removed after achieving saturation (The value of B at point E on the hysteresis
curve).
Residual Magnetism or Residual Flux - The magnetic flux density B that remains in a material when
the magnetizing field intensity H is zero. Residual magnetism and retentivity are same only when the
material is magnetized to the saturation point. However, it may be lower than the retentivity value
otherwise.
12. Theory
When a light of wavelength λ is incident
normally on a narrow slit of width b, the
resultant intensity of the transmitted light is
given by,
where, θ being the angle of diffraction. The
diffraction pattern consists of a principal
maximum for β = 0, where all the secondary
wavelets arrive in phase, and several secondary
maxima of diminishing intensity with equally
spaced points of zero intensity at β = mπ. The
positions of the minima of a single-slit
diffraction pattern are,
mλ = b sin θ, m = ±1, ±2, ±3, . . . .
mλ = b sin θ, m =
±1,±2,±3……..
If θ is small i.e. the slit to screen distance D is
large compared to the distance xm between two
m-th order minima (on either side of principal
maximum), then
The above equation can be used to determine
the wavelength of the monochromatic light
source, laser in present case, by measuring b, D
and xm for various m. The positions of the
minima can be obtained by averaging the two
extremities of the zero intensity region
13. Double Slit
Experiment
The double-slit experiment is a demonstration that light and
matter can display characteristics of both classically defined
waves and particles; moreover, it displays the fundamentally
probabilistic nature of quantum mechanical phenomena. This
type of experiment was first performed, using light, by Thomas
Young, as a demonstration of the wave behavior of light.
In the basic version of this experiment, a coherent light
source, such as a laser beam, illuminates a plate pierced by
two parallel slits, and the light passing through the slits is
observed on a screen behind the plate. The wave nature of
light causes the light waves passing through the two slits to
interfere, producing bright and dark bands on the screen –
a result that would not be expected if light consisted of
classical particles.
14. String Drum
The general wave equation for a
string wave
These are called normal modes of vibrations in a
string.
The string if vibrated in any of the normal mode,
remains in that mode with amplitude varying
sinosuidally with time, but a string vibrated in any
random fashion is superposition of various normal
modes harmonics which have time varying
coefficients.
The general wave equation in a 2D membrane is
given by :
∂2
z/∂x2
+ ∂2
z/∂y2
= 1/c2
(∂2
/∂t2
)z
Waves in String and Drum
15. Fourier Series
Any periodic function can be written as linear superposition of sine
and cosine functions of different frequencies. The usual Fourier series
involving sines and cosines is given by taking f1(x)= cos(x) and f2(x)=
sin(x) since these functions form a complete orthogonal system over
[-π,π]. Fourier series of function f(x) is given by
16. Hydrogen Atom Gas Molecules
An atomic orbital is known as the wave
function ψ for an electron in an atom.
The principal quantum number ‘n’ It tells the
size and energy of the orbital. All the orbitals
of ‘n’ contains a single shell of an atom.
Azimuthal quantum number ‘l’ is referred to
as subsidiary quantum number or orbital
angular momentum number and defines an
orbital’s three-dimensional shape.
Magnetic orbital quantum number
‘ml’ describes an orbital’s spatial orientation
in accordance with the co-ordinate axis.
The air molecules surrounding us are not all traveling at
the same speed, even if the air is all at a single
temperature
The volume occupied by the molecules of the gas is
negligible compared to the volume of the gas itself.
The molecules of an ideal gas exert no attractive forces on
each other, or on the walls of the container.
The molecules are in constant random motion, and as
material bodies, they obey Newton's laws of motion.
Collisions are perfectly elastic; when two molecules collide,
they change their directions and kinetic energies, but the
total kinetic energy is conserved. The average kinetic energy
of the gas molecules is directly proportional to the absolute
temperature.
Hydrogen Atom and Gas Molecule
17. Hartley ColpitT
The resistors R1, R2 and Re provide necessary bias
condition for the circuit. The capacitor Ce provides a.c.
ground thereby providing any signal degeneration. The
capacitors Cc and Cb are employed to block d.c. and to
provide an a.c. path. The radio frequency choke (R.F.C)
offers very high impedance to high frequency currents
which means it shorts for d.c. and opens for a.c.
The auto-transformer made by the inductive coupling of
L1 and L2 helps in determining the frequency and
establishes the feedback. As the CE configured transistor
provides 180o phase shift, another 180o phase shift is
provided by the transformer, which makes 360o phase
shift between the input and output voltages.
This makes the feedback positive which is essential for
the condition of oscillations. When the loop gain |βA| of
the amplifier is greater than one, oscillations are
sustained in the circuit
The resistors R1, R2 and Re provide necessary bias condition for the circuit. The
capacitor Ce provides a.c. ground thereby providing any signal degeneration. The
capacitors Cc and Cb are employed to block d.c. and to provide an a.c. path. The
radio frequency choke (R.F.C) offers very high impedance to high frequency
currents which means it shorts for d.c. and opens for a.c.
The auto-transformer made by the inductive coupling of L1 and L2 helps in
determining the frequency and establishes the feedback. As the CE configured
transistor provides 180o phase shift, another 180o phase shift is provided by the
transformer, which makes 360o phase shift between the input and output voltages.
This makes the feedback positive which is essential for the condition of oscillations.
When the loop gain |βA| of the amplifier is greater than one, oscillations are
sustained in the circuit
Hartley & Colpitt Oscillator
