MODERN PHYSICS

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					                      Unit – II                  MODERN PHYSICS
Syllabus: Dual nature of light, Matter waves – De broglie’s hypothesis – Davison & Germer
experiment, Heisenberg’s uncertainty principle and its applications (non-existence of electron in
nucleus, Finite width of spectral lines), one dimensional time independent Schrödinger’s wave
equation – Physical signification of wave function – Particle in a box(one dimension), Nuclear
radiation detectors – GM counter, Scintillation counter and solid state detector, Qualitative
treatment (without derivation) of Fermi Dirac distribution function and Fermi Energy level concept
in semi conductors, NMR – principle and technique, photo cells and its applications.


Matter waves:
         A wave is specified by its frequency, wavelength, phase, amplitude and intensity, where as the
particle is specified by its mass, velocity, momentum and energy. The radiation has a dual nature i.e.,
radiation is a wave and also a particle. It cannot exhibit its particle and wave properties simultaneously.
Definition:- The waves associated with the moving particles of matter ( ex. Electrons, protons etc.,) are
known as matter waves or piolet waves or de Broglie waves.
Properties:-
i)      Lighter is the particle, greater is the wavelength associated with it.
ii)     Smaller is the velocity of the particle, greater is the wavelength associated with it.
iii)    The velocity of matter waves is greater than the velocity of light.
iv)     Matter wave representation is a symbolic representation.
v)      They are neither mechanical waves nor electromagnetic waves.
vi)     These are generated by the motion of particles
vii)    Wavelengths of these waves are independent of charges of the particles.
viii)   The wave and particle aspects of moving bodies can never appear together in the same
        experiments.

de-Broglie hypothesis:
Like radiations, matter also exhibits dual characteristic. For example light can act like wave sometime and
like a particle at other times, then the material particles (ex. Electron, neutron etc.,) should act as wave at
some other times.
According to de – Broglie hypothesis, a moving particle is associated with a wave which is known as de-
Broglie wave or matter wave.
i)      Wavelength of matter wave :
        From Planck‟s theory of radiation, the energy of photon is given by,
                                 E = h = hc /                    --      (1)
        From Einstein‟s mass – energy relation, the energy of photon is given by,
                                   E = mc2                               --      (2)
        Since the energy of the photon in the two cases is the same, therefore
                 h = mc2          => hc / = mc2                 => = h / mc
        If the particle is electron and its velocity is v then,
                 Wavelength of matter wave,            = h / mv         --      (3)
ii)     Wavelength associated with electrons:
        Let us consider the case of an electron of mass m and charge e, accelerated by a potential V volt
        from rest to velocity v. then
                 Energy gained by electron = eV
PYS 1002      (2007-08)                             Page 1 of 12                                 Unit - 2
                              KE of electron = ½ mv2
                  eV = ½ mv2               =>          v =  2eV / m           --      (4)
        Now       = h / mv = h / [m  2eV / m]        = h /  2eVm     = 12.26 /  V   Ao
If an electron is accelerated through a potential difference of 100 volt, the de – Broglie‟s wavelength
associated with it is 1.226 Ao
iii)    Wave velocity:
From eq‟s (1) & (2)         E = h          &          E = mc2
                          h = mc2          or          = mc2/ h               --      (5)
The wave velocity (W) is given by, W =  = [mc2/ h ][h / mv] = c2/ v           --      (6)
As particle velocity (v) can not exceed velocity of light (c), hence W is greater than velocity of light.
iv)     If E is the K.E of the particle, then
        E = ½ mv2 = m2v2 / 2m = p2 / 2m
        p=     2mE
                                                 h
         de - broglie wave length, λ =
                                                2mE


Experimental demonstration of wave nature of electron (Davisson – Germer experiment)
The wave nature of the material particles as predicted by de- Broglie was confirmed by Davisson and
Germer.
The apparatus consists of an electron gun G where the
electrons are produced and obtained in a fine pencil of
electronic beam of known velocity. The electron gun
consists of a tungsten filament F heated to dull red so
that electrons are emitted and accelerated in the
electric field of known potential difference. A narrow
hole in the anode renders the electrons into a fine beam
and allows it to strike the nickel target T. The electrons
are scattered in all directions by the atoms in the
crystal. The intensity of the electron beam scattered in a
given direction is found by the use of detector.
         By rotating the detector about an axis through the point „O‟, the intensity of scattered beam can be
measured for different values of , the angle between incident and the scattered direction of electron
beam. The graph is plotted between angle  and intensity of scattered beam. In each graph, the intensity
of electron beam in a given direction is proportional to the distance of curve from the point „O‟, in that
direction.




From the figures it is observed that
i)     There is a strong diffracted beam for  = 500 and V = 54 v.


PYS 1002      (2007-08)                               Page 2 of 12                                Unit - 2
ii)     Intensity of scattered electrons depends upon the angle of scattering .
        From fig,          = (180 - ) / 2
        For        = 500         =>         = 650
        From Bragg formula, 2d Sin  = n
        Where d – interplanar distance ( for nickel crystal d = 0.909 A0)]
                   2 x 0.909 x Sin 650 =           [ for first order n=1 ]
                              = 1.65 A  0

According to de- Broglie electron wave,  = 12.25 /  V
                                            = 12.25 /  54 = 1.67 A0
As the values are in good agreement, hence confirms the de- Broglie concept of matter waves.

Heisenberg’s uncertainty principle:
         “ It is impossible to know both the exact position and momentum of a particle simultaneously”
         If p is the uncertainty in determining the momentum and x is the uncertainty in determining the
position of the particle then,
                           x. p  h / 2
The exact statement of uncertainty principle is,
         The product of uncertainties in determining the position and momentum of the particle can never
smaller than the order of h / 2.
         If E and t are the uncertainties in determining the energy and time then,
                           E. t  h / 2
         If J and  are the uncertainties in determining the angular momentum and angle then,
                           J.   h / 2

Experimental illustration of uncertainty principle:
i)       Determination of the position of a particle by microscope:
The resolving power of a microscope is given by,
                                    x   / 2Sin           --      (1)
where  - wavelength of light used
           - the semi vertical angle of the cone of light and
         x – the uncertainty in determining the position of the particle.
In order to observe the electron it is necessary that at least one photon must
strike the electron and scatter inside the microscope. When a photon of
initial momentum p = h /  , after scattering enters the field of view of
microscope, it may be any where within angle 2. Thus its x-component of
momentum i.e., px may lie between pSin and - pSin. As the momentum is
conserved in the collision, the uncertainty in the x- component of momentum is given by,
                 px = pSin - ( - pSin) = 2pSin = (2h/) Sin -- (2)
From eq(1) & (2), we have
                        x.  px  [ / 2Sin ] x [(2h/) Sin]  h
This shows that the product of uncertainties in position and momentum is of the order of Planck‟s constant.
ii)      Diffraction by a single slit:
Suppose a narrow beam of electrons passes through a single
narrow slit and produces a diffraction pattern on the screen as
shown in fig. The first minimum of the pattern is obtained by
putting n=1 in the equation describing the behavior of diffraction
pattern due to a single slit ( i.e., d Sin = n ). Hence
                 y Sin =               --       (1)
where, y is the width of the slit and  is the angle of deviation corresponding to first minimum.

PYS 1002     (2007-08)                           Page 3 of 12                                  Unit - 2
        In producing the diffraction pattern on the screen all the electrons have passed through the slit but
we cannot say definitely at what place of the slit. Hence the uncertainty in determining the position of the
electron is equal to the width y of the slit.
From eq(1),    y =  / Sin          -- (2)
The y-component of momentum may lie anywhere between pSin                     and -pSin , uncertainty in y
component of momentum is,
       py = 2p Sin = (2h /  ) Sin -- (3)
from eq‟s (2) & (3),      y. py = [ / Sin] x [(2h /  ) Sin]  2h  h
This relation shows that the product of uncertainties in position and momentum is of the order of Planck‟s
constant.

Applications of Uncertainty principle:
i)     Non-existence of electrons and existence of protons and neutrons in nucleus.
ii)    Binding energy of an electron in atom
iii)   Finite width of spectral lines and
iv)    Strength of nuclear force.
v)     Calculating the radius of the Bohr‟s first orbit.

i) Non-existence of electrons and existence of protons and neutrons in the nucleus:
The radius of the nucleus of any atom is of the order of 10-14 m. If an electron is confined inside the
nucleus, then uncertainty in the position x = 2 x 10-14 m. Using the Heisenberg‟s uncertainty relation, the
uncertainty in momentum of electrons is given by,
                           h      1.055 x1034                                             h
                 px                           kg ms-1             ( x = 2 x 10-14,        = 1.055 x 10-34 )
                        2 .x       2 x10 14
                                                                                          2
                                0.527 x 10-20 Ns.
It means that the momentum component px and hence the magnitude of total momentum p of the
electron in the nucleus must be at least of the order of magnitude,
    i.e., p  px  px  0.527 x 10-20 Ns.
    Since the mass of the electron is 9.1 x 10-31 Kg, the order of magnitude of momentum ( 0.527 x 10-20
kg ms-1)is relativistic. Using the relativistic formula for the energy E of the electron, we have, E2 = p2C2 +
m02C4
    As the rest energy m0c2 of the electron is of the order of 0.511 MeV, which is much smaller than the
value of first term, hence it can be neglected. Thus,
                                     E2 = p2C2           or       E  pC
                            E  (0.527 x 10   -20) x (3 x 108) Joule

                              (0.527 x 10-20 ) x (3 x 108 )
                                                                eV  10 MeV
                                        1.6 x 10-19

         This means that if the electrons exist inside the nucleus their energy must be of the order of 10
MeV. However, we know that the electrons emitted by radioactive nuclei during beta decay have energies
only 3 to 4 MeV. Hence, in general electrons cannot exist in the nucleus.
         For protons and neutrons, m0  1.67 x 10-27 kg. This is a non-relativistic problem as v = p/m0 = 3 x
10 6 m/s. The Kinetic energy E in this case is given by,

                         E = (p2 / 2m0) = (0.527 x 10-20)2 / (2 x 1.67x 10-27) joule
                          = 52 KeV.
Since this is smaller than the energies carried by these particles when emitted by the nuclei, both these
particles can exist inside the nuclei.


PYS 1002      (2007-08)                           Page 4 of 12                                   Unit - 2
ii)   Finite width of spectral lines: From Heisenberg‟s Principle of energy and time relation, we have
                 E. t  h / 2Π
        Since the life time of electron in an excited orbit is finite (  10-8 Sec), the energy difference is
given by E = h / 2Π , the excited levels must have a finite energy spread i.e., the radiation given out when
an electron jumps must be truly monochromatic. It means that the spectral lines never sharp but must have
a natural finite width.

Schrodinger’s time independent wave equation:
Newton‟s laws of motion can be applied only to macroscopic systems and events. But the Schrodinger
wave equation can be applied both to macroscopic and microscopic systems and events.
In general, displacement of a particle vibrating about its mean position is given by,
                             Y = a Sin 2 ( t – x /  )             --      (1)
         Where  - frequency of vibration and  - wavelength
Differentiating eq(1) twice with respect to „ x‟ we get,
                             d 2 y 4 2
                                   2 y0                            --      (2)
                             dx 2   
At each point along the wave in space, Y varies periodically with . According to Schrodinger, for atomic
particle like electron, one must take the whole solution of Y, since one cannot determine the momentum
and position of it simultaneously. He called this complex displacement as wave function „‟.
The total energy E of a particle is sum of its KE and PE.
                                     i.e., E = ½ mv2 + U             --      (3)
                 ½ mv2 = E – U =>             mv2 = 2( E – U)
                                     =>       m2v2= 2m(E – U)        --      (4)
The de-Broglie wavelength is given by,
                                  h            h
                             =      =                               --      (5)
                                  mv       2 m( E  U )

substitute eq(5) in eq(2),
                  d 2 y 4 2 2m ( E - U)
                                        y0
                  dx 2         h2
if Y is replaced by  then,
                  d 2 8 2 m ( E - U)
                                       0
                  dx 2       h2
                  d 2 2m ( E - U)
         or                        0                         --   (6)     where ħ = h/2
                  dx 2      2


eq(6) is Schrodinger‟s time independent wave equation in one - dimension.
In the dimensional notation it becomes,
                             2 + 2m (E – U)  / ħ2 = 0             where 2 = 2/x2 + 2/y2 + 2/z2
PYS 1002      (2007-08)                              Page 5 of 12                              Unit - 2
Special case - In case of free particle (i.e., a particle not acted by external force) U=0 and so total energy
is K.E. only.
         2 + 2mE / ħ2 = 0


Physical significance of wave function ‘  ’ :
i)      „‟ measures the variations of the matter wave. So it converts the particle and its associated wave
        statistically.
ii)     The wave function or complex displacement  is a complex quantity and we cannot measure it.
iii)    The matter wave can be represented by wave function. This wave function is used to identify the
        state of a particle in an atomic structure.
iv)     It tells us where the particle is likely to be not where it is.
v)      The probability of finding a particle in a particular volume element d is given by,
                   P( r) d =   d
                   Where  is called the complex conjugate of .
vi)     ∫∫∫2 d = 1             when the particle presence is certain in the space.  satisfying above
        requirement is said to be normalized.
vii)    Being a complex function, it does not have a direct physical meaning, but when we multiply this
        with its complex conjugate, the product 2 has physical meaning. [ We will speak normally the
        intensity of light at a point rather than the amplitude of light at a point since intensity (square of
        amplitude) is a measurable and real quantity ].
Application of Schrodinger wave equation ( Particle in a box):
Consider a particle moving inside a box along the x- direction. The particle is bouncing back and forth
between the walls of the box. The box is supposed to have walls of infinite height at x=0 and x=L. The
particle has a mass m and its position x at any instant is given by 0 < x < L.
The potential energy U of the particle is infinite on both sides of the box and is assumed to be zero
between x=0 and x=L.
Since the potential energy outside the box is infinitely high, the probability of finding the particle outside
must be zero.       2 = 0 in the region 0 > x > L
          = 0 at x = 0 and x=L
inside the box the wave function is finite
         2  0, in the region 0 < x < L ; U = 0
Within the box, the one - dimensional schrodinger wave
equation is,
         d 2 2m E                           d 2
               2  0             =>              k 2  0
         dx 2                                dx 2


where K2 = 2mE / ħ2                --        (1)
PYS 1002        (2007-08)                           Page 6 of 12                               Unit - 2
The general solution of above equation is,
           = A Sin Kx + B Cos Kx
To evaluate the constants A and B we must use the boundary conditions namely,
           = 0 at x=0 and hence B=0
           = 0 at x=L and hence 0=A Sin KL
Since A  0, because if A=0 the entire function will be zero as B=0
          Sin KL = 0                  or    KL = n           =>       K = n / L     --       (2)         where n is an
integer

                    2mE                n 2 2                 n 2 2 2   n2h2
from (1) & (2)               2
                                             =>       En             =              En - Energy of the particle
                                         L2                    2mL2      8mL2
To find the value of A. Obviously,            ∫Ln2 dx= 1
                                              0

Since the electron should exist within the box,
                    ∫LA2 Sin2 (nx / L)dx = 1
                    0


                                 Sin 2 n x
                             L
                    A2                     dx =1
                             0
                                     L

                         1       2 nx 
                             L
                    A2  1  Cos         dx =1
                       0
                         2         L  

                                               2 nx 
                                                       L
                        A2             L                         A2 L
                                  x  2 n Sin L  =1         =>      1
                        2                           0            2

                                   2
          =>        A=
                                   L

                                                                              2      n 
Therefore the normalized wave function of the particle, n =                    Sin      x.
                                                                              L      L 
Nuclear radiation detectros:
The phenomenon of spontaneous emission of radiations from radioactive substance is known as
radioactivity. The substances which emit these radiations are known as radioactive.
Ex: uranium, polonium, radium, radon and thorium etc.,
The instruments which are used for the detection of nuclear radiations are known as nuclear radiation
detectors.
Most of the radiation detectors are based on the principle that gases become electrical conductors due to
ionization produced by their exposure to radioactive or nuclear radiations. Electrometer, ionization
chamber, scintillation counter, semi conductor detectors and nuclear emulsions are the different types of
radioactive detectors.




PYS 1002         (2007-08)                                    Page 7 of 12                                Unit - 2
i)      Geiger – Muller Counter: It consists of a fine tungsten wire placed along the axis of a hallow
metal- cylinder electrode (cathode) enclosed in a thin
glass tube. The tube contains a mixture of 90% argon
and 10% ethyl alcohol. At one end of the tube, a
window covered with thin mice sheet is provided
through which the ionizing particles or radiations may
enter the tube. A d.c. Potential of about 1200 volt is
applied between the cathode and the wire, which acts
as an anode. A high resistance R is connected in
series with battery.
When a charged particle passes through the counter, it ionizes the gas molecules. The central wire attracts
the electrons while the cylindrical electrode attracts the +ve ions. This causes ionization current which
depends upon the applied voltage. At sufficiently high voltages, the electrons gain high KE and cause
further ionization of argon atoms. Thus a larger number of secondary electrons are produced. The number
of secondary electrons is independent of the number of primary ions produced by incoming particle.
     The incoming particle serves the purpose of triggering the release of an avalanche of secondary
electrons. The electrons quickly reach the anode and cause ionization current. The positive ions move
more slowly away from anode and they form a sheath around the anode for a short while. They reduce the
potential difference between the electrodes to a very low value because ion sheath depresses electric field
near anode. The current therefore stops. So a brief pulse of current flows through resistance R. This
current creates a P.D across R. The pulse is amplified, fed to counter circuit. As each incoming particle
produces a pulse, hence the incoming particles can be counted.
        Efficiency = [observed counts / Sec] / No.of ionizing particles entering the counter per second
Advantages:- The G.M. Counter is very useful for counting  - particles. It can also be used for measuring
 - ray intensities. The G.M. Counter can count about 500 particles per second.
Disadvantages:- i) it is insensitive for a period of 200 to 400s following each pulse, which prevents its use
at very high counting rates.
ii) It cannot provide information about the particle or photon causing a pulse.


ii) Scintillation Counter:
 It consists of Scintillation chamber, photomultiplier tube and electronic counter. The scintillation chamber
consists of an aluminium casing in which a suitable scintillation crystal or phosphor [Examples of phosphor:
– Anthracene, Sodium & Potassium Iodide] is placed. The aluminium case shields the crystal from all stray
light. The scintillation chamber is fitted at the end of photomultiplier tube. High-energy radiations are
allowed to incident on the crystal, which produces tiny flash of light (photons). The photons from
scintillation chamber enter the photo-multiplier tube and strike the photo- cathode. Now photoelectrons are

PYS 1002      (2007-08)                          Page 8 of 12                                 Unit - 2
emitted due to photoelectric emission. The electrons are accelerated towards first dynode D 1. When these
electrons hit D1, secondary electrons are
emitted. The process is repeated at each
dynode resulting in a large multiplication of the
electrons. Finally a highly amplified electric
pulse impinges on the anode acting as a
collector of electrons. These pulses are fed into
an electric system where they are counted. The
scintillation counter can count 1016 particles per second.
Advantages: i) It counts 1016 particles per second.
ii)        It is possible to determine the energies of individual incoming particles.


iii) Solid state detector:- It consists of a P-N junction formed between P-type and N-type silicon. If it is
connected in reverse biased condition, a depletion region is
formed within the device as shown in fig. The depletion region
has no carriers of either sign. When charged particles enter this
region, they interact with the electrons of the crystal. Due to this,
electron -hole pairs are produced. The charge carriers
(electrons & holes) are then quickly swept away by the electric
field and thus produce a voltage pulse across the resistor R.
The out put pulse is then amplified and is either measured or counted.
Advantages: - It has much better energy resolution than other radiation detectors.

Fermi – Dirac distribution function:
In a system of fermions, the presence of a particle in a certain state prevents any other particles from
occupying that state. The probability for a fermion is given by,              f(E) = 1/ [e eE / KT +1]
The +1 term in the denomination is a consequence of the uncertainty principle, f(E) can never exceed
unity, whatever the values of , E & T.
In the above equation, if the values of  takes – Ef / KT
           i.e.,       Ef = - KT                            ( Ef – fermi energy)
then                  f(E) = 1/ [e(E - Ef) / KT +1]
also                  f(E) = ½ when E = Ef = - KT & T  0
if we consider a system of fermions (say electrons) at T=0, then
           for E < Ef           ,          f(E) = 1/ [e -  +1] = 1
      and for E > Ef            ,          f(E) = 1/ [e  +1] = 0
Thus at T=0, all the energy states upto Ef are completely filled and no state above Ef is filled. The highest
state to be filled will have energy E = Ef.
PYS 1002           (2007-08)                               Page 9 of 12                                   Unit - 2
As temperature increases, an electron may get energy of the order of KT and go to higher vacant state,
and so Fermi function falls.

Fermi level concept in Semiconductors:
 Fermi - Dirac statistics is applicable to those electrons in a solid crystal, which obeys pauli‟s exclusion
principle.
According to Fermi, the probability f(E) that a state of energy E is filled is given by,
                            f(E) = 1/ [e(E - Ef) / KT +1]     where Ef is called the Fermi energy level.
Fermi Energy (Ef): Fermi energy is the highest energy of the electron in the valence band of a crystal in its
ground state. It is also defined as the energy for which the probability f(E).
                                   f(E) = ½
Fermi level is used as a reference level. For a semiconductor crystal when all the electrons are present in
the valence band the probability, f(E) = 1
In this state the conduction band is vacant and the probability of the conduction band will be f(E) = 0.
Therefore, fermi level having f(E) = ½ must be some where in between these two bands. In an intrinsic
semiconductor the position of the fermi level (Ef) is midway in the forbidden energy gap as shown in fig(a).
        When we add a donor impurity like phosphorous, arsenic etc., to an intrinsic (pure) semiconductor
the fermi level rises above the mean level and when we add an acceptor impurity like aluminium, boron
etc., the fermi level falls below the mean level in the forbidden gap.




        The fermi level is independent of temperature. At 0K all the energy bands below E f are completely
filled. At this temperature the conduction band is empty. At higher temperature some of the electrons from
the top of valence band may be thermally excited into conduction band.


Nuclear Magnetic Resonance (NMR) :-
Spectroscopy is the study of the interaction of electromagnetic radiation with matter. Nuclear magnetic
resonance spectroscopy is the use of the NMR phenomenon to study physical, chemical, and biological
properties of matter. As a consequence, NMR spectroscopy finds applications in several areas of science.
NMR spectroscopy is routinely used by chemists to study chemical structure using simple one-dimensional
techniques. Two-dimensional techniques are used to determine the structure of more complicated
molecules.




PYS 1002      (2007-08)                          Page 10 of 12                                   Unit - 2
Background:
Over the past fifty years nuclear magnetic resonance spectroscopy, commonly referred to as NMR, has
become the preeminent technique for determining the structure of organic compounds. Of all the
spectroscopic methods, it is the only one for which a complete analysis and interpretation of the entire
spectrum is normally expected. Although larger amounts of sample are needed than for mass
spectroscopy, NMR is non-destructive, and with modern instruments good data may be obtained from
samples weighing less than a milligram. To be successful in using NMR as an analytical tool, it is
necessary to understand the physical principles on which the methods are based.
The nuclei of many elemental isotopes have a characteristic spin (I). Some nuclei have integral spins (e.g.
I = 1, 2, 3 ....), some have fractional spins (e.g. I = 1/2, 3/2, 5/2 ....), and a few have no spin, I = 0 (e.g. 12C,
16O, 32S, ....). Isotopes of particular interest and use to organic chemists are 1H, 13C, 19F and 31P, all of

which have I = 1/2. Since the analysis of this spin state is fairly straight forward, discussion of NMR will be
limited to these and other I = 1/2 nuclei.
The following features lead to the NMR phenomenon:

1. A spinning charge generates a magnetic field, as shown in fig. The resulting spin-magnet has
a magnetic moment (μ) proportional to the spin.
2. In the presence of an external magnetic field (B0), two spin states
exist, +1/2 and -1/2. The magnetic moment of the lower energy +1/2
state is aligned with the external field, but that of the higher energy -
1/2 spin state is opposed to the external field. Note that the arrow
representing the external field points North.
3. The difference in energy between the two spin states is dependent on the external magnetic field
strength, and is always very small. The fig. illustrates that the
two spin states have the same energy when the external field is
zero, but diverge as the field increases. At a field equal to B x a
formula for the energy difference is given (remember I = 1/2 and
μ is the magnetic moment of the nucleus in the field).
Strong magnetic fields are necessary for NMR spectroscopy.
Modern NMR spectrometers use powerful magnets having fields of 1 to 20 T. Even with these high fields,
the energy difference between the two spin states is less than 0.1 cal/mole. To put this in perspective,
recall that infrared transitions involve 1 to 10 kcal/mole and electronic transitions are nearly 100 times
greater.
For NMR purposes, this small energy difference (ΔE) is usually given as a frequency in units of MHz (10 6
Hz), ranging from 20 to 900 MHz, depending on the magnetic field strength and the specific nucleus being
studied. Irradiation of a sample with radio frequency (rf) energy corresponding exactly to the spin state
separation of a specific set of nuclei will cause excitation of those nuclei in the +1/2 state to the higher -1/2
spin state. This electromagnetic radiation falls in the radio and television broadcast spectrum. NMR
spectroscopy is therefore the energetically mildest probe used to examine the structure of molecules.
The nucleus of a hydrogen atom (the proton) has a magnetic moment μ = 2.7927, and has been studied
more than any other nucleus.
4. For spin 1/2 nuclei the energy difference between the two spin states at a given magnetic field strength
will be proportional to their magnetic moments.

Technique of NMR:

This important and well-established application of nuclear magnetic resonance will serve to illustrate some
of the novel aspects of this method. To begin with, the NMR spectrometer must be tuned to a specific
nucleus, in this case the proton. The actual procedure for obtaining the spectrum varies, but the simplest is
referred to as the continuous wave (CW) method. A typical CW-spectrometer is shown in the following
PYS 1002      (2007-08)                            Page 11 of 12                                    Unit - 2
diagram. A solution of the sample in a uniform 5 mm glass tube is oriented between the poles of a powerful
magnet, and is spun to average any magnetic field variations, as well as tube imperfections. Radio
frequency radiation of appropriate energy is broadcast into the sample from an antenna coil (colored red).
A receiver coil surrounds the sample tube, and emission of absorbed rf energy is monitored by dedicated
electronic devices and a computer. An NMR spectrum is acquired by varying or sweeping the magnetic
field over a small range while observing the rf signal from the sample. An equally effective technique is to
vary the frequency of the rf radiation while holding the external field constant.




As an example, consider a sample of water in a 2.3487 T external magnetic field, irradiated by 100 MHz
radiation. If the magnetic field is smoothly increased to 2.3488 T, the hydrogen nuclei of the water
molecules will at some point absorb rf energy and a resonance signal will appear. An animation showing
this may be activated by clicking the Show Field Sweep button. The field sweep will be repeated three
times, and the resulting resonance trace is colored red.

Applications of NMR:

01) NMR is used to study the chemical structures and reactions.
02) Based on the intensity ratio of the resonance peaks, how atoms are located in a molecule can be
    known.
03) NMR imaging is very much safer compared with X- rays tomography.
04) Magnetic resonance imaging (MRI) is the most powerful tool in diagnosis of even very minute defects
    in the body.
05) Water content in biological materials can be estimated with NMR.
06) Using NMR absorption spectroscopy structures of non – metallic solids can be determined.
07) NMR is used in petroleum industry, to measure rock porosity, to estimate permeability from pore size
    distribution.
08) NMR is used in process control and process optimization in oil refineries and petrochemical plants.
09) NMR is used to study DNA, RNA and proteins.



Photo cells:
A Photoelectric cell is an arrangement, which converts light energy into electrical energy

Photo cells are basically classified into three categories, they are 1) photo emissive cells 2) photo
conductive cells and 3) photo voltaic cells.



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