EMT
1. If electric flux density D is given by
D = [(2y2 + z)i + 4xyj + xk] units. Find the volume charge density at (0,0,0)
and (-1,0,4).
(a) (i)
How much electric flux will come out through a surface S = 10j kept in an electric field, E = 2i+4j+7k?
[40 units]
(ii)
If 1C charge is placed at the center of a cube of side 10cm. Calculate the flux coming out of any face of
[1.883 x 1010 Nm2/C2]
the cube.
2. A thin spherical shell of metal has a radius of 0.25 m and carries a charge of 0.2 μC. Calculate the electric field
at a point
(i) 3.0 m from the centre of the shell,
[ E = 200 N/C ]
[ E = 2.888 x 104 N/C ]
(ii) Just out side the shell,
[Eo = 8.85 x 10-12 C2 / N-1 m2]
(iii) Inside of the shell.
3. 71. Find the skin depth‘d’ at a frequency of 1.6 MHz in aluminum where σ= 38.2 Ms/m and µ r=1.
(0.0643 mm)
4. An infinite charged sheet has a surface density σ of 1.0 x 107 C/m2. Find the separation between those
equipotential surfaces which have potential difference of 5.0 volts.
[ d = 8.85 x 10-4 m ]
5. Show that the vector
A = ( z2 + 2x + 3y )i + ( 3x + 2y + z )j + (y + 2zx )k
is irrotational.
6. What is the value of constant ‘a’ for which the vector,
A = ( x + 3y )i + ( y – 2z )j + (x + az )k
is solenoidal.
[ a = -2 ]
7. The surface density of charge on a conductor in dry air is 2.67 x 10-5 c/m2. What is the force per unit area due
[ force / area = σ/2ε0 = 4.02 x 109 Nm-2]
to this charge?
8. Find the conduction and displacement current densities in a material having conductivity of 10-3 S/m and r = 2.5
if the electric field in the material is
E = 5.0 x 10-6 sin (9.0 x 109 t) V/m. [ Jc = 5 x 10-9 sin 9x109t A/m2 , JD = 1 x
10-6 cos 9x109t A/m2 ]
9. An electron accelerated by a potential difference of 1000 V enters at right angles into a uniform magnetic field of
induction 1.9 x 10-3 Wb/m2. Compute the radius of the electron trajectory in the magnetic field.
[ 8.962 cm]
10. A beam of charged particles is focused by 180° magnetic focusing method. The beam rotates in a circle of
radius 30 cm. If the beam enters with a divergence of angle 2° about the normal direction, find the spread of the
focus point. [ Hint: spread = Rθ2 where θ = 2° = 2 x π/180 rad]
[0.000365 m]
11. An electron has a velocity of 104 m/s normal to a magnetic field of 0.1 Wb/m2 flux density. Find the radius of the
electron path and also its frequency.
[ 5.7 x 107 m , 2.8 x 109 Hz]
12. An e- beam passes through a magnetic field of 2 x 10 -3 Wb/m2 and an electric field of 3.4 x 104 V/m, both acting
simultaneously at the same point. If the path of e - remains undeviated, calculate the speed of e-. If the electric
field be removed, what will be the radius of electron path?
[1.7 x 107 m/s, 4.78 x 10-2 m ]
13. A stream of protons and deuterons in a vacuum chamber enters a uniform magnetic field. Both protons and
deuterons have been subjected to the same accelerating potential; hence the kinetic energies of the particles
are the same. If the magnetic field is perpendicular and the protons move in a circular path of radius 15 cm, find
the radius of the path traversed by the deuterons.
[ R2 = 0.212 m ]
14. A proton with velocity 5 x 105 m/s enters an electric field of -500j N/C at the origin making an angle of 42° with
x axis. Determine the time period required for proton to reach the maximum height in electric field.
[ 6.98 μs]
15. A proton is moving in a circular orbit of radius 20 cm in the magnetic field of 0.36 T. Determine the orbital
speed of proton.
[ 6.9 x 106 m/s]
16. In the velocity selector of Bainbridge mass spectrograph, the electric field is 250 V/cm and magnetic field is
0.18 T. A mixture of single charged ions of carbon isotopes C 12 and C13 is analyzed with this mass
spectrograph. The magnetic field in the main chamber is 0.22 T (B’). Calculate the separation on photographic
plate. (hint: separation = 2(R2-R1)= 2v(m2-m1)/eB’ )
[ 1.31 cm]
17. An electron accelerated by a potential difference of 1000 volts enters at right angles into a uniform magnetic
field of induction 1.19 x 10-3 Wb/m2. Find (i) the radius of the electron trajectory in the magnetic field (ii) the
angular momentum of the electron.
[ (i) R = 89.62 x 10-8 m (ii) 1.529 x 10-24 kgm2/sec]
18. 5000 electric lines of force enter a given volume and 3000 leave it. Find the total charge contained in it.
[ -17.72 x 10-9 C]
19. A uniformly charged sphere has a total charge of 300μC and the radius of 8 cm. Find the electric intensity (a)
at a point 16 cm (outside) from center of sphere, (b) at a point on the surface of the sphere, (c) at a point 4cm
from the center of the sphere i.e. at a point inside the sphere.
[ (a) 10.5 x 107 N/c (b) 42.13 x 107 N/C (c) zero ]
20. A charge 1μC is placed at the center of a hollow cube. Calculate the electric flux diverging (i) through the
center (ii) through each face.
[ (i) 1.12 x 105 volt-m (ii) 5.6 x 104 Volt –m ]
21. An electric field in a region is given by E = 3 i+ 4 j – 5 k. Calculate the electric flux through the surface S = 2.0
x 10-5 k m2.
22. Show that force F = yz i + xz j + xy k is conservative.
23. The electric field due to a point charge is expressed as E = q/r2 r. Show that the divergence of electric field
due to that point charge is zero.
24. State Gauss’s law and express it in integral and differential forms. Show using the Gauss’s law that any excess
charge placed on the isolated conductor at rest resides entirely on its surface.
25. Copper wire carries conduction current 1 amp at 60 Hz. Find i d assuming ε = ε0 , μ = μ0 and σ =
5.8 x 107
mho/s.
26. The electromagnetic wave intensity received on the surface of the earth from the sun is found to be 1.33
kW/m2. Find the amplitude of electric field vector associated with sunlight as received on the surface of the
earth. Assume sun’s light to be monochromatic (λ= 6000Å).
[ E0 = 1000.8292 V/m]
27. If the earth receives 2 Cal min-1 cm-2 solar energy, what are the amplitudes of electric and magnetic field of
radiation?
28.
[ E0 = 1024.3 V/m , H0 = 2.717 Amp/m]
The relative permittivity of distilled water is 81. Calculate refractive index and velocity of light in it.
[ v = 3.33 x 107 m/s , μ = 9.0]
29.
For silver σ = 3.0 MS/m. Calculate the frequency at which the penetration depth is 1 mm.
30.
A plane em wave traveling in the +ve z direction in an unbounded lossless dielectric medium with relative
[ 106 mHz]
permeability μr = 1 and relative permittivity εr = 3 has an electric field intensity E = 6 Volts/m. Find (i) speed of
the em waves in the given medium (ii) impedance of the medium iii) Peak Poynting vector.
[ 2.17 x 102 Ohms, 0.165 W/m2 ]
31.
Find the penetration depth, ∂ of an EM wave in copper at v = 60 Hz and v = 100 Hz. For copper σ = 5.8 x 107
mho/m, km =1, ke =1.
[ ∂ = 8.53 x 10-3 m, 6.608 x 10-6 m]
32. The light is generally characterized by electric vector, although it also possesses the magnetic vector, why?
33. When the amplitude of magnetic field in a plane wave is 2 A/m (a) determine the magnitude of the electric
field for the plane wave in free space. (b) Determine the magnitude of electron field when the wave propagates
in a medium which is characterized by σ=0 and μ=μ0 and ε=ε0.
[ (a) E = 240π V/m (b) E = 120π V/m]
34. Find out the current density and electric field intensity for aluminum conductor with conductivity σ= 3.82 x 10 7
Seimen /m and the mobility of electron μe = 0.0014 m2/ (Volt-sec) and drift velocity = 5.3 x 10-4 m/s.
[E = 0.3786 V/m, J = 1.446x 107 Amp/m2]
35. Calculate the skin depth for an e.m. wave of frequency 1 MHz traveling through copper. Given σ = 5.8 x 10 7
S/m and μ= 4 x 10-7.
[ 66 μm ]
36. Calculate the penetration depth for 2 MHz e.m. wave through copper. Given σ = 5.8 x 107 S/m and μ= 4 x 107.
[ 46.7 μm ]
37.
Find the skin depth at a frequency 1.6 MHz in aluminum where σ = 3.82 MS/m and μ = 1.
[ 7.21 x 10-8 m]
38. The conduction current density in a lossy dielectric is given as
Jc = 0.02 sin (109t) Amp/m2, find the displacement current
Density if σ = 103 mho/m, ke = 6.5 and ε0 = 8.854 x 10-12.
39.
[ jd = 1.151 cos(109t) μA/m2 ]
A plane 200 MHz wave is traveling in a medium for which σ = 0, μ r = 2, εr = 4. If average Poynting vector is 5
W/m2, Find Erms, Hrms, phase velocity and impedance of the medium.
[ Erms = 36.51 V/m, Hrms = 136.9 A/m ]
47. Find the capacitance of a parallel plate capacitor using Gauss’s law.
48. A uniformly charged sphere has a total charge of 300 µC and a radius of 8 cm. find electric intensity at
(a) A point 16 cm from the center of the sphere.
(b) At a point on the surface of the sphere.
(c) At a point 4 cm from the center of the sphere i.e. at a point inside the sphere.
((a)Eo=10.5×107N/C, (b)Es=42.13×107 N/C )
49. A 5.0 MeV proton is falling vertically downward in a uniform field of magnetic induction 1.5 Wb/m 2, pointing
(F=7.37×10-12m)
horizontally from south to north. Find the force exerted on it.
50. An electron is moving with a velocity (2i+3j)m/s in an electric field of intensity (3i+6j+2k) and a magnetic field of
(2j+3k) tesla. Find the magnitude and direction of the Lorentz force acting on the electron.
(F=2.15×10-18N, θ=cos-1(2/
))
54. An electron is accelerated by a potential difference of 1000 volts enters at right angles into a uniform magnetic
field of
induction 1.19×10-3 Wb/m2. Find (i) radius of the electron trajectory in magnetic field (ii) angular
momentum of the electron.
(15293.04×10-28 kg m2/ sec)
59. If the magnitude of H in plane e.m wave is 1 amp/m, calculate the magnitude of E for plane wave in free space.
Assume the values of constant used.
( E = 376.7 V/m)
60. An electromagnetic wave is traveling in z-direction in an unbounded lossless dielectric medium with relative
permeability µr=1 and relative permittivity єr =2. It has peak electric field strength E0= 5 V/m. Find (i) impedance
of the medium (ii) peak magnetic field intensity and (iii) the velocity of the wave. (Z = 266.8 ohms,
H0=1.87×10-2 A/m, v= 2.12×108 m/s)
61. In a plane electromagnetic wave, the electric field oscillates at a frequency of 3×1011 Hz and amplitude 50 V/m.
What is the wavelength of the wave? What is the amplitude of the oscillating magnetic field?(B0= 1.67×10-7 T)
62. If the average distance between the sun and earth is 1.5×10 11 m and power radiated by sun is 3.8×1026 watt,
show that the average solar energy incident on the earth is 2 cal/cm 2 min (approx.).
63. Calculate the magnitude of Poynting vector at the surface of the sun. Given that power radiated by sun =
3.8×10 26 watts and radius of sun =7×108 m.
64. Calculate the skin depth for an em wave of frequency 1 MHz traveling through copper. Given µ= 4Π×10-7 and σ
=
5.8×107 s/m.
(d= 0.0661 mm)
67. Deduce an expression for the velocity of propagation of a plane em wave in a medium of dielectric constant ϵ
and relative permeability µ.
68. Discuss the propagation of e.m waves through conductor. Derive an expression for phase velocity, wave
impedance and Poynting vector.
70. In a plane electromagnetic wave, the electric field oscillates with a frequency of 2×1010 Hz and the amplitude is
48 V/m. What is the wavelength of electromagnetic field and amplitude of the oscillating magnetic field?
( 1.5×10-2m, 10×108 T)
QUANTUM MECHANICS
1. Using the relation, m = m0 (1 – v2/c2) where m0 is rest mass of the particle moving with velocity v and c is the
velocity of light. Show that the de Broglie wavelength of particle is equal to its Compton wavelength when its
velocity is 0.707c.
2. How does the concept of Bohr orbits violate the principle of uncertainty?
3. An electron has a de Broglie wavelength equal to that of a photon. Show that the ratio of the kinetic energy
of electron to the energy of the photon is,
[ (m2c4 + h2ν2)1/2 – mc2 ] / ( hν )
4. Show that the phase velocity of the de Broglie waves of a particle of rest mass m0 and de Broglie
wavelength is given by
vp = c [ 1 + (m0cλ/h )2 ]1/2
5. Explain why the wave nature of matter is not apparent in our daily observation? Justify with an example.
6. Electrons are accelerated by 844 Volt and are reflected from a crystal. The reflection maximum occurs when
the glancing angle is 58°. Determine the crystal spacing.
7. A proton is accelerated through a potential difference of 1000V. What is its de Broglie wavelength?
8. What will be the kinetic energy of an electron if its de Broglie wavelength equals the wavelength of the
yellow line of sodium (5890Å). The rest mass of electron is m0=9.1 x 10-31 kg and h= 6.63x10-34 Js.
9. Compare the uncertainties in the velocities of an electron and a photon confined to a 1nm box. Their masses
are 9.1x10-31kg and 1.67x10-27kg respectively.
10. An excited atom has an average lifetime of 10-8 sec. That is, during this period it emits a photon and returns
to the ground state. What is the minimum uncertainty in the frequency of this photon?
11. Using the relation, m=m0 / (1-v2/c2)1/2 where m0 is rest mass of the particle moving with velocity v and c is
the velocity of light, Show that the de Broglie wavelength of particle is equal to its Compton wavelength
when its velocity is 0.707c.
12. Show that the phase velocity of the de Broglie waves of a particle of rest mass m0 and de Broglie waves of
a particle of rest mass m0 and de Broglie wavelength is given by,
Vp = c ( 1 + (m0cλ/h)2)1/2
13. An electron has a de Broglie wavelength equal to that of a photon. Show that the ratio of the kinetic energy
of electron to the energy of the photon (hv) is,
( v is frequency)
[ (m2c4 + h2ν2)1/2 – mc2 ] / hv
14. What is the de Broglie wavelength for a particle moving with speed 2 x 106 m/s if the particle is
a) an electron
b) a proton
c) a 0.2 kg ball ?
15. Show that a particle of rest mass m0 has a kinetic energy ‘K’ has de Broglie wavelength given by
λ = hc / [ k(k + 2m0c2) ]1/2 . Hence calculate the wavelength of an electron of kinetic energy 1 MeV.
16. Calculate the wavelength associated with a
i)
1 MeV K.E of electron
ii)
1 MeV K.E of proton
iii)
1 MeV photon.
17. The uncertainty in the location of a particle is equal to its de Broglie wavelength. Show that the uncertainty
in its velocity is equal to its velocity.
18. Why an electron cannot stay in the nucleus?
19. An electron is confined to move between two rigid walls separated by 10 -9m. Find the de Broglie wavelength
representing the 1st three allowed energy states of the electron and the corresponding energies.
20. Find the probabilities of finding a particle trapped in a box of length L in the region from 0.45L to 0.55L for
the ground state and the 1st excited state.
21. Derive the equation for the momentum and energy of the particle in a 1-D box with impenetrable walls, for
n=1 and n=2. Assume that the potential energy is zero.
22. The wave function ψ of a particle is given by,
Ψ
= A e-kx
for 0<x<∞
= zero
for -∞<x<0
Find A in terms of k and evaluate the probability of the particle lying in the region, 2/k < x < 3/k
23. For a free particle show that the Schrödinger wave equation leads to the de Broglie relation, λ = h/p.
24. Give de Broglie theory of matter waves. Derive an expression for the de Broglie wavelength of matter
waves.
25. A proton and an –particle have the same velocity. Compare the wavelengths, phase velocities and group
velocities of the de Broglie waves?
26. Electrons are accelerated by 844 Volt and are reflected from a crystal. The reflection maximum occurs when
the glancing angle is 58°. Determine the crystal spacing.
27. Show that electrons accelerated through a potential difference of V volt have a wave of wavelength 12.27 /
V1/2 Å associated with them.
28. In the Davisson - Germer experiment, a beam of 54 eV electrons was diffracted by the [111] planes of a
Nickel crystal, a sharp maximum occurred at an angle of incidence and scattering of 65°. Prove that the
interplanar spacing of the above mentioned planes of Nickel supports de Broglie hypothesis?
29. An electron has a speed of 600m/s. With an accuracy of 0.005%, calculate the uncertainty with which we
can locate the position of the electron?
30. Find the kinetic energy of a proton whose de Broglie wavelength is 1 Fermi, What is roughly the proton
diameter?
[ K.E = 617 MeV ]
31. Establish Bohr’s Quantization condition on the basis of de Broglie’s conception of matter waves.
32. Explain why the quantum effects are felt for microscopic particles and not for a ball of mass 10 gm in a box
of side 0.1 m.
33. Explain the difference between wave velocity and group velocity in wave motion.
34. Show that the phase velocity of de broglie waves is greater than the velocity of light. Show that this violates
the Einstein’s Special theory of relativity? Justify your answer.
35. Find the kinetic energy of a proton whose de Broglie wavelength is 1 Fermi. What is roughly the proton
diameter?
[ K.E = 617 MeV ]
36. What is potential barrier and tunnel effect? Explain the tunnel effect on the basis of wave mechanics. How
does it explain the emission of α–particles from a nucleus?
37. Calculate the wavelength associated with an electron subjected to a potential difference of 1.25kV.
(11 Å)
38. Find the energy of the neutron in the units of electron bolt whose de-Broglie wavelength is 1 Å. Given the
mass of neutron = 1.674 x 10-27 Joule-sec.
(E=0.08134 eV)
39. A spectral line has wavelength 4000 Å. Calculate frequency and the energy in eV of the photon associated
with it.
40. Find the energy of the neutron in eV whose de-Broglie wavelength is 1Å.
(E= 8.13 x 10-2 eV)
41.The photo-electric threshold wavelength for a certain metal is 6000 Å. Find the energy of the photoelectrons
emitted from the surface by light having frequency 6 x 1014 sec-1.
(Energy=0.413 eV)
42. What will be the de-Broglie wavelength of an electron having kinetic energy of 500 eV?
(λ=0.55 Å)
43. Derive formula for the de-Broglie wavelength of a particle in terms of Kinetic energy.
44. What voltage must be applied to an electron microscope to produce electrons of wavelength 0.5 Å? Given
e=1.6 x 10-19 Coulomb, m=9 x 10-31 kg. h=6.62 x 10-31 Joule-sec.
(602.4 volts)
45. What is the energy of gamma photon having wavelength of 1 Å (h=6.62 x 10 -34 J-c).
(1.24 x 104 eV)
46. An electron is confined to a box of length 10-8 m; calculate the minimum uncertainty in its velocity. Given m
= 9 x 10-31 kg and ħ = 1.05 x 10-34 j-s.
((Δv)min = 1.17 x 104 ms-1)
47. An electron of energy 200 eV is passed through a circular hole of radius 10 -6m. What is the uncertainty
introduced in the angle of emergence.
(Δθ =5.76 x 10-6 radians)
48. The average period that elapses between the excitation of an atom and the time it emits radiation in 10 8sec.
find the uncertainty in energy emitted and the uncertainty in the frequency of light emitted.
(Δv=1.59 x 107Hz)
49. Calculate the smallest possible uncertainty in the position of the electron moving with velocity 3 x 10 7ms-1.
((Δx)min=3.8 x 10-12)
50. Find the uncertainty in the momentum of a particle when its position is determined win 0.0001 m. Find also
the uncertainty in the velocity of an electron and α-particle respectively when they are located within 5 x 1010
m.
(Δv=31.4 ms-1)
51. An electron of energy 200 eV is passed through a circular hole of radius 10-4 cm. What is the uncertainty
introduced in the angle of emergence?
(Δθ=1 sec of arc)
52. An electron has a speed 1.05 x 104 ms-1 within the accuracy of 0.01%. Calculate the uncertainty in the
position of the electron. Given ħ=1.05 x10-34 J.s, m=9 x 10-31 kg.
(Δx=1.1 x 10-4 m)
53. The average time that an atom retains excess excitation energy before re-emitting it in the form of electromagnetic radiations in 10-8 sec. Calculate the limit of accuracy with which the excitation energy of the
emitted radiation can be determined.
(ΔE=6.56 x 10-8 eV)
54. The speed of a bullet of mass 50 g is measured to be 300 ms-1 with an uncertainty of 0.01%. With what
accuracy can we locate the position of the bullet if it is measured simultaneously with its speed?
(Δx ≥ 7 x 10-32 m)
55. Find the value of momentum and energy for an electron in a box of length 1 Å for n=1.2.
(E2=241.6 x 10-10 J)
56. A particle is in motion along a line between x = 0 and x = a with zero P.E. and at point for which
x<0
and x > a, the P.E. is infinite. The wave function for the particle in the nth state is given
Ψn = A sin(nπ/a). Find the expression for the normalized waved function.
( Ψn(x) =
sin
)
57. Show that the wave function for two different states is orthonormal for a particle in one dimensional box.
58. Write an expression for the energy eigen values of a particle of mass ‘m’ confined in one-dimensional box
of length ‘L’. State whether the permitted energy levels are quantized or continuous.
59. Solve Schrödinger wave equation for a particle in a one dimensional box and show that the eigenvalues are
discrete. Obtain the expression for normalized wave function and plot them for first four energy levels.
60. A particle moving in a one – dimensional potential is given by V = 0 for x < 0 and V = V0 for x ≥ 0. Write
down the Schrödinger equation for the particle and solve it. Find the reflection and transmission coefficient
for E > V0 and E < V0, where E is the total energy of the particle.
61. The potential function for moving along the positive x-direction is given by V(x) = 0 for x < 0 and V(x) = V 0
for x > 0. Calculate the transmittance and reflectance at the potential discontinuity and show that R + T = 1.
STATISTICAL MECHANICS
1) Compare the salient features of the three statistical distribution functions: Maxwell-Boltzman (MB), Bose Einstein
(BE), Fermi Dirac (FD) distributions. Give one example of particles in each of these categories. Give graphical
comparison of distribution laws with temperature.
2) Calculate the Fermi energy of copper assuming that each atom contributes one free electron (Free electron Model).
Given MCu: 63.54 kg/k-mol, ρCu: 8.93 x 103 kg/m3.
Hint: Fermi Energy εF is given by εF = h2/2m (3n/8π)2/3 where n is number of Free electrons per unit volume. It is
equal to n = N avogardo ρCu / MCu.
3) If the Fermi energy of a metal is 10 eV, calculate
i)
The average energy of free electrons in the metal at 0K.
hint: ε= 3/5 εF
ii)
Corresponding Classical Temperature and
hint: ε= 3/5 kT
iii)
Speed of the electrons for the average energy calculated.
hint: ε= ½ mv2
4) Using Fermi Dirac Statistics, Show that at absolute zero temperature: all states are filled ( for ε < εF ) and empty (
for ε > εF ).
5) Differentiate between Bose Einstein (BE) and Fermi Dirac (FD) statistics. Assuming two particles and two available
states, write the wave functions for each case. Hence show that Pauli’s exclusion principle follows directly from the
FD wave function.
SUPERCONDUCTIVITY
1) Calculate the critical current which can flow through a long thin wire of aluminum of diameter 10-3 m. The critical
magnetic field for aluminum is 7.9 x 103 Amp/m.
2) Calculate the critical current density for 1 mm diameter wire of lead at 4.2k. A parabolic dependence of H c upon T
may be assumed. Given: Tc for Pb is 7.18K and H0 for Lead is 6.5 x 104 Amp/m.
3) The Transition Temperature for Pb is 7.2 k. However, at 5k it losses the superconducting property if subjected to a
magnetic field of 3.3 x 104 A/m. Find the maximum value of H which will allow the metal to retain its
superconductivity at 0k.
4) The critical field for niobium is 1 x 105 A/m at 8k and 2 x 105 A/m at 0k. Calculate the transition temperature of the
element.
5) The Transition Temperature for Pb is 7.2 k. The maximum critical field for the material is 8 x 105 A/m. Lead has to
be used as a superconductor subjected to a magnetic field 4 x 104 A/m. What precaution will have to be taken?
6) Calculate the value of the London penetration depth λ0 at 0°k for lead whose density is 11.3 x 103 kg/m3 and the
atomic weight is 207.19. Its Tc is 7.22 °k. Calculate the increase in λ at 3.61°k from its value at 0°k.
7) Estimate the London penetration depth from the data:
Critical Temperature
Tc = 3.7k
Density
ρ = 7.3 x 103 kg/m3
Atomic Weight
W = 118.7
Effective Mass
m* = 1.9 m
SEMICONDUCTORS
1) Explain the construction and working of tunnel diode. Illustrate your answer with appropriate energy level
diagrams and a voltage vs current plot. Name one application of tunnel diode.
2) For a Ge diode, the reverse saturation current at room temperature (T=300k) is found to be 100nA. What should
be diode current when the applied voltage is
a) 0.2 V
b) 1.0 V
c) -5 V
d) 0.8 V
e) -0.2 V. hint : I = I0[ exp( ηqV/kT ) – 1 ]
3) The diode current is 0.6 mA when the applied voltage is 400 mV and 20 mA when the applied voltage is 500
mV. Determine η. Assume VT = 25mV.
4) A semi conductor is known to have an electron concentration of 8 x 10 13 per cm3 (nc) and a hole concentration
of 5 x 1013 per cm3 (nh).
a) Is the semiconductor n type or p type?
b) What is the resistivity of the sample if the electron mobility is 23000 cm2/Vs (μe) and hole mobility is 23000
cm2/Vs (μh)?
hint : resistivity ρ= 1/σ = neμee + nhμhp
5) A sample of silicon at a given temperature T in intrinsic condition has resistivity of 25 x 104 cm. The sample is
now doped to the extent of 4 x 1010 donor atoms/cm3 and 1010 acceptor atoms/cm3. Find the total conduction
current density if an electric field of 4 V/cm is applied across the sample. Given that μe is 1250 cm2/Vs and μh is
475 cm2/Vs at the given temperature. Assume VT = 25mV.
Hint: Donor Density ND (=n) and hole concentration pN is ni2/ND.
6) State Law of mass action and Einstein relation for semiconductor.
7) A Zener diode shunt regulator has to supply a load current that changes from 0-200 mA at 10V. The input
voltage to the regulator circuit varies from 15V – 20V. Zener diode stabilizes at a minimum current of 10 mA.
Find out the series resistance.
8) A 5 Volt Zener diode is used which provides regulation for 5mA ≤ Iz ≤ 1 Amp. Determine the range of load
current for which regulation is achieved if the unregulated Vs varies between 8V and 10V. Given Rs = 5Ω.
9) What is the basic physical property responsible for the presence of energy bands rather than specific energy
levels in a solid?
10) How are the band structures of insulators and semiconductors similar? How are they different?
11) (a) Why are some solids transparent to visible light and others opaque? (b) The forbidden band is 1.1 eV in
silicon and 6 eV in diamond. To what wavelengths of light are these substances transparent?
12) Explain the working of
(a) Half wave and (b) Full wave rectifier. Also derive an experiment for efficiency of
Half wave and Full wave rectifier.
13) What is ripple factor? Derive its value for Half wave rectifier.
14) What is Zener diode? Draw the equivalent circuit of an ideal Zener in Break down region. What are its ON and
OFF states.
15) What is p-n junction? Explain the formation of Potential Barrier in a p-n junction.
16) Discuss the behavior of p-n junction for forward and reverse biasing. Draw and explain V-I characteristics of pn junction diode.
17) Prove that for intrinsic semiconductor Fermi level lies half way between the conduction and valence band, i.e.
EF = Eg/2 = ( Ec + Ev )/2.