Physics Question Bank
Physics Question Bank
Physics Question Bank
49. A cantilever of rectangular cross section has a length of 50 cm, breadth 3 cm and thickness
0.6 cm. If a weight of 1 kg is attached at the free end the depression produced is 4.2 cm.
Calculate the young’s modulus of the material of the bar.
3
4 1 9.8 (50 10 2 ) 3
Ans: Y 4Mgl 2 2 3 2
4.9
1.8 1010 N/m
2
3
bd y 3 10 (0.6 10 ) 4.2 10 2.7216 X 10 10
50. Uniform rectangular bar 1 m long, 2 cm broad and 0.5 cm thick is supported on its flat
face symmetrically on two knife edges 70 cm apart. If loads of 200 g are hung from the two
ends, find the elevation of the center of the bar. Given Young’s modulus of the material of
the bar is 18 ×1010 Pa.
3Mgal 2 3 200 10 3 9.8 (15 10 2 ) (70 10 2 ) 2 0.43218
Ans: y 2 2 3
= 4.802 x10-4 m.
2 (2 10 ) (0.5 10 ) (18 10 )
3 10
2bd Y 900
51. A cantilever of steel fixed horizontally is subjected to a load of 225 gm at its free end.
The geometric moment of inertia of the cantilever is 4.5x10-11 m4. If the length of cantilever
and Young’s modulus of steel are 1 m and 200 × 109 Pa respectively. Calculate the depression
at the loaded end.
Mgl 3 225 10 3 9.8 (1) 3 2.205
Ans: y 11
0.0816 m
3IY 3 (4.5 10 ) (200 10 ) 9
27
52. What couple must be applied to a 1m long wire with 1mm diameter, in order to twist one
end of it through 90̊, the other end remaining fixed? Given n = 2.8 × 1010 Nm-2.
Ans: The couple required to twist the wire through 90̊
πnr4 πnr4 π
C= ϕ=
2l 2l 2
π2 nr4 π2 × 2.8 × 1010 × (0.5×10−3 )4 0.01725
C = 4l = = 4 ; C = 4.3179 × 10-3 Nm.
4×1
53. A Uniform metal disc of diameter 0.1 m and mass 1.2 kg is fixed symmetrically to the lower
end of a torsion wire of length 1m diameter 1.44 mm, the upper end is fixed. The time period
of torsional oscillations is 1.98 s. Calculate the modulus of rigidity of a wire.
𝐼 πnr4
Ans: 𝑡 = 2𝜋 √𝐶 here I = MR2/2, C = 2l
𝑀𝑅 2 𝑙 𝑀𝑅 2 𝑙
𝑡 = 2𝜋 √ 𝜋𝑛𝑟 4 𝑡 2 = 4𝜋 2 ( 𝜋𝑛𝑟 4 )
𝑀𝑅 2 𝑙 4×3.14×1.2 ×(0.05)2 ×1
n = 4𝜋 ( 𝑡 2 𝑟 4 )= ; n = 3.578 × 1010 Nm-2.
(1.98)2 ×(0.72 ×10−3 )4
54. An elastic wire is cut into half its original length. How will it affect the maximum load the
wire can support? (Nov ‘15)
𝑙𝑜𝑎𝑑 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
Ans: (i)𝐸 = (𝑎𝑟𝑒𝑎) × (𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑙𝑒𝑛𝑔𝑡ℎ)
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑙𝑜𝑎𝑑
(ii)𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎
When original length is halved, strain is changed so that the maximum load that the wire can
support will remain the same as elastic modulus is constant.
PART B
1. Derive an expression for the elevation at the center of a beam which is loaded at both ends. Describe
an experiment to determine Young’s modulus of a beam by uniform bending. (Dec ‘16, May ‘17)
2. Give the theory of the loaded cantilever. Using the above theory, describe the experimental method
to find the Young’s modulus of the material.
3. Derive an expression for the depression of a cantilever fixed at one end horizontally and loaded at
the free end.
4. Explain stress-strain diagram. Discuss the factors affecting the elasticity of a material.
5. Write an essay about the elastic behavior of materials.
6. What are the different types of elastic moduli? Derive the necessary mathematical relation.
7. Derive an expression for the internal bending moment of a beam in terms of radius of curvature.
(Nov ‘08, Dec ‘16)
8 (i) What is cantilever?
(ii) Derive an expression to find the depression in a cantilever fixed at one end and loaded at the
other end.
(iii) Describe an experimental method used to find the Young’s modulus of a cantilever.
9. (i). What is uniform bending?
(ii) Derive an expression for elevation for a rectangular beam loaded in such a way that the bending
is uniform.
(iii) Describe an experimental method used to find the Young’s modulus of a rectangular bar
loaded in uniform bending.
10. A cantilever of length 50 cm fixed at one end is depressed by 20 mm at the loaded end. Calculate
the depression at a distance of 40 cm from the fixed end. (Nov ‘07)
11. Derive the expression for the couple per unit twist on a thin cylinder and show that a hollow
cylinder is better than the solid cylinder of the same material, same mass and same length for
manufacturing shafts.
12. Derive the expression for the moment of inertia of a disc and rigidity modulus of a cylindrical
wire using torsional pendulum. (Jan ‘18)
13. Derive an expression for the period of oscillation of a torsional pendulum. How can it be used to
determine the torsional rigidity of the wire? (May ‘93, ‘95, Nov’ 95, Dec ‘97)
14. Give the theory of torsional pendulum and describe a method to fine the moment of inertia of an
irregular body. (Dec ‘93, ‘94, ‘97)
15. (i) Derive an expression for depression at the free end of cantilever due to load.
(ii) Give an account of I – shape girders. (Jan ‘14)
16. Derive an expression for the deflection produced at the free end of a rectangular cantilever
subjected to point load at free end. What will be the deflection produced at the free end, with same
load, if the is of circular cross section. (Jan ‘18)
12. A particle executes a S.H.M of period 10 seconds and amplitude of 1.5 m. Calculate its
maximum acceleration and velocity.
2𝜋 2𝜋 2 𝑋 3.14
Ans: 𝑇𝑖𝑚𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 𝑇 = 𝜔 or 𝜔 = 𝑇 = 10 = 0.628 𝑟𝑎𝑑/𝑠
32. In InP Laser diode, the wavelength of light emission is 1.55 µm. What is its band gap in eV?
(May ’03)
ℎ𝑐 6.625 × 10−34 × 3 × 108
Ans:𝐸𝑔 = 𝜆 = = 0.8014 𝑒𝑉
1.55 × 10−6
33. Calculate the number of photons from green light of mercury λ = 4961 Å requires doing one
joule of work (May ’03)
ℎ𝑐 6.625 ×10−34 × 3 𝑥 108
Ans:𝐸𝑔 = = = 4.006 × 10−19 𝐽
𝜆 4961 × 10−10
1𝐽
𝑁= = 2.4961 × 1018 / m3
4.006×10−19 𝐽
34. Calculate the relative population of sodium atoms in sodium lamp in the first excited state
and the ground state at a temperature of 250 ˚C. (λ = 590 nm)
Ans:
Let N2 and N1 be the population of the first excited state and the ground state.
𝑁2 𝑒 −𝐸2 /𝑘𝑇
W. K.T, = = 𝑒 − (𝐸2 − 𝐸1 )/𝑘𝑇 = 𝑒 −ℎ𝛾/𝑘𝑇 = 𝑒 −ℎ𝑐/λ𝑘𝑇
𝑁1 𝑒 −𝐸1 /𝑘𝑇
6.625 ×10−34 ×3×108
𝑁2 −( )
=𝑒 5.9 𝑋10−7 ×1.38×10−23 ×523
𝑁1
= 𝑒 −46.673875 = 5.36776 × 10−21;
𝑁2
= 5.367 × 10−21
𝑁1
35. Calculate how many photons are emitted in each minute in a helium neon laser which emits
light at a wavelength of 6328 Å. The output power of the source 3 mW.
Ans:
𝑐
Frequency 𝛾 = 𝜆 = 4.74 × 1014 𝐻𝑧
E = hυ = 3.14 ×10 -19 J
Energy emitted by the laser = 3mW= 3 × 10 -3 × 60 J / minute
3 x 10 −3 × 60
No of photons emitted = 𝑁 = 3.14 ×10 – 19 = 5.732 × 10 17 photons / min
36. Define acceptance angle.
Ans: The maximum angle with which a ray of light can enter through one end of the fiber and still
be totally internally reflected is called acceptance angle of the fiber.
37. Define numerical aperture of a fiber. (June ‘14)
Ans: It is the light gathering efficiency of the fiber. It is a measure of the amount of light rays that
can be accepted by the fiber. It is equal to the sine of acceptance angle.
38. What are the conditions to be satisfied for the total internal reflection?
Ans:
Light should travel from denser medium to rarer medium.
The angle of incidence on core should be greater than the critical angle
39. What are the types of optical fibers based on number of modes?
Ans: Single mode fiber – one mode and Multi-mode fiber – many modes
40. What are the types of fibers based on refractive index profile?
Ans: Step-index fiber & Graded-index fiber
41. Differentiate single mode and multimode fibers.
Single mode fiber Multimode fiber
In single mode fiber only one mode can be Allows large number of modes of light to
propagated. propagate through it.
Smaller core diameter and difference between Core diameter is large, difference between the
refractive index of core and cladding is small. refractive index of core and cladding is also large.
No dispersion of signal. Dispersion of signal takes place.
62. A step index optical fiber has a core refractive index of 1.5 and cladding refractive index of
1.48. Calculate the critical angle at the core-cladding interface. (Dec ‘16)
Ans:
𝑛 1.48
Critical angle θc = sin−1 (𝑛2 ) = sin−1 ( 1.5 )
1
Critical angle = sin−1 (0.9866) = 80̊ 37’
63. How will you classify optical fibers based on material?
Ans: The optical fiber can be classified as glass and plastic fiber based on the type of material used
for manufacturing. Glass fiber is mostly a combination of silica with mixed metal oxides and plastic
fibers are made with polymers.
Part – B
1. What are damped vibrations? Establish a differential equation of motion for a damped harmonic
oscillator and obtain an expression for displacement. Discuss the conditions for over damped,
critical damped and under damped oscillations.
2. Derive and discuss the theory of forced oscillations. How does sharpness of resonance depend on
damping?
3. (i) For atomic transitions, derive Einstein relation and hence deduce the expressions for the ratio
of spontaneous emission rate to the stimulated emission rate. (June ‘12, Dec ‘16)
(ii)What is pumping action? Explain the methods commonly used for pumping action. (Jun‘09)
4. (i)Describe the principle, construction, working and energy level diagram of semiconductor laser.
(ii) What are the advantages of heterojunction laser over homojunction semiconductor laser?
5. Compare a homojuction semiconductor laser with a hetero junction semiconductor laser and detail
their features. (Jan‘18)
6. (i) What are the applications of semiconductor laser?
(ii) Describe the construction and working of a hetero-junction Ga-As laser. (Jan ‘09)
7. (i) Explain the propagation of light through an optical fibre.
(ii) What are numerical aperture and acceptance angle of a fiber?
(iii) Explain two applications of an optical fiber. (Dec ‘15, Jan ‘16, Dec ‘16)
8. Derive an expression for acceptance angle and numerical aperture of an optical fiber. Bring out the
differences between step index and graded index fiber. (Nov‘01, June ‘12, Jan ‘18)
9. Classify the optical fibres on the basis of materials, modes of propagation and refractive index
difference.
10. Describe the losses that occur in fibers and give the remedies for it. (June ‘09)
11. (i) What is dispersion in fiber optics? Explain different types of dispersion.
(ii) What are the different types of fibre optic sensors? Explain the working of any one sensor.
36. What is the basic principle behind Lee’s disc method in determining thermal conductivity
of bad conductor?
Ans: The given bad conductor is taken in the form of disc and is placed in between the Lee’s disc
and steam chamber. The steam is passed through bad conductor. Heat conducted through the bad
conductor per second is calculated. Amount of heat lost per second by the disc is also calculated.
At steady state,
Heat conducted through the bad conductor per second = Amount of heat lost per sec by the disc.
From this, thermal conductivity of the bad conductor is calculated.
37. How much heat will be conducted through a slab of area 90×10-4 m2 and thickness
1.2 × 10-3m in one sec? When it’s opposite faces are maintained at temperature difference
of 20 K. The coefficient of thermal conductivity of that material is 0.04 Wm-1 K-1.
KA1 2 t
Ans: Amount of heat conducted Q
x
0.04 90 10 4 20 1
= 6 Joules
1.2 10 3
38. A rod 0.25 m long and 0.892 x 10-4 m2 area of cross section is heated at one end through
393 K while the other end is kept at 323 K. The quantity of heat which will flow in 15 mins
along the rod is 8.811 × 103 joules. Calculate thermal conductivity of the rod.
Qx
Ans: K
A1 2 t
8.811 10 3 0.25
K = 391.97 W/m/K
0.892 10 4 70 900
39. A 20 cm length iron rod is heated at one end to 100 ˚C, while the other end is kept at a
temperature of 30 ˚C. The area of cross section of the iron rod is 0.685 cm2. Assume that the
iron rod is thermally insulated. Calculate the amount of heat conducted through the rod in
10 minutes along the way. Given the thermal conductivity of the iron K = 62 Wm-1K-1.
KA1 2 t 62 0.685 10 4 373 303 600
Ans: Q = 891.87 J
x 0.2
The iron rod conducts 891.87 J of energy in 10 minutes.
40. What is a heat exchanger?
Ans: A heat exchanger is a device used to transfer heat between a solid object and a fluid, or
between two or more fluids
41. Write some uses of heat exchangers.
Ans: They are used in reducing space heating, refrigeration, air conditioning, power
stations, chemical plants, petrochemical plants, petroleum refineries, natural-gas processing
and sewage treatment.
42. Mention the methods to determine thermal conductivity of good and bad conductors.
Ans: Searle’s method – for good conductors like metallic rod
Forbe’s method – for determining the absolute conductivity of metals
Lee’s disc method – for poor conductors
Radial flow method – for bad conductors.
43. If a fridge is left open in a closed room, will the room become cooler?
Ans: If a fridge is left open in a closed room, the chillness coming out from the front door of the
fridge is cancelled by the heated air coming out from behind the fridge. In addition to this effect,
in any electrical appliances, a small amount of electricity is wasted as heat energy .Thus heat will
raise the temperature of the room.
44. Define coefficient of performance.
Ans: Coefficient of performance is the ratio of the heat extracted and the work done.
45. Why do glass tumblers break when filled with hot water?
Ans: Glass is a bad conductor of heat. The inner layer of glass gets heated immediately as it comes
in contact with the hot water. But the outer layer remains at a lower temperature; as a result, the
inner surface tends to expand more than the outer layer and leads to cracking.
46. Define solar power.
Ans: Solar power is the process of converting (or) utilizing the abundantly available solar energy
either directly as heat (or) indirectly by converting it into electrical power using photo-voltaic
cells.
47. Mention few applications of solar power.
Ans: Solar power can be used to generate electricity to homes, business and industrial structures.
Solar power can also be used to fuel a number of other electronic devices, including water heaters,
furnaces, ovens, watches and phone chargers.
48. How the solar energy is beneficial than the other types of energy?
Ans: Solar power is virtually inexhaustible. The use of solar power generates no greenhouse gas
emissions, air or water pollution and it doesn't require the use of non-renewable natural resources.
49. Name the types of solar power.
Ans: (i) Active solar power (ii) Passive solar power
50. Define refrigerator
Ans: It is a machine which consists of a thermally insulated compartment and a heat pump that
transfers the heat from the inside of the fridge to its external environment so that the inside of the
fridge is cooled to a temperature below the ambient temperature of the room.
51. Define oven.
Ans: It is a thermally insulated chamber used for heating, baking or drying of a substance and
most commonly used for cooking. Kilns and furnaces are special purpose ovens used in pottery
and metal working respectively.
PART B
1. Explain the working of heat exchangers. (Jan ‘18)
2. a) Define refrigerator b) Describe the principle and working of a refrigerator.
3. Explain the different modes of heat transfer in detail.
4. a) Define coefficient of thermal conductivity.
b) Describe with necessary theory the Forbe’s method of determining the thermal conductivity of
a rod of uniform cross – section. (Apr’ 97, ’98, Dec ‘97,’99)
5. Explain the concept of thermal effects in buildings.
6. Describe with relevant theory, the method of determining the coefficient of thermal conductivity
of a bad conductor by Lee’s disc method. (Jan’ 18, ‘14, Dec ‘15)
7. A solid of square of side 50 cm and thickness 10 cm is in contact with steam at 100 oC on one side.
A block of ice at 0 ˚C rests on the other side of the solid. 5 kg of ice is melted in 1 hour. Calculate
the thermal conductivity of the solid.
8. By means of an electric heater of 12 kW, the temperature in a room with 6 m2 windows is to be
maintained so that the inner surface of the glass is 10 ˚C above the outer surface. Ignoring the heat
losses through the walls of the room and assuming that the heat is lost through the window glass
of thickness 6 mm what is the coefficient of thermal conductivity of the glass?
9. A composite metal bar of uniform cross section is made up of 0.25 m of metal A and 0.1 m of metal
B and each being in perfect thermal contact with the adjoining part. There is no heat loss at these
sides. The thermal conductivities of metals A and B are 920 and 140 S.I. units respectively.
The end A is maintained at 100 °C and the end B is maintained at 24 °C. Calculate the temperature
at A – B junction.
10.Deduce the mathematical expression for thermal conduction in a compound medium.
11.A wall consists of layer of wood and a layer of cork insulation of same thickness. The temperature
inside is 20 ˚C and the temperature outside is 0 ˚C. Calculate the temperature at the interface
between wood and cork, if the cork is inside and the wood is outside also find the temperature at
the interface if the wood is inside and the cork is outside. (Thermal conductivity of wood and cork
are 0.13 W/m/K and 0.046 W/m/K respectively).
12. a) Describe the principle, construction and working of solar water heater.
b) Mention its merits and demerits.
13. Derive the equation for one dimensional flow of heat and solve it under steady state condition.
(Nov ‘01, Dec’ 97, ‘98)
17. Write an expression for the wavelength of matter waves. (or) What is de-Broglie’s wave
equation? What are the other forms of de-Broglie wavelength?
Ans:
h h
mv p
Where h – Planck’s constant, m – mass of the particle, v – velocity of the particle, p – Momentum
of the particle.
h
De-Broglie wavelength in terms of energy =
2mE
h
De-Broglie wavelength in terms of voltage =
2meV
h
De-Broglie wavelength in terms of temperature =
3mK BT
18. What do you understand by the term wave function?
Ans: Wave function ψ is a variable quantity that is associated with a moving particle at any
position (x, y, z) and at any time‘t’. It relates the probability of finding the particle at that point
and at that time.
19. What is the physical significance of a wave function?
Ans:
1. The probability of finding a particle in space at any given instant of time is characterized by
a function ψ (x, y, z) called wave function.
2. It relates particle and wave statistically.
3. It is a complex quantity and it does not have any meaning.
20. Write any two applications of Schroedinger’s wave equation.
Ans:
1. It is used to find the electrons in the metal.
2. It is used to find the energy levels of an electron in an infinite deep potential well.
21. Write down the one dimensional Schroedinger’s time independent equation and write the
same for a free particle.
𝑑2 𝜓 2𝑚
Ans: 𝑑𝑥 2 + ħ2 [𝐸 − 𝑉]𝜓 = 0
For a free particle, V = 0.
𝑑2 𝜓 2𝑚𝐸
So, 𝑑𝑥 2 + ħ2 𝜓 = 0.
22. Define Eigen value and Eigen function.
Ans: Eigen value is defined as energy of the particle and is denoted by the letter (En). Eigen
function is defined as the wave function of the particle and is denoted by the letter (ψn)
𝑛2 ℎ2 2 𝑛𝜋𝑥
𝐸𝑛 = 2
; 𝜓𝑛 = √ sin
8𝑚𝑎 𝑎 𝑎
23. Define normalization process.
Ans: The probability of finding a particle inside any potential well is known as normalization
process in quantum theory.
24. What are the merits of quantum theory?
Ans: i. Specific heat of solids at low temperature can be explained.
ii. Theory of atomic structure and spectrum of hydrogen can be explained.
iii. Photoelectric effect, Compton Effect and black body radiation can be explained by this
theory.
100
N = Power / Energy = 2.965 × 10 20 per second
3.3726 10 19
33. Calculate the de-Broglie wavelength of an electron accelerated to a potential of 2 kV.
h 6.625 1034 6.625 1034
Ans: = 0.2742 Å
23
2meV 2 9.11 1031 1.6 1019 2 103 2.414 10
34. X-rays of wavelength 0.124 Å are scattered by a carbon block. Find the wavelength of
scattered beam for a scattering angle of 180 o.
Ans: '
h
1 cos
m0 c
6.625 10 34 6.625 10 34
' 0.124 10 10 1 cos 180 0.124
10 10
(2)
9.11 10 31 3 108 2.733 10 22
' = (0.124 × 10−10 ) + 4.848 × 10−12 = 0.1725 Å
35. In a Compton scattering experiment, the incident photons have a wavelength of 3× 10 -10 m.
Calculate the wavelength of scattered photons if they are viewed at an angle of 600 to the
direction of incidence. (c = 3×108 ms-1) (Apr ‘03)
Ans: '
h
1 cos
m0 c
PART - B
1. Using Quantum theory, derive an expression for the average energy emitted by the black body and
arrive at Planck’s radiation law. (Jan ‘16, Dec ‘16)
2. With the concepts of quantum theory of black body radiation derive an expression for energy
distribution and use it to prove Wien’s displacement law and Rayleigh Jeans law. (Jan ‘10)
3. Define Compton Effect and explain its significance? Derive an expression for the change in
wavelength due to Compton scattering by incident light with matter. (Dec‘15, Jan ‘18)
4.Write down the equation for Compton shift and discuss it for various angles of scattering with an
experimental evidence to prove it. (Jan ‘09, ‘10)
5. What are the drawbacks of classical free electron theory? Derive time independent Schrödinger
wave equation and hence deduce time dependent Schrödinger wave equation. Give the physical
significance of wave function (Jan ‘10, Jan ‘18)
6. Derive time independent Schrödinger equation for one dimensional case. Also prove that for a
particle enclosed in a one dimensional box. (May ‘10)
7. With quantum concepts, explain the energy level of an electron enclosed in an infinite deep one
dimensional potential box.
8. Using Schroedinger’s time independent wave equation normalize the wave functions of electron
trapped in a one dimensional potential well. (Jan ‘04, ‘09, 16, Dec ‘16)
9. Explain G. P. Thomson experiment to prove the wave nature of an electron. (May ‘17)
10. What is the momentum and de-Broglie wavelength of an electron accelerated through a potential
difference of 56 V? (Dec ‘15)
11. The wavelength of the scattered X-ray photons are determined to be 1 Å by the detector at an
angle θ in a Compton experiment. If the wavelength of the scattered photons are found to be
1.018 Å by rotating the detector increasingly through 60̊ further, then calculate the angles of the
scattered X-ray photons. (Dec ‘15)
12. What is the principle of electron microscopy? Draw the construction of an electron microscope
and explain its working. Compare it with optical microscope. (May ‘17)
13. (i) An X-ray photon of wavelength 0.010 nm is scattered through 110̊ by an electron. What is the
kinetic energy of the recoiling electron? (Dec ‘16)
(ii) Find the de Broglie wavelength of an electron accelerated through a potential difference of 80 kV.
Find the wavelength of a X-ray photon that possess an energy same as that of the electron.
14. Explain the principle and working of scanning tunneling electron microscope and list out its
limitations. (Jan ‘11)
4
2 r 3
3 3
For BCC: r = a√3/4; a = 4r/√3 P.F = 3
= 68% (since n=2)
4r 8
3
4
4 r 3
3 2
For FCC: r = a√2/4; a = 4r/√2; P.F = 3
= 74% (since n=4)
4r 6
2
13. Write the c/a ratio and packing factor of HCP.
Ans:
c 8
1.633 ;
a 3
Packing factor = = 74 %
3 2
14. What are Miller indices?
Ans: Miller indices are the three smallest possible integers which have the same ratio as the
reciprocals of the intercepts of the plane concerned along the three axes.
15. Define unit cell. (May ‘17)
Ans: A unit cell is the smallest geometric figure which gives a complete crystal structure by
translational repetition in 3- D space.
16. What are Bravais lattices?
Ans: According to Bravais, there are 14 possible types of space lattices out of seven crystal
systems. These 14 space lattices are called Bravais lattices.
17. Write the expression for inter-planar spacing for a cubic system in terms of lattice
constant and Miller indices.
a
Ans: Inter planar spacing d . a = lattice constant, h k l = Miller indices.
h 2 k 2 l 2
18. What are the lattice parameters of a unit cell?
Ans: The characteristic intercepts on the axes a, b & c and interfacial angles α, β and γ are the
lattice parameters of a unit cell.
21. What is the relation between lattice constant ‘a’ and density ‘ρ’ of the crystal?
1
Ans: a nM 3
N
n -no.of atoms per unit cell: M- atomic weight: N -Avagadro’s number
22. What is a basis or motif?
Ans: It is an unit assembly of atoms or molecules which are identified with respect to the position
of lattice points, identical in composition, arrangement and orientation.
23. Define interatomic distance and inter-planar distance.
Inter atomic distance: The distance between the centres of any two nearest neighboring atoms.
Inter planar distance: The perpendicular distance between any two consecutive parallel planes.
24. What is meant by loosely packed and closely packed crystal structures? Give an example
for each.
Ans: A loosely packed crystal structure has low packing factor that is, in which more vacant sites
are available. Eg: Polonium
Closely packed structure has the highest packing factor of 0.74. Here the atoms are closely
packed leaving a small space as vacant site in the crystal. Eg: Copper – FCC, Zinc – HCP
25. What is diamond structure?
Ans: Diamond structure is a combination of two interpenetrating FCC sub lattices along the body
diagonal at a distance of ¼th of cube edge. Eg: Germanium, Silicon.
26. What is graphite structure?
Ans: In this graphite structure, carbon atoms are arranged in a regular hexagon flat parallel layers
such that each atom is linked by the neighbouring atoms. However there is no strong bonding
between different layers which are therefore easily separable from each other.
27. Which structure has least co-ordination number and maximum bravais lattice?
Ans: Least co-ordination number – Diamond Maximum Bravais lattice – Orthorhombic
28. Name the crystal structure of the following :
Gold - FCC
Calcite - Rhombohedral
Sulphur - Orthorhombic
Zinc - HCP
29. Mention the various crystal growing techniques.
Ans: (i) Melt growth (ii) Low temperature solution growth
(iii) High temperature solution growth (Flux growth) (iv) Epitaxial growth.
30. What is a melt growth?
Ans: Melt growth is a process of crystallization by fusion and resolidification of the starting
materials.
31. Draw the following planes in a cubic structure (001), (100), (110), (111).
(001) (100) (110) (111)
48. How carbon atoms are arranged in diamond and graphite structures? (Dec ‘15)
Ans: The diamond structure is a FCC structure with basis of 2 carbon atoms one located at
(0, 0, 0) and other at (a/4, a/4, a/4) associated with each lattice point.
In the graphite structure, carbon atoms are arranged in regular hexagons in flat parallel layers
such that each atom is linked by the three neighbouring atoms.
49. Calculate the volume of a FCC unit cell in terms of the atomic radius r. (Jan ‘16)
Ans: In FCC a = 4r/√2
Volume = a3 = (4r/√2)3 = (16r3/√2).
50. Metallic iron changes from BCC to FCC at 910 ˚C and corresponding atomic radii vary
from 1.258 Å to 1.292 Å. Calculate the percentage volume change during this structural
change. (Jan ‘16)
Ans: Percentage of change of volume =
𝑣𝑜𝑙𝑢𝑚𝑒 .𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑖𝑛 𝐵𝐶𝐶−𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑖𝑛 𝐹𝐶𝐶
× 100
𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑖𝑛 𝐵𝐶𝐶
Volume of one atom occupied in BCC = volume of BCC unit cell / no. of atoms
(4𝑟⁄ )3
= 2√3 = 96√3(1.258 × 10-10)3 = 12.26 × 10-30 m3
Volume of one atom occupied in FCC = vol. of FCC unit cell / no. of atoms
(4𝑟⁄ )3
= 2√2 = 64√2(1.292 x 10-10)3
= 12.20 × 10-30 m3
Percentage of change of Volume = (12.26 – 12.20) × 100 / 12.26 = 0.5 %
51. An element has FCC structure with atomic radius 0.144 nm. Find its lattice constant.
Ans: In FCC lattice constant a =4r/√2
a = 4×0.144×10-9/1.414 = 0.576×10-9/1.414
a = 0.4073×10-9m (or) 4.073 Å
52. Lattice constant of a BCC crystal is 0.36 nm. Find its atomic radius.
Ans: In BCC atomic radius r = a√3 / 4 = 0.36 x 10-9×1.732 / 4
= 0.62352 ×10-9/4
= 1.558 × 10-10 m.
53. For a cubic system sketch the planes with miller indices (110), (101), (011). (Jan ’18)
54. Determine the lattice constant for FCC lead crystal of radius 1.746 Å.
Ans: a = 4r/√2
a = 4×1.746 ×10-10/1.414 = 6.984 ×10-10/1.414; a = 4.939 × 10-10 m. (Or) a = 4.939 Å
55. Defects in crystals are not always harmful. Justify.
Ans: Doping in pure semiconductor increases there electrical conductivity and given boundaries
increase the mechanical strength of the material. Hence, the crystals are not always harmful.
56. What are point defects or zero dimensional defects?
Ans: The defects which take place due to imperfect packing of atoms during crystallization are
known as point defects.
57. What is line defects or a one dimensional defect?
Ans: the defects which take place due to dislocation or distortion of atoms along a line in some
direction is called line defect.
58. What is edge dislocation?
Ans: It is a region of lattice disturbance extending along an edge inside a crystal due to insertion
of an extra plane of atoms.
59. What is screw dislocation?
Ans: Screw dislocation results from a displacement of the atoms in one part of a crystal relative
to the rest of crystal forming a spiral ramp around the dislocation line,
60. What is meant by stacking fault?
Ans: The stacking faults are planar surface imperfection and, are caused by faults in the stacking
sequence of atomic planes in crystals of FCC and HCP materials.
61. Define Burger vector.
Ans: The vector which indicates the direction and magnitude of the shift of the lattice on the slip
plane is called Burger vector.
62. What are Frenkel and Schottky Imperfections? (Jan ’09, ’10, ’11)
Ans: Frankel defect is an ionic crystal imperfection that occurs when an ion moves into an
interstitial site, thereby creating two defects simultaneously i.e., one vacancy and the other
self-interstitial.
A pair of an ion vacancies in an ionic crystal is termed as Schottky defect.
PART-B
1. What are the lattice parameters of an unit cell? Define the terms atomic radius and packing factor.
Calculate all the above for SC, BCC and FCC structures. (June ‘16)
2. What is a packing factor? Prove that the packing factor of HCP is 0.74. (Jan ‘09)
(i) Describe the arrangement of atoms in a hexagonal closed packed (HCP) structure.
(ii) Determine the c/a ratio and packing factor for an ideal HCP structure. (Dec’15/Jan ‘16)
3. What is packing factor? Obtain packing factors for SC, BCC and FCC structures. (Jan ‘18)
(a) What are Miller Indices? Explain how they are determined with any two planes in SC structure.
Give their significance. (Jan ‘09, May ‘17)
(b) The lattice constant for an unit cell of aluminum is 4.049Å. Calculate the spacing of (220)
plane.
(i). Sketch two successive (110) plane.
(ii). Show that for a cubic lattice, the distance between two successive planes (h k l) is given by
d= a/√ (h2+k2+l2). (Jan ‘13, Dec ‘15 & ‘16)
Show that in a simple cubic lattice the separation between the successive lattice planes (100),(110)
and (111) are in the ratio of 1:0.71:0.58.
(a) Describe the structure of Diamond and graphite (June ‘09, Dec ‘16, May ‘17)
(b) Copper has FCC structure and its atomic radius is 1.273 Å. Find (i) lattice parameter (ii) Density
of copper. Atomic weight of copper = 63.5, Avogadro’s number = 6.023 x1023/k mol.
4. Describe Bravais lattices of the seven crystal systems with neat diagrams.
5. (a)Explain the various types of crystal systems with a neat sketch and example.
(b) (i) Zinc has HCP structure. The height of the unit cell is 0.494 nm. The nearest neighbouring
distance is 0.27 nm. The atomic weight of Zinc is 65.37 g. Calculate the volume of the unit cell
and density of Zinc.
(ii) Calculate the number of atoms per square meter on the planes (100), (110) and (111) for a
simple cubic lattice built of spherical atom of radius R.
6. Explain any two crystal growing techniques.
7. Describe Bridgman method of growing crystal. Mention the merits and demerits. (Dec ‘15)
8. Describe the solution growth of a crystal and list out its advantages and disadvantages.
Solution growth – Slow evaporation method.
9. Explain the vapour growth technique of growing crystals.
10. Explain the Czochralski method of growing crystals. Mention the merits and demerits.
11. Discuss in detail a suitable method to grow single crystal of semiconducting materials.(Dec ‘15)
12. Write a note on point imperfections in crystals. Discuss in detail a suitable method to grow single
crystal of semiconducting materials. (Jan 2018)
13. Describe any one method of growing single crystal from melt along with the advantages and
limitations of the method. (Dec ‘16)
14. Calculate the interplanar spacing for (110) and (111) planes in a simple cubic lattice whose lattice
constant is 0.424 nm. Also sketch these planes. (Dec ‘16)