Assignment 5
Chapter - Quantum mechanics (Applications of Schrodinger’s equation)
Q1. Calculate ground state energy of an electron confined to a box 1Ǻ wide.
(Ans: 0.37eV)
Q2. An electron confined to a 1-D well of width 0.2nm.It is found that when
the particle’s energy is 230eV, its eigen function has five antinodes. Find the
mass of the particle.
(Ans: 9.1*10ֿ³¹ kg)
Q3. Is it possible to have energy states of a ball of mass 10g moving in a box
along its length which is 10cm. Explain.
( Ans: No)
Q4. An electron is confined to move between two rigid walls separated by
1nm.Find the Debroglie wavelength representing the first three allowed
energy states of the electron and the corresponding energies.
(Ans: 20Å,10 Å,5 Å,0.38eV,1.52eV,3.42eV)
Q5.Electron with energy 2eV are incident on a barrier 10eV high and 1.0nm
wide. Find transmission probability of electrons.
(Ans: 6.784*10-13 )
Q7. Obtain the expectation value of particle’s position and momentum for
particle in a box of width L.
(Ans: L/2,0)
Assignment 6
Chapter 6- Statistical mechanics
Q1. Show that the pauli-exclusion principle follows directly from the
distribution function for Fermi-dirac statistics.
Q2. A Bose-Einstein gas has two particles in the i-th state whose degeneracy is
three, find the number of independent ways of selecting the particle in the
state.
(Ans: 6)
Q3. Write the Fermi dirac function.Plot it for temperature goes to 0,how does
it change when T>0.
Q4. Explain the significance of Fermi energy .
Q5. Which type of statistics shall be applicable for a gas of (i)Photons and
(ii)Electrons. Justify your answer.
Assignment 7
Chapter - Solid State Physics
Q1. Draw the labeled energy band diagram for P-N junction for
(a) no bias (b) forward bias condition?
Q2. With the help of energy diagram explain the principle of operation of
tunnel diode. Plot its V-I characteristics and mark the region of negative
resistance. Give one of its important uses?
Q3. Distinguish between intrinsic and extrinsic semiconductor?
Q4. Explain, Why a semiconductor acts as an insulator at 0 K?
Q5. Draw a labeled diagram for a P-N diode. Show also the Fermi energy?
Q6. For what voltage will the reverse current in a P-N junction germanium
diode attain a value of 90% of its saturation value at room temperature?
Ans: V= -59.86 V
Q7. Explain the formation of Potential barrier in a P-N junction?
Q8. A 10 volt Zener diode is used to regulate the voltage across a variable load
resistor. The input voltage varies between 13 Volt and 16vVolt and the load
current varies between 10 to 85 mA. The minimum Zener current is 15 mA.
Calculate the value of series resistance R?
Ans: 30 Ω
Q9.
What is difference between N-type and P-type semiconductor?
Q10. On the basis of band theory explain why diamond is transparent to
visible light. Given forbidden gap in diamond is 6 eV?
Q11. What is Zener diode? Explain the working of Zener diode as a voltage
stabilizer?
Assignment 8
Chapter - Superconductivity
Q1. Calculate the critical current which can flow through a long thin
superconducting wire of Al of diameter 10-3m. The critical magnetic field for Al is
79X103 Amp/m.
(Ans: 24.806 A)
Q2. Calculate the critical current density for 1 mm diameter wire of lead at 4.2K. A
parabolic dependence of Hc on T may be assumed. Given Tc for lead=7.18 K and Hc
for lead= 6.5X104 Amp/m.
(Ans: Jc = 1.71X108 Amp/m2)
Q3. For a superconducting specimen, the values of critical fields are 1.4X105 and
4.2X105 A/m at 14K and 13K. Calculate the transition temperature and critical
fields at 0K and 4.2K.
(Ans: Hc (at 0K)= 20.7X105 A/m, Hc(at 4.2K)= 18.9X105 A/m)
Q4.The penetration depth of mercury at 3.5 K is 750 Ǻ. Estimate the penetration
depth at 0K.
(Ans: 519.2 Ǻ)
Q5. Find London penetration depth for lead having superconducting electron
density of 3X1028 m-3. The transition temperature for lead is 7.22K.
(Ans: 278 nm)
Q6. The London penetration depths for a superconductor at 3K and 7.1K are 39.6
nm and 173 nm, respectively. Determine the Superconducting transition
temperature.
(Ans: 7.193 K)
Q7. Calculate the London penetration depth at 0K for lead whose density is
11.3X103 kg/m3 and atomic weight is 207.19 gram.
(Ans: 208 Ǻ)
Q8. Prove that Meissner effect contradicts the Maxwell’s equation.
Q9. Compute the superconducting electron density of mercury at 3.5K.
(Ans: 2.138X1028/m3)
Assignment 9
Chapter - X-rays
Q1. X- rays of wavelength 2x 10-11 m suffer first order reflection from (111) crystal
plane at an angle of 45°. What is the interatomic spacing of the crystal?
(Ans: 0.25Å)
Q2. Calculate the glancing angle of the (110) plane of simple cubic crystal (a=
2.814Å) corresponding to second order diffraction maxima for the X-rays of
wavelength 0.710 Å.
(Ans: 20° 55’)
Q3. The smallest angle of Bragg’s scattering in potassium chloride is 28.4° for
0.30nm X-rays. Find the distance between atomic planes in potassium chloride.
(Ans: 3.15Å)
Q4. Find the shortest wavelength present in radiation from a X-ray machine,
where accelerating potential is 50kV.
(Ans: 0.248Å)
Q5. A Coolidge tube operates at 50kV. Find:
a) the maximum velocity of electrons striking the anticathode,
b) minimum wavelength of X-rays generated.
Given: e = 1.6 x 10-19 C and m= 9.1 x 10-31 kg.
(Ans: v = 1.36 x 10 8 m/s and λ= 0.24Å)
Q6. The radiation from a X-rays tube operated at 40KV is analysed with a Bragg
spectrometer using calcite crystal cut along the cleavage plane (100):
a) calculate the shortest wavelength of X-rays coming from the tube.
b) what is the smallest glancing angle at which the wavelength will be reflected?
Given: h= 6.625 x 10-27 erg-sec , e = 4.803 x 10-10 esu , c = 3 x 1010 cm/s and d100 =
3.029 Å
(Ans: λmin = 0.31 Å, θ1 = 2° 57’)
Assignment 10
Chapter - Ultrasonics
Q1. What is piezoelectric effect? Explain the production of ultrasonic waves using
piezoelectric and magnetostriction methods in production of ultrasonic waves.
Q2. What are ultrasonics? Discuss its properties and some of its engineering
applications.
Q3. An ultrasonic source of 0.07 MHz sends down a pulse towards the sea bed
which returns after 0.65 s. the velocity of sound in sea water is 1700m/s. show
that the depth of the sea is 552.5m and the wavelength of the pulse is 0.0242m.
Q4.Calculate the natural frequency of ultrasonic waves using the following data:
a) thickness of quartz plate = 5.5 x 10-3 m
b) young’s modulus of quartz = 8.0 x 1010 N/m2
c) density = 2.65 x 103 kg/m3
(Ans: 4.99 KHz)
Q5. A piezoelectric x-cut crystal plate has a thickness of 1.6mm. If the velocity of
sound wave along the x-direction is 5760 m/s, calculate the fundamental
frequency of the crystal.
(Ans: 1.8 MHz)
Q6. What is the shortest wavelength of ultrasonic waves in air at room
temperature?
(Ans: 331/2000 m)
Q7. Discuss the properties of ultrasonics. Mention two of its important
applications.
Q8. What frequency ranges constitute ultrasonics and infrasonics?