Thapar University 2007-2nd Year M.Tech Thermal Science M.E Nanomaterials & Nanotechnology Year - Question Paper
Thapar University School of Physics & Materials Science M. Tech. First Year, Second Semester, 2006-2007 End Semester Examination
Course Code: MS 112 Date: May 24, 2007
Course Name: Nanomaterials & Nanotechnology Time Allowed: 3 hr
Instructor: S. D. Tiwari Maximum Marks: 45
Note: Attempt all questions. Show all steps in your derivations/calculations.
1. (a) What is quantum well? Solve the Schrodinger equation for an infinitely deep quantum well of width I. to find eigen functions and eigen values.
(b) What are the energies of first and second energy levels in a 100 A GaAs quantum well? Assume that you can treat the problem by an infinite barrier approximation? Effective mass of an electron in GaAs is 0.067 mo- (4.5 + 4.5)
2. (a) Consider a cube of dimensions 1 nm * 1 nm *1 nm. Calculate the energy
difference between the ground state and first excited state of an electron in this cube. Can we observe the quantum size effect in this cube at room temperature?
(b) Calculate the number of atoms in a 5 nm particle of an element. The element has a FCC structure with lattice constant 4.2 A. Calculate the number of atoms lying on the surface of the particle assuming that surface of the particle has thickness of one lattice constant. Also calculate fraction of atoms lying on the surface of the particle.
(4.5 + 4.5)
3. (a) Full width at half maximum of an x-ray diffraction peak (at 2 0b = 43) from small particles of iron is 2.76.The full width at half maximum of same peak from bulk iron is 0.32. Calculate the average crystallite size of the sample of small particles. The wavelength of x-ray used is 1.54 A.
(b) Magnetization M as a function of magnetic field H is performed on small particles of a magnetic material at 300 K. The magnetization increases linearly with increasing magnetic field with a slope 3.5 * 10"1 emu g'1 gauss'1. Calculate the average particle magnetic moment in Bohr magnetons. Number of particles in one gram sample is given to be 3.4 * 1018. (4.5 + 4.5)
(b) In a given SAD pattern of an unknown sample radii of first, second, third, ... rings from center are 8.85 mm, 10.15 mm, 14.40 mm, 16.85 mm, 17.60 mm, ... respectively. Determine the crystal structure of the sample. Also calculate the d values corresponding to the observed rings. D and X are given to be 60 cm and 0.035 A respectively. (4.5 + 4.5)
5. (a) What are the advantages of chemical methods over physical methods for the preparation of nanoparticles?
(b) What is coprccipetation method? Discuss this method for the preparation of nanoparticles of MnFe:04. Also write the required precautions for this method.
(4.5 + 4.5)
Useful information:
(i) Planks constant h = 6.63 * 10'34 J s
(ii) Mass of free electron mo = 9.1 * 10'3 kg
(iii) Boltzmann constant k = 1.38 * 1016 emu gauss K.*1
(iv) 1 Bohr magneton = 0.9271 x 1 O'20 emu
(a) In a selected area electron diffraction pattern from nanoparticles of a given sample, concentric rings are observed. Derive a relation among d, r, D and X. Where r is radius of ring in the pattern corresponding to a family of parallel atomic planes with spacing d. D and X are normal distance between sample and screen and wavelength of electron beam respectively.
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| Earning: Approval pending. |
