Assignment 1

Due on 19th Sep, 2003

 

  1. Solve the Schrödinger equation for the hydrogen atom.

                        Ref: http://scienceworld.wolfram.com/physics/HydrogenAtom.html

                                http://electron6.phys.utk.edu/qm2/modules/m1-3/hydrogen.htm

 

  1. Assuming Vanderwalls potential find out the elastic modulus and the mean interatomic distance along <100> direction of a simple cubic solid. 

 

  1. If the electron Beam is coming along [001] direction towards the (001) face of a simple cubic lattice. If the lattice spacing a=1.28 Å calculate the angle between the direct transmintted beam and another beam that has been diffracted by any one of the atomic planes clearly indicating the indices of the planes you are considering.

 

  1. If a Bragg angle of   41.31o   is observed for the  1st  order diffraction  from {110 plane of bcc niobium using copper Ka  radiation ( l =  0.1541 ), What is the interplanar spacing of the {110} planes in this metal?  If electron is used find out what should be the accelerating voltages required that will allow 3rd order diffraction to be observed on the florescent screen of a TEM. Assume that the effective magnification will allow electrons diffracted upto 45o be observed. (ref: Reed-Hill problem 2.1)

 

  1. In a particular AFM, the cantilever used to measure the force was mounted on a piezoelectric crystal and can be oscillated by applying a sinusoidal voltage signal to the crystal. If the dimensions of  cantilever made of silicon is length =  125 mm width = 30 mm and thickness = 4 mm calculate the frequency of the voltage signal applied to the piezoelectric crystal in tapping mode operation. If the voltage applied to the crystal is 10 * sin(wt) where w is the frequency calculated above, plot the amplitude of the vibration of the AFM tip as it is brought near a  surface which interacts with the tips through the potential ; with A= 10-77 J m6 and B = 10-134 J m 12