A monoatomic. cubic material has lattice spacing of a. The sound velocity for longitudinal and transverse phonons is approximately equal. C_{T} = C_{L} = C, is isotropic. The debye frequency of the phonons will be
Graphite lias a layered crystal structure in which the coupling between carbon atoms in different lasers is much weaker than the atoms in the same layer. Using Debye theory, the specific heat is proportional to (where T is the temperature)
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All Xray beam of wavelength 1.7 Å is diffracted by a cubic KC1 ciystal of density 1.99 x 10^{3} kg m^{3}. The interplance spacing for (200) planes and the glancing angle for the second order reflection from these planes will be (given that molecular weight of KC1 is 74.6 amu)
Elections of mass m are confined to one dimension. A weak periodic potential described by the fourier series
The energy gap (to first order) at (between the first and second band is)
All electron of mass m moves in a square lattice of lattice spacing a. Assume that the nearly free electron approximation holds good. If there are two electrons per site, then which of the following is correct?
A paramagnetic substance lias 10^{28} atoms/m^{3}. The magnetic moment of each atom is 1.8x10^{23} Am^{2}. Wliat would be the dipole moment of a bar of this material 0.1 meter long and 1 cnr crosssection placed in a field of 8x 10^{4 }Am^{1}?
A uniform silver wire has a resistivity of 1.54 x 10^{8} Clm at room temperature and there are 5.8 x 10^{28} conduction electrons per m^{3}. If an electric field of 1 volt cm is applied along the wire, the relaxation time of electron will be
Assuming that there are 10^{27} molecules /m^{3} in HCl vapour. The oiientation polarization at room temperature if the vapour is subjected to an electric field of 10^{6} V/m will be (given that dipole moment of HCl molecule is 3.46x10^{30 }cm)
Assume that the energy of the two particles in the field of each other is given by where
α and β are cosntants and r is the distance between the centres of paiticles. In stable configuration, the ratio of energy of attraction to the energy of repulsion will be____________(Answer should be an integer)
Sodium transforms frombcc to hep at about T = 23 K. Assumig that the density remains fixed and c/a ratio is
ideal. The hcp lattice spacing, a [given that the cubic lattice spacing a' = 4.23Å in the cubic phase] is_______Å (Answer should be upto two decimal places)
Atoms are arranged in a onedimensional chain with lattice spacing a. Each atom is represented by the potential V(x) = . The energy gaps between the bands, assuming that the nearly free electron approximation holds good, is
The effective mass tensor (M_{ij}) for electrons in a simple cubic tight binding band at the centre (k = (0, 0,0) of the brillion zone will be
Consider a two dimensional hexagonal lattice if lattice spacing a = 3 Å and sound velocity c = 10^{3} m/sec. The debye frequency, w_{D} is (provide a numerical value in sec^{1})
For a diatomic linear chain, the phonon dispersion relation ω (k) has two branches corresponding to + and  sign respectively
There are two atoms in the unit cell with masses and M2 and the force constant of nearest neighbour interaction is F and the effective mass is kept constant. The velocity of sound will be
Consider a two dimensional square lattice with one atom of mass m per lattice point interacting with only nearest neighbours with force constant k. Take the phonon dispersion curve to be At high temperature the mean square displacement of an atom from its equilibrium position will be
For a hexagonal closed packed structure with periodic potential (G being a reciprocal lattice G
vector). If G corrosponding to the first brillion zone face in the C direction C that is normal to the face is in the (001) direction), then the value of V_{G} is
A typeII superconducting wire of radius R carries current uniformly through its crosssection. If die total current earned by the wire is I. the magnetic energy per unit length of the wire is I. the magnetic energy per unit length of the wire is
The penetrating depth of mercury at 3.5 k is about 750 Å. The penetration depth at OK will be
Consider two dimensional electrons subjected to a weak periodic potential coming from a square lattice of spacing a = 5Å. For k vectors for away from the bu llion zone boundaries, the wavefunctions can be well
described by plane waves. Assume we want to write the wavefunction in block form,. Consider a state of energy E and wavevector The lowest energy at this wave number will be ________________eV (upto second decimal places)
Assume that the E vs k relationship for electrons in the conduction band of a hypothetical tetravalent ntype semiconductor can be approximated by E = ak^{2} + constant. The cyclotron resonane for electrons in a field B = 0.1 Weber/m^{2} occurs at an angular frequency ω_{e }= 1.8 x 10^{11} rad s^{1}The value of a is_______x 10^{38}(in the untis of Jm^{2})
1 docs34 tests

1 docs34 tests
