2.(i) How many atoms are present in a unit cell of a BCC lattice? (ii) Find the volume density ofatoms of the BCC lattice if lattice constant is 5 Å.
3. (i) Prove the lattice constant of a FCC lattice is 𝑎 =2√2𝑟 where r is the atomic radius. (ii) If
the atomic radius for a FCC lattice is 0.175nm, find the volume of the unit cell.
[6+4=10] 4. Find out the atomic packing factor of a BCC crystal lattice whose lattice constant is ‘a’.
5. Find out the Miller Indices of the following.
(i) (ii) (iii)
6.Find out the (i) momentum and (ii) de-Broglie wavelength of an electron travelling with avelocity of 107 cm/s. Consider mass of electron as 9.1×10-31 Kg.
7. Determine the probability that an energy level 3KT above Fermi level is occupied by an
electron at T = 300 K. [Hint: Difference between E and EF is 3KT]
8. Calculate the (i) probability that a state in the conduction band is occupied by an electron f(EC)
and calculate the (ii) thermal equilibrium electron concentration (n0) in silicon at T= 100 K.
Assume the Fermi energy is 0.25 eV below the conduction band. The value of NC for silicon
at T = 100 K is 2.8 x I019 cm-3.
[5+5 = 10] 9. Calculate the intrinsic carrier concentration in gallium arsenide at T = 300 K. The values of NC
and NV at 300 K for gallium arsenide are 4.7 x 1017 cm-3 and 7.0 x 1018 cm-3, respectively.
Assume the bandgap energy of gallium arsenide is 1.42 eV.
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