[UPSC CSE 2005] Crystal Structure \& its Determination (Q41, 6+8+6M)

{cse-q-8-119-fig-1} An In As semiconductor sample is cut in the form of a small bar of size 1 \cdot 0 \text{ cm} \times 1 \cdot 0 \text{ cm} \times 2 \cdot 0 \text{ mm}. Its lengthwise resistance is 1 \cdot 25 \ \Omega. A Hall field of 1 \cdot 7 \text{ V/m} develops when a current of 0 \cdot 12 \text{ A} is passed lengthwise and a magnetic field of 0 \cdot 05 \text{ T} is applied normal to its length as shown above. Calculate the carrier density. (iii) Determines the reciprocal lattice vectors of an fcc lattice.