Question 1. (16 points) a) Show using appropriate diagrammatical construction that the reciprocal lattice of a reciprocal lattice is the real lattice (Hint: (i) Start from unit cell of a real lattice, (ii) construct the reciprocal lattice (iii) construct the real lattice from the reciprocal lattice.) (8 points) b) What are the reciprocal lattice vectors of a lattice with real vectors = 1/2 13/2),c = 10 0 12. a = 10b 10 = (Hint: Volume of the unit cell extended on the vectors a, b and c is calculated as : , determinant of 3x3 matrix, with rows of the matrix being vectors a, b, c, i.e., 07 = V3/20 (8 points) 0 V = det|1/2 v3/2