Question

1. Write a set of matrices describing the effect of all the operations in group C2h on a point (x, y, z). 2 Pts 2. Fill in the missing characters in the character table below, which is presented in standard format. The symbols A, B, C, D and F represent certain symmetry operations, and E is identity. 2A 3B 2D 3F 0 I2 1 1 0 Is 2 2.5 Pts

Answer 1

C_2h -(point group): It contains C_2h identicalto {E, C_2(z), I, sigma_h} [1 0 0 0 1 0 0 0 1] [x y z] = [1 0 0 0 1 0 0 0 1] for example - Matrix representation is given as: [1 0 0 0 1 1 0 0 1] [-1 0 0 0 -1 0 0 0 1] [-1 0 0 0 -1 0 0 0 -1] [1 0 0 0 1 0 0 0 1] where, E is the identity element i is the m version of symmetry sigma_h horizontal plane C_2(z)-is the principle axis of symmetry along (z - 9) \r\n Here, A = C_3, B = C_2, C = sigma_n D = s_3, F = sigma_v According to great orthogonally theorem: Order of the point group is = 12 sigma_R [T�_i (R)_mn] [T�_j (R)�_m�n�] = h/squareroot l_i l_j S_i j S_m Rule - i)sigma^2_ii = h ii) sigma_R [T_i (R)]^2 = h where I notequalto j iii) sigma_R T_i