Question 2 The ammonia molecule, NH3, has a trigonal pyramidal molecular shape. Its Cartesian coordinates are given below. Atom X/A Y/A Z/Å N 0.000000 0.000000 0.096922 H 0.000000 0.969142 -0.226150 H -0.839302 -0.484571 -0.226150 H 0.839302 -0.484571 -0.226150 a) Calculate the length of the N-H bond. (6 marks) b) Calculate the H-N-H bond angle. c) (6 marks) The overall dipole moment of NH3 is 1.42 D. Calculate the dipole moment of an individual N-H bond. (6 marks) d) In two-dimensional space, the rotation matrix that transforms the coordinates (x,y) to (x2,y2) is given by (x2,y2) R(0) = [cos-sine], 0 (x₁₁) where | = R()] x Fig. 1. Transformation of (x,y) to (x2,y2) by rotation about angle 0. A sketch illustrating the angle 0 and the coordinates (x,y) and (x2,y2) is given in Fig. 1. Show that the three H atoms in NH3 are spaced 120° apart. (7 marks) 3