ASSIGNMENT IV

Answer to Problem I

QuestionsAnswers
The Unit Celldue to the packing of the atom/molecule in a crystal
The Crystal Latticedue to the packing of the atom/molecule in a crystal
The origin in reciprocal latticeChoosen by the crysallographer
The origin in the crystalChoosen by the crysallographer
The space group symmetr of the crystalChoosen by the crysallographer

Answer to Problem II

When a ceter of symmetry acts on a point at coordinates (x,y,z)it converts to a point at (-x, -y, -z). The same coordinates can be obtained if we perform 2/m operation i.e C2 axis along b and mirror along ac plane.
Similarly, in an ortho rhombic unit cell if a center of symmetry were addded to 222 groups (which is non-centrosymmetric) they become equal to a centrosymmetric 2/m2/m2/m. Measurement of a centrosymmetric property on a non-centrosymmetric crystal causes the it to rewpond as if it possessed a center of symmetry. Such classes or groups are called Laue groups.

Crystallographic symmetry operations may be grouped into 5 distinct groups, namely, lattice translations, rotations, rotary-inversions, screw-rotations, and mirror/glide planes.

Answer to Problem III

The structure of D-glucose is shown below

the molecule does not possess any symmertry operations. This is further confirmed by its optical activity (dextro rotatory)

Answer to Problem IV

The co-ordinates for the organo metallic Co compound viewing down the c-axis is worked out to ab as follows;

Co-ordinates

(0,0,0)
(1/2,0,0)
(1,0,0)
(1,0,0)
(1/2,y,1/4)
(1/2,1/2,0)
(0,1/2,0)
(0,y,1/4)
(x,1/4,z)

Since Cobalt forms predominantly Octahedral complexes with m-3m point group symmetry it is expected to occupy special positions.

Answer to Problem V

The diagram indicates the staggered conformation of 1,2-dichloro ethane. There is a center of inversion (i) between the two carbon atoms (seen clearly from view A) Therefore the point group symmetry for this molecule is -1.

Answer to Problem VI

(i) The diagram indicates the following 3 types of symmetry elements

a. two fold axis parallel c-axis
b. ac plane
c. bc plane