(c) (x, y), (x–y, x), (y, x–y), (x, y), (y-x, x), (y, y-x)
(d) (x, y-x), (x, y), (x, y), (y-x, x), (y, y-x), (y-x, y)
10. A unit cell has the following dimensions: a = 3 Å, b = 4 Å and c = 115°. The
two distances between the points with fractional coordinates: (i) 0.210, 0.150
and 0.410, 0.050, (ii) 0.210, −0.150 and 0.410. 0.050 are:
(a) 0.95 Å, 0.87 Å
(b) 0.85 Å, 0.77 Å
(c) 0.75 Å, 0.67 Å
(d) 0.65 Å, 0.57 Å
11. A unit cell has the following dimensions: a = 5 Å, b = 8 Å and c = 50°. The
length of vectors with the help of following components: (i) [0.50, 1.0] and
(ii) [0.75, −0.25] can be found to be:
(a) 6.8 Å, 5.9 Å
(b) 7.8 Å, 4.9 Å
(c) 8.8 Å, 3.9 Å
(d) 9.8 Å, 2.9 Å
12. A unit cell has the following dimensions: a = 2 Å, b = 3 Å and c = 90°. The
two distances between the points with fractional coordinates: (i) 0.100, 0.250
and 0.200, 0.050, (ii) 0.100, −0.250 and 0.210. 0.050 are:
(a) 0.632 Å, 0.922 Å
(b) 0.532 Å, 0.822 Å
(c) 0.432 Å, 0.722 Å
(d) 0.332 Å, 0.622 Å
13. A unit cell has the following dimensions: a = 5 Å, b = 7 Å, c = 9 Å, a = 120°,
b = 85° and c = 75°. The length of vectors with the help of following components: (i) [0.2, −0.3, 0.6] and (ii) [0.5, 0.7, −0.1] can be found to be:
(a) 4.76 Å, 4.44 Å
(b) 5.76 Å, 5.44 Å
(c) 6.76 Å, 6.44 Å
(d) 7.76 Å, 7.44 Å
14. The sides of a primitive rectangle are 4 Å and 3 Å. Construct another unit cell
whose one side is the diagonal of the rectangle. The angle made by this with the
horizontal side is:
(a) 26.87°
(b) 36.87°
3.6 Packing Efficiency
129
(d) (x, y-x), (x, y), (x, y), (y-x, x), (y, y-x), (y-x, y)
10. A unit cell has the following dimensions: a = 3 Å, b = 4 Å and c = 115°. The
two distances between the points with fractional coordinates: (i) 0.210, 0.150
and 0.410, 0.050, (ii) 0.210, −0.150 and 0.410. 0.050 are:
(a) 0.95 Å, 0.87 Å
(b) 0.85 Å, 0.77 Å
(c) 0.75 Å, 0.67 Å
(d) 0.65 Å, 0.57 Å
11. A unit cell has the following dimensions: a = 5 Å, b = 8 Å and c = 50°. The
length of vectors with the help of following components: (i) [0.50, 1.0] and
(ii) [0.75, −0.25] can be found to be:
(a) 6.8 Å, 5.9 Å
(b) 7.8 Å, 4.9 Å
(c) 8.8 Å, 3.9 Å
(d) 9.8 Å, 2.9 Å
12. A unit cell has the following dimensions: a = 2 Å, b = 3 Å and c = 90°. The
two distances between the points with fractional coordinates: (i) 0.100, 0.250
and 0.200, 0.050, (ii) 0.100, −0.250 and 0.210. 0.050 are:
(a) 0.632 Å, 0.922 Å
(b) 0.532 Å, 0.822 Å
(c) 0.432 Å, 0.722 Å
(d) 0.332 Å, 0.622 Å
13. A unit cell has the following dimensions: a = 5 Å, b = 7 Å, c = 9 Å, a = 120°,
b = 85° and c = 75°. The length of vectors with the help of following components: (i) [0.2, −0.3, 0.6] and (ii) [0.5, 0.7, −0.1] can be found to be:
(a) 4.76 Å, 4.44 Å
(b) 5.76 Å, 5.44 Å
(c) 6.76 Å, 6.44 Å
(d) 7.76 Å, 7.44 Å
14. The sides of a primitive rectangle are 4 Å and 3 Å. Construct another unit cell
whose one side is the diagonal of the rectangle. The angle made by this with the
horizontal side is:
(a) 26.87°
(b) 36.87°
3.6 Packing Efficiency
129