Potassium crystallizes in body centred cubic lattice with a unit cell length a = 5.2 . What is the distance between nearest neighbours?
Answers
In Potassium (bcc crystal lattice);
a) Distance between the nearest neighbours: Taking the center atom in consideration; as we know in a bcc lattice each center atom is attached to eight corner atoms which are the nearest neighbour atoms.
Hence, distance between the nearest neighbour atoms; is half the diagonal length of a diagonal line joining two corners and center atom i.e, as we know side of the cube a = 4r/√3 and the length of diagonal = √3a
Thus the distance between the center atom and nearest neighbour = √3a/2 =4r/2 =2r
In case of K, radius r = 235 pm (as known) hence, distance = 2r = 2X 235 = 470 pm
b) Distance between next neighbours: The next nearest neighbour of center atom will be the next center atom.
The distance between the two center atoms = parameter of the bcc lattice i.e, "a"
or, a = 4r/√3
Hence , the distance = 4 x 235 /√3 = 940/1.732 = 542.72 pm
c) Since, in bcc lattice the corner atoms are called as the nearest neighbours and also a bcc structure has 8 corner aroms, so the K- atom will have 8 nearest neighbours.
d) The next neighbour of a center atom in bcc lattice is the next center atom and in a bcc structure one center atom is surrounded by 6 center atoms of six cubes, hence the no. of next neighbours for center K-atom will be six.
Hope u understood well