
Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?
(A)-
(B)-
(C)-
(D)-

Answer
488.1k+ views
3 likes
Hint: The packing efficiency accounts for the fraction of the unit cell occupied by the atoms, by taking the percent of the volume of the total atoms to the volume of the cube.
Complete step by step answer:
It is given that both the solids are body-centred cubic unit cells, that is, there are eight atoms at the corner of the cell and one whole atom in the centre of the unit cell. Each corner atom in the cell is shared among eight other adjacent unit cells. So, the contribution of a single corner atom is in the unit cell. Therefore, having a total eight corner atoms, the total contribution is 1 atom. In solid 2, there are eight corner A atoms, and one whole B atom at the centre of the unit cell. The total contribution from the eight corner A atoms is 1 atom and the contribution from the B atom is one. So, two total atoms are present in the unit cell. Then, the packing efficiency, that is the fraction of the unit cell occupied by the atoms is ----------- (a)
-Let the radius of atom A be , then given that radius of atom B is twice that of A, so . ------------ (b)
-Then, the volume of atom A is
And volume of atom B is = --------- (c)
-Also, in the bcc unit cell, the relation of the length of body diagonal to the side of the cube is given by: , where r is the radius and a is the length of side of the cube.
-Given, the length of the side of solid 2, is more than of solid 1. So, we have,
From solid 1, we have the relation or -------- (d)
Substituting the value of in , we have
-Then volume of the unit cell is ---------- (e)
-Substituting the value of (c) and (e) in equation (a), we get,
Packing efficiency
Therefore, the approximate packing efficiency in solid 2 is option (C)-
Note: The atoms are taken to be spheres to account for its contribution in the unit cell, so the volume of the sphere is considered. There are a total two atoms in a body-centred cubic unit cell.
Complete step by step answer:
It is given that both the solids are body-centred cubic unit cells, that is, there are eight atoms at the corner of the cell and one whole atom in the centre of the unit cell. Each corner atom in the cell is shared among eight other adjacent unit cells. So, the contribution of a single corner atom is
-Let the radius of atom A be
-Then, the volume of atom A is
And volume of atom B is =
-Also, in the bcc unit cell, the relation of the length of body diagonal to the side of the cube is given by:
-Given, the length of the side of solid 2,
From solid 1, we have the relation
Substituting the value of
-Then volume of the unit cell is
-Substituting the value of (c) and (e) in equation (a), we get,
Packing efficiency
Therefore, the approximate packing efficiency in solid 2 is option (C)-
Note: The atoms are taken to be spheres to account for its contribution in the unit cell, so the volume of the sphere is considered. There are a total two atoms in a body-centred cubic unit cell.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 4 Maths: Engaging Questions & Answers for Success

Trending doubts
Give 10 examples of unisexual and bisexual flowers

Draw a labelled sketch of the human eye class 12 physics CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Differentiate between insitu conservation and exsitu class 12 biology CBSE
