Chemistry Class 12 NCERT Solutions: Chapter 1 The Solid State Part 7

Q: 11. Silver crystallises in fcc lattice. If edge length of the cell is Equation and density is Equation , calculate the atomic mass of silver.

Ans:

It is given that the edge length, Equation

Density, Equation

As the lattice is fcc type, the number of atoms per unit cell, Equation

We also know that, Equation

Using the relation

Equation

Equation

Equation

Equation

Therefore, atomic mass of silver Equation

Q: 12. A cubic solid is made of two elements P and Q. Atoms of Q are at the corners of the cube and P at the body-centre. What is the formula of the compound? What are the coordination numbers of P and Q?

Ans:

It is given that the atoms of Q are present at the corners of the cube.

Therefore, number of atoms of Q in one unit cell Equation

It is also given that the atoms of P are present at the body-centre.

Therefore, number of atoms of P in one unit cell = 1

This means that the ratio of the number of P atoms to the number of Q atoms, Equation

Hence, the formula of the compound is PQ.

The coordination number of both P and Q is 8.

Q: 13. Niobium crystallises in body-centred cubic structure. If density is Equation , calculate atomic radius of niobium using its atomic mass Equation .

Ans:

It is given that the density of niobium, Equation

Atomic mass, Equation

As the lattice is bcc type, the number of atoms per unit cell, Equation

We also know that, Equation

Applying the relation:

Equation

Equation

Equation

Equation

So, Equation

For body-centred cubic unit cell:

Equation

Equation

Equation

Equation

Equation

Q: 14. If the radius of the octahedral void is r and radius of the atoms in close packing is R, derive relation between r and R.

Ans:

A sphere with centre O, is fitted into the octahedral void as shown in the above figure. It can be observed from the figure that Equation is right-angled

Equation

Now, applying Pythagoras theorem, we can write:

Equation

Equation

Equation

Equation

Equation

Equation

Equation

Equation

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