An alloy of copper, silver and gold is found to have copper constituting the ccp lattice. If silver atoms occupy the edge centres and gold is present at body centre, the alloy has a formula:

a) Cu₄Ag₂Au
b) Cu₄Ag₄Au
c) Cu₄Ag₃Au
d) CuAgAu
Correct answer is option `C`. Can you explain this answer?

Question

An alloy of copper, silver and gold is found to have copper constituting the ccp lattice. If silver atoms occupy the edge centres and gold is present at body centre, the alloy has a formula:

a) Cu₄Ag₂Au
b) Cu₄Ag₄Au
c) Cu₄Ag₃Au
d) CuAgAu

Correct answer is option `C`. Can you explain this answer?

Answer

Solution:

Given:
Copper exists in the C.C.P lattice.
Silver atoms occupy the edge centres.
Gold is present at the body centre.

To find:
The formula of the alloy.

Explanation:

Copper exists in the C.C.P lattice, which means that each corner of the cube contains one copper atom, and each face centre also has one copper atom. The number of atoms per unit cell in the C.C.P lattice is 4.

Silver atoms occupy the edge centres, which means that each edge of the cube contains one silver atom. The number of atoms per unit cell in this case is 12.

Gold is present at the body centre, which means that there is one gold atom at the centre of the cube. The number of atoms per unit cell in this case is 1.

Using these values, we can calculate the total number of atoms per unit cell as follows:

Total number of atoms per unit cell = Number of copper atoms + Number of silver atoms + Number of gold atoms
= 4 + 12 + 1
= 17

Therefore, the formula of the alloy can be written as Cu4Ag3Au, as it has 4 copper atoms, 3 silver atoms and 1 gold atom per unit cell. Hence, option C is the correct answer.

Answer

Similar Chemistry Doubts

Atoms having radius 1.50 Å are arranged in a simple cubic lattice. Radius of the largest atom that can be placed at the body centre of the cubic cell, without affecting the unit size is

In a fcc lattice, atom A occupies the corner position and atom B occupies the face centre position. If one atom of B is missing from one of the face centred points, the formula of the compound is

In fcc lattice, atom A occupies the corner position and B occupies the face center positions. If one atom of B is missing from one of the Face centered positions, the formula of compound is?

K crystallizes in BCC lattice and has unit cell length a = 5.2 A. How many nearest neighbours does each K atom have?

Top Courses for Chemistry

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams