Question:
A compound contains two types of atoms $A$ and $B$. Its crystal structure is a cubic lattice with '$A$' atoms at the corner of the unit cells and '$B$' atoms at the body centres. The simplest formula of the compound will be
A compound contains two types of atoms $A$ and $B$. Its crystal structure is a cubic lattice with '$A$' atoms at the corner of the unit cells and '$B$' atoms at the body centres. The simplest formula of the compound will be
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Always remember the contribution of lattice positions in a cubic unit cell:
- Corner = $\frac{1}{8}$
- Face center = $\frac{1}{2}$
- Edge center = $\frac{1}{4}$
- Body center = $1$
Multiplying the number of positions by their contribution directly yields the empirical formula.
- Corner = $\frac{1}{8}$
- Face center = $\frac{1}{2}$
- Edge center = $\frac{1}{4}$
- Body center = $1$
Multiplying the number of positions by their contribution directly yields the empirical formula.
Updated On: May 25, 2026
- $A_2B$
- $AB$
- $AB_2$
- $AB_3$
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
We need to find the simplest formula of a crystalline solid compound containing atoms of elements $A$ and $B$ arranged in a cubic lattice.
Step 2: Key Formula or Approach:
The contribution of an atom to a unit cell depends on its position in the lattice:
- An atom at a corner of a cubic unit cell is shared by 8 adjacent unit cells, so its contribution to one unit cell is $\frac{1}{8}$.
- An atom at the body center of a unit cell is not shared by any other unit cell, so its contribution is $1$.
Step 3: Detailed Explanation:
Let us calculate the number of atoms of $A$ and $B$ per unit cell:
- Number of '$A$' atoms at the corners = $8$.
- Effective number of '$A$' atoms per unit cell = $8 \times \frac{1}{8} = 1$.
- Number of '$B$' atoms at the body center = $1$.
- Effective number of '$B$' atoms per unit cell = $1 \times 1 = 1$.
The ratio of atoms of $A$ to $B$ in the unit cell is:
\[ A : B = 1 : 1 \]
Therefore, the simplest empirical formula of the compound is $AB$.
Step 4: Final Answer:
The correct option is (B).
We need to find the simplest formula of a crystalline solid compound containing atoms of elements $A$ and $B$ arranged in a cubic lattice.
Step 2: Key Formula or Approach:
The contribution of an atom to a unit cell depends on its position in the lattice:
- An atom at a corner of a cubic unit cell is shared by 8 adjacent unit cells, so its contribution to one unit cell is $\frac{1}{8}$.
- An atom at the body center of a unit cell is not shared by any other unit cell, so its contribution is $1$.
Step 3: Detailed Explanation:
Let us calculate the number of atoms of $A$ and $B$ per unit cell:
- Number of '$A$' atoms at the corners = $8$.
- Effective number of '$A$' atoms per unit cell = $8 \times \frac{1}{8} = 1$.
- Number of '$B$' atoms at the body center = $1$.
- Effective number of '$B$' atoms per unit cell = $1 \times 1 = 1$.
The ratio of atoms of $A$ to $B$ in the unit cell is:
\[ A : B = 1 : 1 \]
Therefore, the simplest empirical formula of the compound is $AB$.
Step 4: Final Answer:
The correct option is (B).
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