In salt AB, B forms simple cubic lattice and A particles are present at the body centre of each unit cell. If one of the B goes missing from every unit cell, the molecular formula of the salt will become-

$A_8B_7$

The correct answer is Option (3) → $A_8B_7$.

To solve this question, we need to analyze the crystal structure and the effect of missing B atoms in the unit cell.

Given:

\(B\) particles form a simple cubic lattice.

\(A\) particles are present at the body center of each unit cell.

One of the \(B\) atoms goes missing from every unit cell.

In a simple cubic lattice, the \(B\) atoms are located at the corners of the unit cell. Since there are 8 corners in a cube, each corner atom contributes \( \frac{1}{8} \) of its atom to the unit cell (because each corner is shared by 8 unit cells).

So, the total number of \(B\) atoms in one unit cell of a simple cubic lattice is:

\(\text{Number of B atoms} = 8 \times \frac{1}{8} = 1 \text{ atom of B per unit cell}\)

The \(A\) particle is located at the body center of the unit cell, which is completely within the unit cell and fully contributes to the unit cell.

So, the total number of \(A\) atoms in one unit cell is:

\(\text{Number of A atoms} = 1\)

The problem states that one of the \(B\) atoms goes missing from every unit cell. Since we only have 1 \(B\) atom per unit cell (from the simple cubic lattice), removing 1 \(B\) atom means that there are no \(B\) atoms left in the unit cell. However, since this can't imply zero \(B\) atoms, it likely refers to reducing the total number of \(B\) atoms proportionally in multiple unit cells.

So, if 1 out of every 8 \(B\) atoms goes missing, the effective number of \(B\) atoms per unit cell becomes:

\(\text{Effective B atoms} = 1 - \frac{1}{8} = \frac{7}{8} \text{ B atoms per unit cell}\)

Now, for every 1 \(A\) atom, we have \( \frac{7}{8} \) \(B\) atoms. To express this as a molecular formula, we multiply the numbers by 8 to eliminate the fraction:

\(\text{Molecular formula} = A_8B_7\)

The molecular formula of the salt after one \(B\) atom goes missing from every unit cell is \(A_8B_7\).