Atomicity of white or yellow phosphorus is 4 annd it is represented as `P_(4)` molecule
Calculate the value of expresion`(x*y)/(z)` regarding this molecule.
Where x: total number of vertex angles in `P_(4)` molecule.
y: Total number of lone pairs in `P_(4)` molecule
z: total number of P-P bonds in `P_(4)` molecule.

Explanation

To solve the problem, we need to calculate the value of the expression \((x \cdot y) / z\) for the molecule \(P_4\) (white or yellow phosphorus). We will find the values of \(x\), \(y\), and \(z\) based on the definitions provided.

### Step 1: Determine \(x\) (Total number of vertex angles in \(P_4\) molecule)

1. **Understanding the structure of \(P_4\)**: The \(P_4\) molecule has a tetrahedral structure. Each phosphorus atom is connected to three other phosphorus atoms.
2. **Counting vertex angles**: In a tetrahedral structure, each vertex (corner) has three angles. Since there are four phosphorus atoms (vertices), we calculate:
\[ x = \text{Number of vertices} \times \text{Angles per vertex} = 4 \times 3 = 12 \]

### Step 2: Determine \(y\) (Total number of lone pairs in \(P_4\) molecule)

1. **Valence electrons of phosphorus**: Each phosphorus atom has 5 valence electrons.
2. **Bonds formed**: Each phosphorus in \(P_4\) forms three bonds with other phosphorus atoms, using 3 of its 5 valence electrons.
3. **Calculating lone pairs**: Each phosphorus atom will have:
\[ \text{Lone pairs} = \text{Total valence electrons} - \text{Bonds formed} = 5 - 3 = 2 \]
Since there are 4 phosphorus atoms, the total number of lone pairs in \(P_4\) is:
\[ y = 4 \times 1 = 4 \]

### Step 3: Determine \(z\) (Total number of P-P bonds in \(P_4\) molecule)

1. **Counting P-P bonds**: In the \(P_4\) structure, each phosphorus atom is bonded to three other phosphorus atoms. The total number of P-P bonds can be counted as follows:
- Each bond is counted twice (once for each atom), so we count the bonds formed by each atom and divide by 2.
- The total number of bonds is:
\[ z = \frac{4 \times 3}{2} = 6 \]

### Step 4: Calculate the expression \((x \cdot y) / z\)

Now that we have the values:
- \(x = 12\)
- \(y = 4\)
- \(z = 6\)

We can substitute these values into the expression:
\[ \frac{x \cdot y}{z} = \frac{12 \cdot 4}{6} \]
Calculating this gives:
\[ \frac{48}{6} = 8 \]

### Final Answer
The value of the expression \((x \cdot y) / z\) for the \(P_4\) molecule is **8**.

---