The number of vacant orbitals in the valence shell of phosphorous is ____.

Explanation

To determine the number of vacant orbitals in the valence shell of phosphorus, we will follow these steps:

### Step 1: Identify the Atomic Number of Phosphorus
Phosphorus has an atomic number (Z) of 15.

### Step 2: Write the Electronic Configuration
The electronic configuration of phosphorus can be written as:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^3 \]

### Step 3: Identify the Valence Shell
The valence shell for phosphorus is the third shell (n=3), which includes:
- 3s orbital
- 3p orbitals
- 3d orbitals (though they are not filled in phosphorus)

### Step 4: Count the Electrons in the Valence Shell
In the valence shell:
- The 3s orbital has 2 electrons (3s²).
- The 3p orbitals have 3 electrons (3p³).
- The 3d orbitals can hold a maximum of 10 electrons but are empty in phosphorus.

### Step 5: Determine the Number of Vacant Orbitals
- The 3s orbital is fully occupied (2 electrons).
- The 3p orbitals have 3 electrons, which means there are 3 orbitals and one of them is half-filled (3p³).
- The 3d orbital has 5 orbitals, all of which are vacant.

Now, we can count the total number of vacant orbitals:
- 3s: 0 vacant orbitals (fully occupied)
- 3p: 3 orbitals - 3 electrons = 0 vacant orbitals (one is half-filled)
- 3d: 5 orbitals - 0 electrons = 5 vacant orbitals

### Step 6: Calculate Total Vacant Orbitals
Total vacant orbitals = 0 (from 3s) + 0 (from 3p) + 5 (from 3d) = 5 vacant orbitals.

### Conclusion
The number of vacant orbitals in the valence shell of phosphorus is **5**.

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