Which of the following is false?

Options

A. The number of orbital for a given value of l is equal to `2l + 1`
B. The number of orbitals for a given value of an is equal to `n^(2)`
C. An atom having unpaired electrons is diamagnetic in nature
D. All s orbitals arte spherical symmetrical is shape

Explanation

To determine which statement is false among the given options, we will analyze each statement step by step.

### Step 1: Analyze Option 1
**Statement:** The number of orbitals for a given value of L is equal to \(2L + 1\).

- For \(L = 0\) (s orbital):
\[ 2(0) + 1 = 1 \quad \text{(1 type of s orbital)} \]
- For \(L = 1\) (p orbital):
\[ 2(1) + 1 = 3 \quad \text{(3 types: \(p_x\), \(p_y\), \(p_z\))} \]
- For \(L = 2\) (d orbital):
\[ 2(2) + 1 = 5 \quad \text{(5 types: \(d_{xy}\), \(d_{yz}\), \(d_{zx}\), \(d_{x^2-y^2}\), \(d_{z^2}\))} \]
- Conclusion: This statement is **true**.

### Step 2: Analyze Option 2
**Statement:** The number of orbitals for a given value of n is equal to \(n^2\).

- For \(n = 1\):
\[ n^2 = 1^2 = 1 \quad \text{(1 orbital: s)} \]
- For \(n = 2\):
\[ n^2 = 2^2 = 4 \quad \text{(1 s orbital + 3 p orbitals = 4 total)} \]
- For \(n = 3\):
\[ n^2 = 3^2 = 9 \quad \text{(1 s + 3 p + 5 d = 9 total)} \]
- Conclusion: This statement is **true**.

### Step 3: Analyze Option 3
**Statement:** An atom having unpaired electrons is diamagnetic in nature.

- **Definition of Diamagnetic:** Materials with all electrons paired (total spin = 0).
- **Definition of Paramagnetic:** Materials with unpaired electrons, which are attracted to magnetic fields.
- Conclusion: This statement is **false**.

### Step 4: Analyze Option 4
**Statement:** All s orbitals are spherical symmetrical.

- **Shape of s Orbitals:** The s orbitals are indeed spherical in shape.
- Conclusion: This statement is **true**.

### Final Conclusion
The false statement among the options is **Option 3**: "An atom having unpaired electrons is diamagnetic in nature."

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