For which of the following electron distribution in ground state the Pauli's exclusion principle is violated ?

Options

A.
B.
C.
D.

Answer

To determine which electron distribution violates the Pauli's exclusion principle, we need to understand the principle itself. The Pauli's exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers. This means that in any given orbital, if two electrons are present, they must have opposite spins.

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- Each electron in an atom is described by four quantum numbers:
- Principal quantum number (n)
- Azimuthal quantum number (l)
- Magnetic quantum number (m)
- Spin quantum number (s)

2. **Identify the Electron Configurations**:
- We will analyze the given options to see the distribution of electrons in different orbitals.

3. **Evaluate Each Option**:
- **Option A**:
- 2s orbital: 2 electrons (opposite spins)
- 2p orbitals: 2 electrons (1 in 2px and 1 in 2py)
- This configuration does not violate the Pauli's exclusion principle.

- **Option B**:
- All orbitals have one electron each.
- No two electrons share the same quantum numbers, thus no violation occurs.

- **Option C**:
- 2s orbital: 2 electrons (same spin)
- This means they have the same values for n, l, m, and s, violating the Pauli's exclusion principle.

- **Option D**:
- 2s orbital: 2 electrons (opposite spins)
- 2p orbitals: 3 electrons (each in different orbitals)
- This configuration does not violate the principle.

4. **Conclusion**:
- The only option where the Pauli's exclusion principle is violated is **Option C**, where both electrons in the 2s orbital have the same spin.

### Final Answer:
**Option C** is the answer where the Pauli's exclusion principle is violated.

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