Which of the following pair of electrons is excluded from an atom ?

Options

A. `n=2, l=0, m=0, s=+(.^(1)//_(2))` and `n=2, l=0, m=0, s=+(.^(1)//_(2))`
B. `n=2, l=1, m=+1, s=+(.^(1)//_(2))` and `n=2, l=1, m=-1, s=+(.^(1)//_(2))``
C. `n=1, l=0, m=0, s=+(.^(1)//_(2))` and `n=1, l=0, m=0, s=-(.^(1)//._(2))`
D. `n=3, l=2, m=-2, s=+(`^(1)//_(2))`` and `n=3, l=0, m=0, s=+(`^(1)//_(2))``

Answer

To determine which pair of electrons is excluded from an atom, we need to analyze the quantum numbers associated with each pair. According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of all four quantum numbers (n, l, m, s).

Let's break down the solution step by step:

### Step 1: Understand the Quantum Numbers
Each electron in an atom is described by four quantum numbers:
- **n** (Principal Quantum Number): Indicates the energy level or shell.
- **l** (Azimuthal Quantum Number): Indicates the subshell (s, p, d, f).
- **m** (Magnetic Quantum Number): Indicates the orientation of the orbital.
- **s** (Spin Quantum Number): Indicates the spin of the electron (+1/2 or -1/2).

### Step 2: Analyze Each Pair
Now, we will analyze the given pairs of quantum numbers one by one.

1. **Pair 1**: (n=2, l=0, m=0, s=+1/2)
2. **Pair 2**: (n=2, l=0, m=0, s=+1/2)
3. **Pair 3**: (n=2, l=1, m=0, s=-1/2)
4. **Pair 4**: (n=3, l=1, m=1, s=+1/2)

### Step 3: Identify Identical Quantum Numbers
Now, we check for identical quantum numbers:
- **Pair 1 and Pair 2**: Both have (n=2, l=0, m=0, s=+1/2). They are identical in all four quantum numbers.
- **Pair 3**: Has different values for l and s compared to the first two pairs.
- **Pair 4**: Also has different values for n, l, m, and s compared to the first two pairs.

### Step 4: Apply the Pauli Exclusion Principle
Since Pair 1 and Pair 2 have the same set of quantum numbers, they cannot coexist in the same atom according to the Pauli Exclusion Principle. Therefore, this pair is excluded from an atom.

### Conclusion
The pair of electrons that is excluded from an atom is **Pair 1 and Pair 2** because they have identical quantum numbers.

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