Two electrons in K shell will not have

Options

A. Same principle quantum number
B. Same azimuthal quantum number
C. Same magnetic number
D. Same spin quantum number

Explanation

To solve the question "Two electrons in K shell will not have...", we need to analyze the quantum numbers associated with electrons in the K shell (the first energy level).

### Step-by-Step Solution:

1. **Identify the K Shell**:
- The K shell corresponds to the first principal energy level, denoted by the principal quantum number \( n = 1 \).

2. **Determine the Quantum Numbers**:
- For the K shell, the only subshell available is the 1s subshell.
- The quantum numbers for electrons in the K shell are:
- Principal quantum number (\( n \)): 1
- Azimuthal quantum number (\( l \)): 0 (for s subshell)
- Magnetic quantum number (\( m_l \)): 0 (since \( m_l \) can take values from \(-l\) to \(+l\))
- Spin quantum number (\( m_s \)): can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \)

3. **Apply the Pauli Exclusion Principle**:
- According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of four quantum numbers.
- Since both electrons in the K shell will have the same \( n \), \( l \), and \( m_l \) values, the only quantum number that can differ is the spin quantum number (\( m_s \)).

4. **Conclusion**:
- Therefore, two electrons in the K shell cannot have the same spin quantum number. One must have \( m_s = +\frac{1}{2} \) and the other must have \( m_s = -\frac{1}{2} \).

### Final Answer:
Two electrons in the K shell will not have the same spin quantum number.

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