Maximum electron in `1^(st)` shell having `m_(l) =2` will be

Options

A. 2
B. 0
C. 12
D. 24

Answer

To solve the question regarding the maximum number of electrons in the first shell with \( m_l = 2 \), we can follow these steps:

### Step 1: Identify the Principal Quantum Number
The first shell corresponds to the principal quantum number \( n = 1 \).

### Step 2: Determine the Azimuthal Quantum Number
The azimuthal quantum number \( l \) can take values from \( 0 \) to \( n-1 \). Therefore, for \( n = 1 \):
\[ l = 0 \]

### Step 3: Determine the Magnetic Quantum Number
The magnetic quantum number \( m_l \) can take values from \( -l \) to \( +l \). Since \( l = 0 \), the only possible value for \( m_l \) is:
\[ m_l = 0 \]

### Step 4: Analyze the Given Condition
The question states that \( m_l = 2 \). However, since the maximum value of \( m_l \) for \( l = 0 \) is \( 0 \), it is impossible to have \( m_l = 2 \) in the first shell.

### Step 5: Conclusion
Since \( m_l = 2 \) is not a valid value for the first shell, the maximum number of electrons that can exist in the first shell with \( m_l = 2 \) is:
\[ \text{Maximum electrons} = 0 \]

### Final Answer
The maximum number of electrons in the first shell having \( m_l = 2 \) is **0**.

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