The atomic number of chromium is `24` Its electronic configuration in ground state in `1s^(2) 2s^(2)2p^(6)3s^(2)3p^(6)4s^(1) 3d^(5)` Now answer the following questions
The number of electron having `n = 3` and `m_(1) = 0` in chromium atom is

Options

A. 2
B. 5
C. 4
D. 1

Explanation

To solve the question regarding the number of electrons in a chromium atom with principal quantum number \( n = 3 \) and magnetic quantum number \( m_l = 0 \), we will analyze the electronic configuration step by step.

### Step-by-Step Solution:

1. **Identify the Electronic Configuration**:
The electronic configuration of chromium (Cr) is given as:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^5 \]

2. **Determine the Relevant Shells**:
We need to focus on the electrons in the shell where the principal quantum number \( n = 3 \). The relevant subshells for \( n = 3 \) are:
- \( 3s \)
- \( 3p \)
- \( 3d \)

3. **Analyze the \( 3s \) Subshell**:
- The \( 3s \) subshell has \( l = 0 \).
- The magnetic quantum number \( m_l \) can only take the value \( 0 \) for \( s \) orbitals.
- The number of electrons in \( 3s \) is \( 2 \) (from \( 3s^2 \)).

4. **Analyze the \( 3p \) Subshell**:
- The \( 3p \) subshell has \( l = 1 \).
- The magnetic quantum number \( m_l \) can take values of \( -1, 0, +1 \).
- The number of electrons in \( 3p \) is \( 6 \) (from \( 3p^6 \)).
- The number of electrons with \( m_l = 0 \) in \( 3p \) is \( 2 \) (since there are three orbitals, each can hold 2 electrons, and one of them corresponds to \( m_l = 0 \)).

5. **Analyze the \( 3d \) Subshell**:
- The \( 3d \) subshell has \( l = 2 \).
- The magnetic quantum number \( m_l \) can take values of \( -2, -1, 0, +1, +2 \).
- The number of electrons in \( 3d \) is \( 5 \) (from \( 3d^5 \)).
- The number of electrons with \( m_l = 0 \) in \( 3d \) is \( 1 \) (since there is one electron in the \( m_l = 0 \) orbital).

6. **Total Count of Electrons**:
Now, we sum the number of electrons with \( n = 3 \) and \( m_l = 0 \):
- From \( 3s \): \( 2 \)
- From \( 3p \): \( 2 \)
- From \( 3d \): \( 1 \)

Total:
\[ 2 (from \, 3s) + 2 (from \, 3p) + 1 (from \, 3d) = 5 \]

### Final Answer:
The total number of electrons in a chromium atom with \( n = 3 \) and \( m_l = 0 \) is \( 5 \).

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