The set of quantum number for the `19^(th)` electrons in chromium is -

Options

A. `4,0,0,1/2`
B. `4,1,-1,1/2`
C. `3,2,2,1/2`
D. `3,2,-2,1/2`

Answer

To find the set of quantum numbers for the 19th electron in chromium (Cr), we will follow these steps:

### Step 1: Determine the Atomic Number of Chromium
Chromium has an atomic number of 24, which means it has 24 electrons.

### Step 2: Write the Electron Configuration
The electron configuration for chromium is:
\[ \text{Cr: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5 \]

### Step 3: Identify the 19th Electron
To find the 19th electron, we will count the electrons in the configuration:
- 1s: 2 electrons
- 2s: 2 electrons
- 2p: 6 electrons
- 3s: 2 electrons
- 3p: 6 electrons
- 4s: 1 electron
- 3d: 5 electrons

Adding these:
\[ 2 + 2 + 6 + 2 + 6 + 1 = 19 \]

Thus, the 19th electron is in the 4s subshell.

### Step 4: Determine the Quantum Numbers
The quantum numbers consist of:
1. Principal quantum number (n)
2. Azimuthal quantum number (l)
3. Magnetic quantum number (m_l)
4. Spin quantum number (m_s)

For the 4s subshell:
- **Principal quantum number (n)**: For the 4s subshell, \( n = 4 \).
- **Azimuthal quantum number (l)**: For s orbitals, \( l = 0 \).
- **Magnetic quantum number (m_l)**: Since \( l = 0 \), \( m_l = 0 \).
- **Spin quantum number (m_s)**: The first electron in the 4s subshell will have a spin of \( +\frac{1}{2} \) (clockwise).

### Step 5: Compile the Quantum Numbers
Thus, the set of quantum numbers for the 19th electron in chromium is:
\[ (n, l, m_l, m_s) = (4, 0, 0, +\frac{1}{2}) \]

### Final Answer
The set of quantum numbers for the 19th electron in chromium is:
\[ \boxed{(4, 0, 0, +\frac{1}{2})} \]

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