The nineteenth electron of chromium has which of the following set of quantum number?

Options

A. `{:(n,l,m,s),(3,0,0,1//2):}`
B. `{:(n,l,m,s),(3,2,-2,1//2):}`
C. `{:(n,l,m,s),(4,0,0,1//2):}`
D. `{:(n,l,m,s),(4,1,-1,1//2):}`

Explanation

To determine the quantum numbers of the nineteenth electron in chromium, we will follow these steps:

### Step 1: Identify the Atomic Number of Chromium
Chromium has an atomic number of 24. This means it has 24 electrons.

### Step 2: Write the Electronic Configuration of Chromium
The electronic configuration of chromium (Cr) is:
\[ \text{Cr: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^5 \]
This configuration shows that chromium has an exceptional case where one electron from the 4s subshell is promoted to the 3d subshell to achieve a more stable configuration.

### Step 3: Determine the Position of the Nineteenth Electron
To find the nineteenth electron, we count the electrons in the configuration:
- 1s: 2 electrons
- 2s: 2 electrons
- 2p: 6 electrons
- 3s: 2 electrons
- 3p: 6 electrons
- 4s: 1 electron (19th electron)
- 3d: 5 electrons

Thus, the nineteenth electron is in the 4s subshell.

### Step 4: Assign Quantum Numbers
Quantum numbers consist of four values:
1. **Principal Quantum Number (n)**: This indicates the energy level. For the 4s electron, \( n = 4 \).
2. **Azimuthal Quantum Number (l)**: This indicates the subshell. For s subshell, \( l = 0 \).
3. **Magnetic Quantum Number (m_l)**: This indicates the orientation of the orbital. For s subshell, \( m_l = 0 \).
4. **Spin Quantum Number (m_s)**: This indicates the spin of the electron. It can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \). We can choose \( +\frac{1}{2} \) for this electron.

### Step 5: Compile the Quantum Numbers
Thus, the quantum numbers for the nineteenth electron in chromium are:
- \( n = 4 \)
- \( l = 0 \)
- \( m_l = 0 \)
- \( m_s = +\frac{1}{2} \)

### Final Answer
The quantum numbers for the nineteenth electron of chromium are:
\[ (n, l, m_l, m_s) = (4, 0, 0, +\frac{1}{2}) \]