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 for the 19th electron of chromium, we will follow these steps:

### Step 1: Determine the Electron Configuration of Chromium
Chromium (Cr) has an atomic number of 24, which means it has 24 electrons. The electron configuration of chromium is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^5 \]

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

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

### Step 3: Assign the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the electron. For the 4s orbital:
\[ n = 4 \]

### Step 4: Assign the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) defines the shape of the orbital. For s orbitals:
\[ l = 0 \]

### Step 5: Assign the Magnetic Quantum Number (m)
The magnetic quantum number (m) describes the orientation of the orbital. For s orbitals (l = 0):
\[ m = 0 \]

### Step 6: Assign the Spin Quantum Number (s)
The spin quantum number (s) can be either +1/2 or -1/2. For the 19th electron in the 4s orbital, we can assign:
\[ s = +\frac{1}{2} \]
(Note: The spin can also be -1/2, but we will choose +1/2 for this example.)

### Final Quantum Numbers
Thus, the set of quantum numbers for the 19th electron in chromium is:
- \( n = 4 \)
- \( l = 0 \)
- \( m = 0 \)
- \( s = +\frac{1}{2} \)

### Conclusion
The correct set of quantum numbers for the 19th electron of chromium is:
\[ (n, l, m, s) = (4, 0, 0, +\frac{1}{2}) \]