The quantum numbers for the `19^(th)` electron of `Cr (Z=24)` are :

Answer

To determine the quantum numbers for the 19th electron of chromium (Cr, Z=24), we can follow these steps:

### Step 1: Write the electronic configuration of chromium.
The electronic configuration of chromium is:
\[ \text{Cr: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^5 \]

### Step 2: Identify the position of the 19th electron.
In the electronic configuration, we count the electrons:
- 1s: 2 electrons
- 2s: 2 electrons
- 2p: 6 electrons
- 3s: 2 electrons
- 3p: 6 electrons
- 4s: 1 electron
- 3d: 5 electrons

Adding these gives us a total of 24 electrons, confirming that we are dealing with chromium. The 19th electron corresponds to the last electron in the 4s orbital.

### Step 3: Determine the quantum numbers for the 19th electron.
Quantum numbers are defined as follows:
- Principal quantum number (n): Indicates the energy level. For the 4s orbital, \( n = 4 \).
- Azimuthal quantum number (l): Indicates the subshell. For an s orbital, \( l = 0 \).
- Magnetic quantum number (m_l): Indicates the orientation of the orbital. For an s orbital, \( m_l = 0 \).
- Spin quantum number (s): Indicates the spin of the electron, which can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \). We can choose \( +\frac{1}{2} \) for this electron.

### Final Answer:
The quantum numbers for the 19th electron of chromium are:
- \( n = 4 \)
- \( l = 0 \)
- \( m_l = 0 \)
- \( s = +\frac{1}{2} \)