Write down the values of all the quantum numbers for 19 th electron of `Cr (Z = 24)`.

Answer

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

### Step 1: Determine the Electron Configuration of Chromium
Chromium has an atomic number of 24, which means it has 24 electrons. The electron configuration of chromium is:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵

### Step 2: Identify the 19th Electron
To find the 19th electron, we can count the electrons in the configuration:
- 1s² (2 electrons)
- 2s² (2 electrons)
- 2p⁶ (6 electrons)
- 3s² (2 electrons)
- 3p⁶ (6 electrons)
- 4s¹ (1 electron)
- 3d⁵ (5 electrons)

Counting these gives us:
- 2 + 2 + 6 + 2 + 6 + 1 + 0 = 19

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

### Step 3: Assign Quantum Numbers
1. **Principal Quantum Number (n)**: This indicates the energy level of the electron. For the 19th electron in the 4s subshell, n = 4.

2. **Azimuthal Quantum Number (l)**: This indicates the subshell. For the s subshell, l = 0.

3. **Magnetic Quantum Number (m_l)**: This indicates the orientation of the orbital. For the s subshell (l = 0), m_l = 0.

4. **Spin Quantum Number (s)**: This indicates the spin of the electron. The possible values are +1/2 or -1/2. We can choose +1/2 for this electron.

### Summary of Quantum Numbers
- **n** = 4
- **l** = 0
- **m_l** = 0
- **s** = +1/2

### Final Answer
The quantum numbers for the 19th electron of chromium (Cr, Z = 24) are:
- n = 4
- l = 0
- m_l = 0
- s = +1/2