The correct set of four quantum numbers for valence electrons of rubidium atom (Z=37) is

Options

A. `5, 0, 0 +(1)/(2)`
B. `5,1,0,+(1)/(2)`
C. `5,1,1,+(1)/(2)`
D. `5,0,1,+(1)/(2)`

Explanation

To find the correct set of four quantum numbers for the valence electron of a rubidium atom (Z=37), we will follow these steps:

### Step 1: Determine the Electronic Configuration of Rubidium
Rubidium has an atomic number of 37, which means it has 37 electrons. The electronic configuration can be written as follows:

1. Fill the 1s orbital: 1s²
2. Fill the 2s orbital: 2s²
3. Fill the 2p orbital: 2p⁶
4. Fill the 3s orbital: 3s²
5. Fill the 3p orbital: 3p⁶
6. Fill the 4s orbital: 4s²
7. Fill the 3d orbital: 3d¹⁰
8. Fill the 4p orbital: 4p⁶
9. Fill the 5s orbital: 5s¹

Thus, the complete electronic configuration of rubidium is:
\[ \text{1s}^2 \, \text{2s}^2 \, \text{2p}^6 \, \text{3s}^2 \, \text{3p}^6 \, \text{4s}^2 \, \text{3d}^{10} \, \text{4p}^6 \, \text{5s}^1 \]

### Step 2: Identify the Valence Electron
The valence electron is the outermost electron, which in the case of rubidium is found in the 5s orbital. Therefore, the valence electron configuration is:
\[ \text{5s}^1 \]

### Step 3: Determine the Principal Quantum Number (n)
The principal quantum number (n) corresponds to the energy level of the electron. For the 5s electron, n = 5.

### Step 4: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) indicates the subshell type. For s orbitals, l = 0. Therefore, for the 5s electron:
\[ l = 0 \]

### Step 5: Determine the Magnetic Quantum Number (m_l)
The magnetic quantum number (m_l) describes the orientation of the orbital. For an s orbital (where l = 0), the only possible value for m_l is:
\[ m_l = 0 \]

### Step 6: Determine the Spin Quantum Number (m_s)
The spin quantum number (m_s) indicates the spin of the electron. It can have values of +1/2 or -1/2. For the valence electron, we can denote it as:
\[ m_s = +\frac{1}{2} \text{ or } -\frac{1}{2} \]

### Final Set of Quantum Numbers
Combining all the values, the set of quantum numbers for the valence electron in rubidium is:
- Principal quantum number (n) = 5
- Azimuthal quantum number (l) = 0
- Magnetic quantum number (m_l) = 0
- Spin quantum number (m_s) = +1/2 or -1/2

Thus, the complete set of quantum numbers can be expressed as:
\[ (n, l, m_l, m_s) = (5, 0, 0, +\frac{1}{2}) \text{ or } (5, 0, 0, -\frac{1}{2}) \]

### Conclusion
The correct set of quantum numbers for the valence electron of rubidium is:
\[ (5, 0, 0, +\frac{1}{2}) \text{ or } (5, 0, 0, -\frac{1}{2}) \]