For valence electron of rubidium (Z = 37) , the correct set of four quantum number are

Options

A. `5,1,0 +1/2`
B. `5,0,0 +1/2`
C. `5,1,1 +1/2`
D. `6,0,0 +1/2`

Answer

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

### Step 1: Identify the Electronic Configuration
Rubidium has an atomic number of 37. The electronic configuration of rubidium can be derived from the periodic table. It can be written as:
\[ \text{Rb: } [Kr] 5s^1 \]
This indicates that rubidium has one electron in the 5s subshell.

### Step 2: Determine the Principal Quantum Number (n)
The principal quantum number (n) indicates the main energy level or shell in which the electron resides. For the valence electron in rubidium, which is in the 5s subshell, we have:
\[ n = 5 \]

### Step 3: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) describes the shape of the orbital. For the s orbital, the value of l is:
\[ l = 0 \]
This is because s orbitals are spherical in shape.

### Step 4: 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 5: Determine the Spin Quantum Number (m_s)
The spin quantum number (m_s) describes the spin of the electron. It can have two possible values:
\[ m_s = +\frac{1}{2} \quad \text{or} \quad m_s = -\frac{1}{2} \]
For this example, we can choose:
\[ m_s = +\frac{1}{2} \]

### Step 6: Compile the Quantum Numbers
Now we can compile the quantum numbers for the valence electron of rubidium:
- Principal quantum number (n) = 5
- Azimuthal quantum number (l) = 0
- Magnetic quantum number (m_l) = 0
- Spin quantum number (m_s) = +\frac{1}{2}

Thus, the correct set of four quantum numbers for the valence electron of rubidium is:
\[ (n, l, m_l, m_s) = (5, 0, 0, +\frac{1}{2}) \]

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

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