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

Options

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

Explanation

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

### Step 1: Determine the Electronic Configuration
Rubidium (Rb) has an atomic number of 37. The electronic configuration can be determined by filling the orbitals according to the Aufbau principle. The configuration is:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹
This shows that the valence electron is in the 5s orbital.

### Step 2: Identify the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the electron. For the 5s orbital, n = 5.

### Step 3: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) corresponds to the shape of the orbital. For s orbitals, l = 0. Therefore, for the 5s orbital, l = 0.

### Step 4: Identify the Magnetic Quantum Number (m_l)
The magnetic quantum number (m_l) describes the orientation of the orbital. For s orbitals, m_l = 0. Thus, for the 5s orbital, m_l = 0.

### Step 5: Determine the Spin Quantum Number (m_s)
The spin quantum number (m_s) describes the spin of the electron. There are two possible values: +1/2 or -1/2. Since we are considering the first valence electron in the 5s orbital, we can assign it a spin of +1/2.

### Step 6: Compile the Quantum Numbers
Now we can compile the four quantum numbers for the valence electron in rubidium:
- n = 5
- l = 0
- m_l = 0
- m_s = +1/2

Thus, the correct set of quantum numbers for the valence electron of rubidium is:
**(5, 0, 0, +1/2)**

### Final Answer
The correct set of four quantum numbers for the valence electron of rubidium atom (Z=37) is (5, 0, 0, +1/2).

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