Give the sets of quantum number that describe an electron in a `3p` orbital

Answer

To determine the sets of quantum numbers that describe an electron in a `3p` orbital, we need to identify the four quantum numbers: principal quantum number (n), angular momentum quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s). Here’s how we can derive them step by step:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the electron. For a `3p` orbital, the principal quantum number is:
- **n = 3**

### Step 2: Determine the Angular Momentum Quantum Number (l)
The angular momentum quantum number (l) defines the shape of the orbital. For `p` orbitals, the value of l is:
- **l = 1** (since `l` can take values from 0 to n-1, and for `p`, l = 1)

### Step 3: Find the Magnetic Quantum Number (m_l)
The magnetic quantum number (m_l) specifies the orientation of the orbital in space. The values of m_l range from -l to +l, which gives us:
- **m_l = -1, 0, +1** (for l = 1)

### Step 4: Determine the Spin Quantum Number (m_s)
The spin quantum number (m_s) describes the spin of the electron. An electron can have one of two possible spins:
- **m_s = +1/2 or -1/2**

### Summary of Quantum Numbers
Now we can summarize the sets of quantum numbers for an electron in a `3p` orbital:
1. **n = 3**
2. **l = 1**
3. **m_l = -1, 0, +1**
4. **m_s = +1/2 or -1/2**

### Final Sets of Quantum Numbers
Thus, the complete sets of quantum numbers for an electron in a `3p` orbital can be represented as:
- (3, 1, -1, +1/2)
- (3, 1, -1, -1/2)
- (3, 1, 0, +1/2)
- (3, 1, 0, -1/2)
- (3, 1, +1, +1/2)
- (3, 1, +1, -1/2)