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

Answer

To describe an electron in a 3p orbital, we need to determine the four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (ms). Here’s how we can find each of these:

### Step 1: Determine 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 Azimuthal Quantum Number (l)
The azimuthal quantum number (l) defines the shape of the orbital. For p orbitals, the value of l is:
- **l = 1** (since p orbitals correspond to l = 1)

### Step 3: Determine the Magnetic Quantum Number (m)
The magnetic quantum number (m) specifies the orientation of the orbital in space. For p orbitals (l = 1), the possible values of m are:
- **m = -1, 0, +1**

### Step 4: Determine the Spin Quantum Number (ms)
The spin quantum number (ms) describes the intrinsic spin of the electron. It can take one of two values:
- **ms = +1/2 or -1/2**

### Summary of Quantum Numbers
Putting it all together, the sets of quantum numbers that describe an electron in a 3p orbital are:
- **(n, l, m, ms) = (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)**

### Final Answer
The complete sets of quantum numbers for an electron in a 3p orbital are:
1. (3, 1, -1, +1/2)
2. (3, 1, -1, -1/2)
3. (3, 1, 0, +1/2)
4. (3, 1, 0, -1/2)
5. (3, 1, +1, +1/2)
6. (3, 1, +1, -1/2)