List all the possible quantum numbers for an electron in the 3p orbital.
The correct answer and explanation is:
✅ Correct Answer:
All possible quantum numbers for an electron in the 3p orbital are:
- Principal quantum number (n) = 3
- Azimuthal (angular momentum) quantum number (l) = 1 (p orbital)
- Magnetic quantum number (ml) = –1, 0, +1
- Spin quantum number (ms) = –½ or +½
🧠 Explanation (Approx. 300 Words):
Quantum numbers are a set of values that describe the unique quantum state of an electron in an atom. They arise from solutions to the Schrödinger equation and define an electron’s position, energy, and spin. An electron in the 3p orbital is characterized by four specific quantum numbers:
1. Principal Quantum Number (n):
This number indicates the main energy level or shell of the electron.
For the 3p orbital, n = 3.
This means the electron is in the third energy level, farther from the nucleus compared to electrons in n = 1 or n = 2.
2. Azimuthal Quantum Number (l):
This number determines the subshell and shape of the orbital:
- For s orbitals, l = 0
- For p orbitals, l = 1
So, a 3p orbital has l = 1.
3. Magnetic Quantum Number (ml):
This number represents the orientation of the orbital in space.
It depends on the value of l, ranging from –l to +l.
- Since l = 1, ml can be –1, 0, or +1.
This gives us 3 possible orientations of a p orbital (px, py, and pz).
4. Spin Quantum Number (ms):
This indicates the spin direction of the electron:
- ms = +½ or –½
Each orbital orientation (ml value) can hold 2 electrons with opposite spins.
🔢 Combining All:
Each of the 3 ml values (–1, 0, +1) can have 2 spin values (±½), resulting in a total of 6 possible sets of quantum numbers for electrons in a 3p orbital.