How many electrons can the 5f subshell/sublevel have? Write down their quantum numbers. (Four quantum numbers for each electron) 5f
The Correct Answer and Explanation is:
The 5f subshell can hold a maximum of 14 electrons, as it consists of 7 orbitals (each orbital can hold 2 electrons, one with spin-up and the other with spin-down).
Quantum Numbers
Each electron in an atom is described by a set of four quantum numbers:
- Principal Quantum Number (n): This indicates the energy level or shell. For the 5f subshell, n=5n = 5n=5.
- Azimuthal Quantum Number (l): This defines the subshell (or type of orbital). For the f subshell, l=3l = 3l=3.
- Magnetic Quantum Number (ml_ll): This describes the orientation of the orbital in space. For an f subshell (l=3l = 3l=3), mlm_lml can have values from -3 to +3, which gives the following values: -3, -2, -1, 0, 1, 2, 3 (7 possible orientations).
- Spin Quantum Number (ms_ss): This describes the spin of the electron. Each orbital can hold two electrons with opposite spins, so the values of msm_sms are +1/2 (spin-up) and -1/2 (spin-down).
The Quantum Numbers for Each Electron in the 5f Subshell
For the 14 electrons in the 5f subshell, the quantum numbers will be:
| Electron | n | l | ml_ll | ms_ss |
|---|---|---|---|---|
| 1 | 5 | 3 | -3 | +1/2 |
| 2 | 5 | 3 | -3 | -1/2 |
| 3 | 5 | 3 | -2 | +1/2 |
| 4 | 5 | 3 | -2 | -1/2 |
| 5 | 5 | 3 | -1 | +1/2 |
| 6 | 5 | 3 | -1 | -1/2 |
| 7 | 5 | 3 | 0 | +1/2 |
| 8 | 5 | 3 | 0 | -1/2 |
| 9 | 5 | 3 | +1 | +1/2 |
| 10 | 5 | 3 | +1 | -1/2 |
| 11 | 5 | 3 | +2 | +1/2 |
| 12 | 5 | 3 | +2 | -1/2 |
| 13 | 5 | 3 | +3 | +1/2 |
| 14 | 5 | 3 | +3 | -1/2 |
Each electron has the same n and l quantum numbers (5 and 3), but they differ in ml_ll and ms_ss values due to the different orientations of the orbitals and the possible spins.
Explanation of the Quantum Numbers
- n = 5: The 5th energy level (shell).
- l = 3: This corresponds to the f orbital, which can hold up to 14 electrons (7 orbitals, each with two possible spins).
- ml_ll: Each orbital can have a different orientation. For f orbitals, these orientations are -3, -2, -1, 0, 1, 2, and 3.
- ms_ss: Since electrons have two possible spin states (spin-up and spin-down), each orbital can hold two electrons with opposite spins.
Thus, the 5f subshell can accommodate 14 electrons with these quantum numbers.
