How many electrons maximum can occupy a 4f sublevel?
The correct answer and explanation is:
The maximum number of electrons that can occupy a 4f sublevel is 14.
Explanation:
In atomic physics, electrons occupy orbitals in specific sublevels, each with a unique capacity based on quantum mechanical principles. The 4f sublevel is one of the f-block sublevels, which corresponds to the fourth energy level (n=4) of an atom.
To understand how many electrons a 4f sublevel can hold, consider the following:
- Types of Orbitals: The f sublevel has 7 orbitals. Each orbital can hold a maximum of 2 electrons. This is a result of the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers.
- Electron Capacity: Since each of the 7 f orbitals can hold 2 electrons, the total number of electrons that can be accommodated in the 4f sublevel is calculated by multiplying the number of orbitals (7) by the number of electrons per orbital (2), i.e.: 7 orbitals×2 electrons/orbital=14 electrons7 \, \text{orbitals} \times 2 \, \text{electrons/orbital} = 14 \, \text{electrons}
- Quantum Numbers: The f orbitals in the 4f sublevel are characterized by specific quantum numbers. The principal quantum number (n) is 4, which means that these orbitals are part of the fourth energy level. The angular momentum quantum number (l) for f orbitals is 3. The magnetic quantum number (mₗ) can take values from -3 to +3, giving 7 distinct values (one for each orbital). The spin quantum number (mₛ) can take values of +½ or -½, accounting for the two possible electron spins.
In conclusion, the 4f sublevel, with its 7 orbitals, can hold a maximum of 14 electrons.