Question

What is the maximum number of electrons in each of the following sublevels? (a) \(2 s\) (b) \(4 p\) (c) \(3 d\) (d) \(5 f\)

Short answer

Maximum electrons: (a) 2s = 2, (b) 4p = 6, (c) 3d = 10, (d) 5f = 14.

Step-by-step solution

Understanding Electron Capacity in Orbitals

Each sublevel can hold a specific number of electrons due to the shape and orientation of its orbitals. The general rule is that the s sublevel has 1 orbital, p has 3 orbitals, d has 5 orbitals, and f has 7 orbitals. Each orbital can hold a maximum of 2 electrons.

Calculate Maximum Electrons in 2s Sublevel

The 2s sublevel consists of only one orbital. Therefore, the maximum number of electrons it can hold is:\[1 ext{ orbital} imes 2 ext{ electrons/orbital} = 2 ext{ electrons} \]

Calculate Maximum Electrons in 4p Sublevel

The 4p sublevel contains three orbitals. Therefore, it can hold:\[3 ext{ orbitals} imes 2 ext{ electrons/orbital} = 6 ext{ electrons} \]

Calculate Maximum Electrons in 3d Sublevel

The 3d sublevel contains five orbitals. Therefore, it can hold:\[5 ext{ orbitals} imes 2 ext{ electrons/orbital} = 10 ext{ electrons} \]

Calculate Maximum Electrons in 5f Sublevel

The 5f sublevel contains seven orbitals. Therefore, it can hold:\[7 ext{ orbitals} imes 2 ext{ electrons/orbital} = 14 ext{ electrons} \]

Key concepts

Atomic Orbitals

Atomic orbitals are regions in an atom where electrons reside. They are defined by three dimensional probability maps which describe where an electron is likely to be located around the nucleus.
Each type of orbital (s, p, d, f) has a distinct shape and energy level. The shapes of orbitals are crucial as they influence how atoms bond with each other in molecules.

• s orbitals are spherical and can be found in all principal energy levels.
• p orbitals have a dumbbell shape and are oriented along the x, y, and z axes, leading to three distinct orbitals (px, py, pz) in a given p sublevel.
• d orbitals are more complex, having cloverleaf shapes. They contain a total of five orbitals in every d sublevel.
• f orbitals are even more intricate, with seven orbitals, often found in the chemistry of heavier elements.

Sublevels

Sublevels, or subshells, are divisions within principal energy levels in an atom. They further structure atomic orbitals based on similar energy levels.
For instance, the second energy level (n=2) includes the 2s and 2p sublevels, each containing orbitals with their unique shapes and orientations.

• The s sublevel has one spherical orbital.
• The p sublevel includes three orbitals, giving it a higher electron capacity.
• The d sublevel, with its five orbitals, is more complex and accommodates more electrons.
• The f sublevel, containing seven orbitals, is the most complex, allowing for substantial electron accommodation.

Sublevels play a key role in the electron configuration of elements, influencing chemical properties and reactivity.

Electron Capacity

When discussing electron capacity, we refer to how many electrons can fit in each type of sublevel. This is based on the number of orbitals each sublevel contains and their capacity to hold electrons.
Every orbital can hold a maximum of 2 electrons, based on the Pauli Exclusion Principle. Hence:

• s sublevels can hold a total of 2 electrons because they have 1 orbital.
• p sublevels can hold 6 electrons as they consist of 3 orbitals.
• d sublevels hold 10 electrons due to their 5 orbitals.
• f sublevels hold the maximum of 14 electrons with 7 orbitals.

Understanding electron capacity is crucial for predicting element behavior as it relates to bonding and chemical reactions. This concept is the backbone of determining how many electrons reside in each sublevel, thereby influencing the atom's electron configuration.