Question

Calculate the total number of electrons that can occupy (a) one \(s\) orbital, (b) three \(p\) orbitals, (c) five \(d\) orbitals, (d) seven \(f\) orbitals.

Short answer

The total number of electrons that can occupy (a) one s orbital is 2, (b) three p orbitals is 6, (c) five d orbitals is 10, and (d) seven f orbitals is 14.

Step-by-step solution

Calculate for s orbital

An s orbital holds a maximum of 2 electrons. Since we have 1 s orbital, the total number of electrons is \(1 * 2 = 2\).

Calculate for p orbitals

A p orbital holds a maximum of 2 electrons. Since we have 3 p orbitals, we multiply the maximum capacity of a p orbital by the number of p orbitals. Thus the total number of electrons is \(3 * 2 = 6\).

Calculate for d orbitals

A d orbital holds a maximum of 2 electrons. Since we have 5 d orbitals, we multiply the maximum capacity of a d orbital by the number of d orbitals. Thus the total number of electrons is \(5 * 2 = 10\).

Calculate for f orbitals

An f orbital holds a maximum of 2 electrons. Since we have 7 f orbitals, we multiply the maximum capacity of an f orbital by the number of f orbitals. Thus, the total number of electrons is \(7 * 2 = 14\).

Key concepts

s orbital electrons

The s orbital is the simplest and most fundamental type of orbital found in an atom's electron cloud. It is spherical in shape and can only hold a maximum of 2 electrons. The reason for this is rooted in the rules of quantum mechanics, specifically the Pauli Exclusion Principle, which states that no two electrons can have the exact same set of quantum numbers.
So, when you hear about one s orbital, imagine a point in space that can host two electrons rotating in opposite spins to comply with this principle.
A simple way to remember this: think of the 's' in s orbital as standing for 'small' and 'simple', which helps in recalling that it holds just two electrons.

p orbital electrons

P orbitals are a bit more complex compared to s orbitals. They come in sets of three, collectively known as the p sublevel. Each p orbital is shaped as a dumbbell and can house up to 2 electrons. Therefore, the entire p sublevel, with its three orbitals, can hold a total of 6 electrons.
Visualizing these, imagine three equal energy orbitals oriented in three different planes — often noted as px, py, and pz. They get filled sequentially, following Hund’s Rule, which suggests that electrons will occupy empty orbitals first before pairing up in orbitals.
This property makes p orbitals crucial in forming the structure of atoms and influencing the chemical properties of elements, especially in non-metals and metalloids.

d orbital electrons

The d orbitals bring an additional layer of complexity and diversity to electron configurations. Each d sublevel consists of five d orbitals, each of which can accommodate 2 electrons, totaling up to 10 electrons for the entire d sublevel.
D orbitals are significant because they play a major role in the chemistry of transition metals. Their shapes are more intricate, often described by some as 'cloverleaf' formations, with multiple lobes. The d electron contribution is essential for elements that display variable oxidation states, color, and are involved in creating complex ions.
Understanding d orbitals is particularly valuable in fields like inorganic chemistry and materials science, where their properties dictate bonding and reactivity.

f orbital electrons

F orbitals are even more complex and are found in the deepest part of the periodic table, within the f sublevel. This sublevel contains seven f orbitals, and each can hold 2 electrons, allowing a total of 14 electrons for the f sublevel.
The f orbitals are crucial for the chemistry of the lanthanides and actinides, the two series of elements at the bottom of the periodic table. These orbitals have a very complex shape, often described as 'flower-like', and play a critical role in the magnetic and spectral properties of certain elements.
Given their role in the inner transitions, understanding f orbitals helps to appreciate the full electronic architecture of atoms and their intricate behaviors across more exotic or less commonly encountered elements in the periodic table.