Question

How many orbitals are in each of the following sublevels? (a) \(4 s\) (c) \(3 d\) (e) \(2 s\) (b) \(2 p\) (d) \(4 f\) (f) \(4 p\)

Short answer

(a) \(4 s\) has 1 orbital, (c) \(3 d\) has 5 orbitals, (e) \(2 s\) has 1 orbital, (b) \(2 p\) has 3 orbitals, (d) \(4 f\) has 7 orbitals, (f) \(4 p\) has 3 orbitals.

Step-by-step solution

Determining the number of orbitals in each sublevel

Assign the number of orbitals to each electron subshell. As mentioned: - \(s\) sublevel always has 1 orbital - \(p\) sublevel always has 3 orbitals - \(d\) sublevel always has 5 orbitals - \(f\) sublevel always has 7 orbitals We can use this information to find the number of orbitals for each sublevel in the provided exercise.

Assigning the number of orbitals for (a) \(4 s\)

Since the \(s\) sublevel always has 1 orbital, the \(4 s\) sublevel has 1 orbital.

Assigning the number of orbitals for (c) \(3 d\)

Since the \(d\) sublevel always has 5 orbitals, the \(3 d\) sublevel has 5 orbitals.

Assigning the number of orbitals for (e) \(2 s\)

Since the \(s\) sublevel always has 1 orbital, the \(2 s\) sublevel has 1 orbital.

Assigning the number of orbitals for (b) \(2 p\)

Since the \(p\) sublevel always has 3 orbitals, the \(2 p\) sublevel has 3 orbitals.

Assigning the number of orbitals for (d) \(4 f\)

Since the \(f\) sublevel always has 7 orbitals, the \(4 f\) sublevel has 7 orbitals.

Assigning the number of orbitals for (f) \(4 p\)

Since the \(p\) sublevel always has 3 orbitals, the \(4 p\) sublevel has 3 orbitals.

Key concepts

Sublevels

In chemistry, the concept of sublevels is pivotal to understanding the arrangement of electrons around an atom's nucleus. Sublevels refer to subdivisions within each principal energy level or electron shell. The principal energy levels, designated by the quantum number \( n \), are the general regions where an electron could be found. However, each of these energy levels can be broken down further into sublevels. This breakdown helps describe the specific 'address' of an electron within an atom.

• The number of sublevels within an energy level is equal to the principal quantum number \( n \).
• For instance, if \( n = 3 \), there are three sublevels: \( s, p, \) and \( d \).
• Each sublevel consists of one or more orbitals, which are spatial distributions of where electrons are likely to be located.

Understanding sublevels is a critical step towards grasping how electrons populate these various regions in atoms. Recognizing sublevels allows students to predict how electrons fill different energy spaces and how this arrangement impacts chemical properties.

s p d f orbitals

Electron orbitals are crucial in determining the electron distribution within an atom. These orbitals are clustered into sublevel categories identified by letters: \( s, p, d, \) and \( f \). Each type of orbital has its own unique shape and energy characteristics that influence electron behavior.

• \(s\) Orbitals: These orbitals are spherical in shape. Each \(s\) sublevel contains exactly one orbital.
• \(p\) Orbitals: These orbitals have a dumbbell shape and each \(p\) sublevel contains three orbitals, allowing more electrons to be accommodated.
• \(d\) Orbitals: These orbitals are more complex in shape, often described as cloverleaf-shaped. A \(d\) sublevel contains five orbitals, which means it can hold even more electrons.
• \(f\) Orbitals: With the most complex shape, \(f\) orbitals contain seven orbitals per sublevel.

This diversity in orbital structures and count helps determine not only the physical structure of complex atoms but also influences chemical reactivity and bonding.

Chemistry Education

Chemistry education plays a significant role in helping students understand fundamental concepts such as electron orbitals and sublevels. By breaking down complex theories into more digestible parts, educators empower students to see the connections between different areas of chemistry.

• Engagement through visualization: Using models and diagrams to represent sublevels and orbitals can help bridge the gap between theoretical knowledge and tangible understanding.
• Building foundational skills: Grasping these basic concepts lays the groundwork for more advanced studies in chemistry, such as quantum mechanics and chemical bonding.
• Encouragement of analytical thinking: Chemistry education encourages students to think critically about how electrons influence the macroscopic properties of materials.

Ultimately, focusing on detailed yet simple explanations ensures that students not only learn but appreciate the beauty and complexity of the atomic world. By fostering curiosity and comprehension, chemistry education opens doors to numerous scientific careers and instills a lifelong appreciation for the subject.