(a) How many sublevels are in the third main energy level?...

(a) How many sublevels are in the third main energy level?
(b) Which, if any, of these sublevels contain a set of equivalent orbitals?
(c) Sketch, on the same relative scale, at least one orbital from each of these sublevels.

Key Concepts

Atomic Orbitals

Atomic orbitals are mathematical functions that describe the spatial distribution of electrons around the nucleus. They represent regions in space where an electron is most likely to be found and are characterized by quantum numbers. Their shapes and relative orientations are fundamental in understanding the electron configuration of atoms.

Principal Quantum Number

This quantum number identifies the main energy level (shell) of an electron in an atom and largely determines its energy difference from other levels. It sets the stage for the number of available sublevels in that energy level, with the possible value of the angular momentum quantum number ranging from 0 to n-1.

Angular Momentum Quantum Number and Sublevels

The angular momentum quantum number, represented as l, determines the type and shape of an orbital within a main energy level. Each value of l corresponds to a sublevel (such as s, p, d, f) and defines the number and type of orbitals present in that sublevel, thereby directly answering questions regarding the structure of energy levels.

Equivalent Orbitals

Equivalent orbitals are orbitals within the same sublevel that have identical energy and shape characteristics. They form a set of degenerate orbitals that hold electrons with similar spatial distributions, and understanding this concept is essential when discussing electron configurations and the geometric arrangement of electrons within an atom.

Transcript

00:02 Hi there.

00:03 Welcome to question number 86.

00:07 86 actually is three questions in one.

00:09 We have a part a, a part b, and a part c.

00:12 So let's get started with part a.

00:15 Part a asks about the third energy level.

00:19 So that means the principal quantum number is n equals three.

00:22 And it wants to know how many sub -levels there are.

00:25 Well, when n equals three, remember, l ranges from zero to n -minus one.

00:32 So l.

00:32 L could be 0, 1, or 2.

00:37 This gives us 3 sub -levels.

00:45 So when n equals 3, there are 3 sub -levels.

00:51 Moving on to question b.

00:54 Question b wants to know about these sub -levels, and if any of them contain a set of equivalent orbitals.

01:02 So let's think about what the letters for l mean, or the numbers rather for l.

01:08 When the angular momentum quantum number or l is zero, that represents s orbitals, when l equals 1, that represents p, and when l equals 2, that represents d.

01:23 So s orbitals, there's only one of those.

01:26 Each time you have an s, there's only one of those...

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