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

(a) How many sublevels are in the second 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

Orbital Representation

Orbital representation involves sketching the geometrical shapes that depict the regions in space where there is a high probability of finding an electron. The sketches illustrate the relative sizes and orientations of orbitals from different sublevels, such as the spherical s orbital and the dumbbell-shaped p orbital, providing a visual understanding of atomic structure.

Main Energy Level

The main energy level (or electron shell) is defined by the principal quantum number (n). It determines the electron's average distance from the nucleus and establishes the overall size and energy of the shell, which is foundational for understanding the arrangement of electrons in an atom.

Sublevels

Sublevels, or subshells, are divisions within a main energy level determined by the azimuthal quantum number (l). Each sublevel is associated with a specific orbital shape (s, p, d, f, etc.) and exists within a main energy level. For example, the second main energy level (n = 2) has two sublevels: one with l = 0 (s) and one with l = 1 (p).

Equivalent Orbitals

Equivalent orbitals are orbitals within the same sublevel that possess the same energy, shape, and orientation properties, meaning that they are degenerate. This concept is significant in understanding how electrons are distributed among orbitals according to Hund’s rule, where orbitals of equal energy are singly occupied before any pairing occurs.

Transcript

00:01 Hi there.

00:02 This is question number 87.

00:06 Question number 87 has three parts to it, an a, a b and a c.

00:10 Part a wants to know how many sub -levels we have when we're on the second main energy level.

00:17 So let's think about what that means.

00:19 That means a principal quantum number of two.

00:21 That would be our second main energy level.

00:24 When the principal quantum number is two, the angular momentum quantum number, or l, is an integer between zero, and n minus 1.

00:38 So that gives us just two possible options, 0 or 1.

00:42 When l equals 0, that corresponds to an s orbital.

00:46 When l equals 1, that corresponds to p orbitals.

00:50 With the point being here, that we have two sub -levels, the s and the p.

01:04 Okay, moving to part b.

01:07 Part b asks us, which of any of these sub -levels contain a set of equivalent orbitals? so s only has one orbital, but p does have a set of equivalent orbitals.

01:23 There's one p orbital that sets up along the y -axis, one along the x -axis in space, and one along the z -axis.

01:35 So in other words, we have three p orbitals that are equivalent.

01:42 So the p orbitals are equivalent...

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