(a) Use the periodic table of Figure 9-13 to determine the ground state configurations for the a

(a) Use the periodic table of Figure 9-13 to determine the...

Key Concepts

Spectroscopic Notation

Spectroscopic notation is a concise way to represent the quantum states of an atom using term symbols written in the form 2S+1L_J. Here, 2S+1 indicates the spin multiplicity, L is denoted by letters (S, P, D, F, …) corresponding to orbital angular momentum values, and J represents the total angular momentum. This notation encapsulates the overall symmetry and energy state of the ground or excited levels.

Hund's Rules

Hund's Rules are guidelines that help predict the ground state term symbol of an atom. They state that the term with maximum multiplicity (largest S) has the lowest energy, and for terms with the same multiplicity, the term with the largest orbital angular momentum (L) is favored. They also provide insights for determining the total angular momentum (J) in cases with multiple possible values.

LS Coupling (Russell-Saunders Coupling)

LS coupling describes how the individual orbital angular momenta (L) and spin angular momenta (S) of electrons combine to form the total orbital and spin angular momenta of an atom. This approach is most applicable to light atoms where spin–orbit coupling is relatively weak, allowing separate summation of orbital and spin contributions before combining them.

Electron Configuration

This concept involves the arrangement of electrons in an atom’s orbitals according to the Pauli Exclusion Principle and the Aufbau Principle. It determines which orbitals are occupied, the order of filling, and how electrons are distributed among subshells based on energy levels.

Transcript

00:01 Hi there.

00:02 So for this problem, for part a of this problem, we are asked to use the periodic table that is shown in here to determine the ground state configuration for the atoms of manisium, aluminum, and silicon.

00:21 So as you can see from the periodic table, you can see that this corresponds to the row 3 .8.

00:36 These elements.

00:38 You can see it in here.

00:39 This is magnesium, aluminum, and silicon.

00:45 So the columns reveal that the last shell is being filled.

00:53 It's being filled.

00:55 So the row, the numbers of the electrons in that shell.

00:58 So therefore, we will have that for 12 magnetion.

01:05 Its configuration is just simply 1 s square s 2 2 s 2 2 p 6 6 and 3 s 2 for aluminum we will have that its configuration is 1 s 2 2 2 2 2 p 6 3 s 2 and then we will have 1 in the p 6 shell.

01:44 Now for silicon, 14 silicon, we're going to have that this is 1s2, 2 s2, 2p6 and 3s2 and 3p2.

02:04 Now for part b of this problem, we are asked about to then predict the ls -caupling quantum numbers from the ground state of each atom.

02:18 So for 12 magnesium, we will have that.

02:29 The configuration represents a field shell.

02:33 And thus, field, shell, so the angular momentum, angular momenta, so all the angular momento, all angular momentum are zero, leading to then 1 s sub -zero.

03:02 Now, for 13 alumina, in this case, we know that there is a single balance electron that is s is equal to s prime, that is equal to 1 divided by 2, does 2 times s prime plus 1 should be equal to 2 and l prime should be equal to 1 given a p state and that p state it has a value g prime equals to 3 divided by 2 or 1 divided by 2 with the smaller j prime line lower and leading this then to 2 p 1 divided by two state...

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