As you have seen, the periodic table is a result of...

As you have seen, the periodic table is a result of empirical observation (i.e., the periodic law), but quantum-mechanical theory explains why the table is so arranged. Suppose that, in another universe, quantum theory was such that there were one sorbital but only two $p$ orbitals (instead of three) and only three $d$ orbitals (instead of five). Draw out the first four periods of the periodic table in this alternative universe. Which elements would be the equivalent of the noble gases? Halogens? Alkali metals?

As you have seen, the periodic table is a result of empirical observation
(i.e., the periodic law), but quantum-mechanical theory explains why the
table is so arranged. Suppose that, in another universe, quantum theory
was such that there were one sorbital but only two $p$ orbitals (instead of
three) and only three $d$ orbitals (instead of five). Draw out the first four
periods of the periodic table in this alternative universe. Which elements
would be the equivalent of the noble gases? Halogens? Alkali metals?

Key Concepts

Quantum Mechanics and Atomic Orbitals

Quantum mechanics explains the structure of atoms through orbitals, which are regions in space where electrons are likely to be found. These orbitals (such as s, p, and d) have specific shapes and energy levels determined by quantum numbers. The quantum mechanical model provides the theoretical basis for understanding the allowed electron arrangements in atoms and how these arrangements influence the chemical properties of elements.

Electron Configuration and the Aufbau Principle

Electron configuration involves the distribution of electrons among the available orbitals of an atom. The Aufbau principle, which means 'building up', allows us to predict the order in which orbitals are filled as the atomic number increases. This systematic filling, along with the Pauli exclusion principle and Hund's rule, is key to explaining the repeating chemical properties observed in the periodic table.

The Periodic Table and Periodic Law

The periodic table organizes elements based on recurring chemical properties that arise from their electron configurations. The periodic law states that the physical and chemical properties of elements are periodic functions of their atomic numbers. This organization emerges directly from the sequential filling of electron orbitals, providing a visual and conceptual framework for understanding element behavior.

Impact of Orbital Degeneracy on Periodic Structure

The degeneracy of orbitals—how many orbitals of a particular type are available in a given energy level—directly influences the number of electrons that can be accommodated in that shell. Alterations in orbital degeneracy, such as having fewer p or d orbitals than in our universe, would change the number of elements in each period of the periodic table. This highlights how fundamental quantum properties are closely linked to the overall structure and periodicity observed in elemental families.

Classification of Element Groups

Elements in the periodic table are classified into groups (such as noble gases, halogens, and alkali metals) based on similar electron configurations and recurring chemical properties. These classifications are a direct consequence of the filling patterns of electron orbitals. In any universe, changes to orbital numbers would shift group boundaries, but the underlying concept of periodicity and element classification would still be governed by electron configuration principles.

Transcript

00:01 So this problem is asking us to draw out the first four periods of an alternate universe's periodic table, where there's a slight difference in the quantum numbers of their orbitals.

00:20 So our s orbital is still going to be holding two, but our p orbital has, um, has two orbits instead of three, so it's only going to be able to hold four electrons, and our d -orbital has three orbits instead of five, so it's only going to be able to hold six electrons.

00:53 And we're being asked to draw out what would that periodic table look like if those were our quantum numbers.

01:00 So what we're looking at here is if we were to draw this out, we would have a 1s1, we would have a 1s2.

01:15 And actually i'm going to move that a little bit further away, just because we're going to need this space, 1s2.

01:27 And then we would have a 2s1, a 2s1.

01:31 A 2s2 and then we would get into our p orbits so then we would have a 2 s 2 2 p 1 2 s 2 2 p 2 2 these a little bit here we would have a 2 s 2 2 p 3 and a 2 s 2 p 4 and that's where it would stop because we would have filled the p shell.

02:24 This one over here.

02:27 1s2.

02:28 If we kept going, our next level would be a 3s1, 3s2, 3s2, 3s2, 3s2, 3p1, 3s2, 3p1, 3s2, 3p2, 3s2, 3p2, 3p2, 3s2, 3s2, 3p2, 3s2, 3s2, 3s2.

02:47 2, 3p4, 3s2, 3p, oops, 3s2, 3p3 here.

02:59 Sorry, skipped a number, and then 3s3p4.

03:03 Then we would get into our fourth period, and this is where we would add in our d -show, so we would have 4s1, 4s2, okay, then we would have, we're going to run out of space here, but we would have 4s2 .3d1.

03:30 4s2, 3d2, 4s2, 3d3, 4s2, 3d3, 4s2, 3d4, 4s2, 3d5, 4s2, 3d5, 4s2, 3d, 4s2, 3d5, 4s2, 3d5, 4s2, 3d, 6 and that fills our d shell because d can only hold 6 and then we would get into our 4 s 2 4p 1 4 s 2 4p 2 4 s 2 4p 3 and 4 s 2 4p 4p 4 so that the messy way of doing it so let's draw it out using boxes and then we can substitute in what those elements are going to be.

04:30 So in our first period, we would have two boxes...

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