Suppose that the solution to the Schrödinger wave equation...

Suppose that the solution to the Schrödinger wave equation were to be changed in one way only: The secondary quantum number / would be allowed to go to as high a value as the principal quantum number. a. Write the order of filling of the eight lowest types of orbitals in an atom. b. Draw a new periodic table showing the arrangement of the first 36 elements. c. Assuming that $n s^2 n p^{\circ}$ remains a noble-gas electron configuration, list the noble gases in your new periodic table. $\mathrm{d}$. If the changeover were made at the stroke of 12 midnight, discuss what would then happen to the water in the world.

Key Concepts

Schrödinger Wave Equation

The Schrödinger wave equation is a fundamental formulation in quantum mechanics that describes how the quantum state of a physical system evolves. It is used to determine the allowed energy levels and the corresponding wave functions of electrons in atoms, which ultimately influence the behavior of matter at the atomic scale.

Quantum Numbers

Quantum numbers specify the properties of atomic orbitals and the electrons within them. The principal quantum number (n) indicates the energy level and relative size of the orbital, while other quantum numbers (such as the angular momentum quantum number, often called the secondary quantum number) determine the shape and orientation of orbitals. Their allowed values under specific rules dictate electron configurations and result in the periodic characteristics of elements.

Electron Orbital Filling Order

The electron orbital filling order describes the sequence in which electrons populate atomic orbitals, typically following principles such as the Aufbau principle, Pauli Exclusion Principle, and Hund's Rule. This order is crucial for understanding the distribution of electrons in atoms and forms the basis for predicting chemical properties and reactivity.

Periodic Table Structure

The structure of the periodic table is derived from the recurring periodicity of chemical properties, which in turn stems from the electronic configurations of the elements. Changes in the allowed quantum numbers or orbital filling patterns would necessitate a rearrangement of the periodic table, reflecting new groupings of elements with similar chemical behaviors.

Noble Gas Electron Configuration

Noble gas electron configurations refer to the completely filled valence shells of noble gases, which give them their characteristic inertness. These configurations serve as benchmarks for understanding stability in electron arrangements, and any alterations in the rules governing orbital quantum numbers could lead to different electron configurations and thus new definitions of noble gases.

Molecular Bonding and Chemical Properties

Molecular bonding and chemical properties arise from the way in which electron clouds overlap and interact between atoms. Changes in electron orbital arrangements and energy levels—resulting from modifications in quantum number rules—could alter the nature of bonds in molecules such as water, potentially affecting their physical properties and chemical behavior.

Transcript

00:01 In this example, we're being asked to think about what a periodic table would look like if it was from another universe with different physical laws, but similar quantum numbers, although they're p, q, r, and s with the following rules.

00:21 P equals integers 1, 2, 3, 4, 5, etc.

00:25 Q is positive odd integers, and q is less than or equal to p.

00:28 R takes on all even integer values from negative q to positive q and s is one half or negative one half.

00:38 And the first thing we're being asked to do is to sketch what that periodic table would look like.

00:43 Based upon these rules, we would have a periodic table for the first, we'll just do the first few elements here, but we would have something that looked a little.

01:02 Little bit more like this.

01:23 There we go.

01:27 So this would be one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, fifteen, sixteen, sixteen, eighteen, nineteen, nineteen, and twenty.

01:51 And it's because of that the odd integers and the, the changes between our q and our r that are going to make our table look a little bit different from the original.

02:04 The next question asks, which ones, which atomic numbers of the first four elements would be expected to be the least reactive.

02:16 And just like with our periodic table, we would expect those to be in the area of our noble gases.

02:22 So it would be the ones to the furthest of the right.

02:25 So 2, 4, 12, and 20 would be the least reactive of the elements.

02:33 The next part is asking us to come up with, using these elements, come up with some examples of some different ionic compounds that could be created using the formulas x, oops, put it to my pen, there we go, using x, y, x y squared x squared y and x y to the third or cubed and x to y3 or cubed and x to y 3.

03:18 So there's a variety of different examples that you could come up with.

03:22 So x y for example could be one with 11, which would be similar to what we see with an ionic compound.

03:33 And for x, y, 2, we could have 6 with 11.

03:44 So this would have 2 and that would have 7, so we would need two of those.

03:50 For x2 .y, you could have 1 and 10.

03:56 For x and y 3, it could be 7 and 11 because 7 would have 3 valence electrons.

04:05 And then finally for x2y 3, we could do 7 and 10 because this would have 3 and this would have 6.

04:16 So you would use the least common multiple be 2 and 3.

04:23 Okay, so for the next part, it's asking us to figure out how many electrons could be held in different orbits...

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