Assume that we are in another universe with different...

Assume that we are in another universe with different physical laws. Electrons in this universe are described by four quantum numbers with meanings similar to those we use. We will call these quantum numbers $p, q, r$, and $s .$ The rules for these quantum numbers are as follows: $p=1,2,3,4,5, \ldots$ $q$ takes on positive odd integers and $q \leq p$ $r$ takes on all even integer values from $-q$ to $+q$. (Zero is considered an even number.) $s=+\frac{1}{2}$ or $-\frac{1}{2}$ a. Sketch what the first four periods of the periodic table will look like in this universe. b. Wh?t are the atomic numbers of the first four elements you would expect to be least reactive? c. Give an example, using elements in the forst four rows, of ionic compounds with the formulas $\mathrm{XY}, \mathrm{XY}_{2}, \mathrm{X}_{2} \mathrm{Y}, \mathrm{XY}_{3}$, and $\mathrm{X}_{2} \mathrm{Y}_{3}$ d. How many electrons can have $p=4, q=3 ?$ e. How many electrons can have $p=3, q=0, r=0 ?$ f. How many electrons can have $p=6$ ?

Assume that we are in another universe with different physical laws. Electrons in this universe are described by four quantum numbers with meanings similar to those we use. We will call these quantum numbers $p, q, r$, and $s .$ The rules for these quantum numbers are as follows:
$p=1,2,3,4,5, \ldots$
$q$ takes on positive odd integers and $q \leq p$ $r$ takes on all even integer values from $-q$ to $+q$. (Zero is considered an even number.) $s=+\frac{1}{2}$ or $-\frac{1}{2}$
a. Sketch what the first four periods of the periodic table will look like in this universe.
b. Wh?t are the atomic numbers of the first four elements you would expect to be least reactive?
c. Give an example, using elements in the forst four rows, of ionic compounds with the formulas $\mathrm{XY}, \mathrm{XY}_{2}, \mathrm{X}_{2} \mathrm{Y}, \mathrm{XY}_{3}$,
and $\mathrm{X}_{2} \mathrm{Y}_{3}$
d. How many electrons can have $p=4, q=3 ?$
e. How many electrons can have $p=3, q=0, r=0 ?$
f. How many electrons can have $p=6$ ?

Key Concepts

Quantum Numbers

Quantum numbers are the discrete values that define the state of an electron in an atom. In this context, the four numbers (p, q, r, s) serve roles similar to the principal, angular momentum, magnetic, and spin quantum numbers in our universe, setting the framework for the allowed electron configurations and energy states according to specific rules.

Electron Configuration and Periodic Table Structure

Electron configuration refers to the systematic arrangement of electrons in atomic orbitals, and it fundamentally determines the structure of the periodic table. The filling order of electron states defined by quantum numbers creates distinct periods (rows) that reflect recurring patterns in chemical properties as shells or subshells are filled, providing insight into atomic size, ionization energy, and other key features.

Degeneracy and State Counting

Degeneracy in quantum mechanics is the number of distinct quantum states that share the same energy level. By applying the specified rules for quantum numbers, one can count how many electrons (or states) exist for particular sets of quantum numbers, which is essential for understanding electron capacity in shells and subshells and for applying principles like the Pauli Exclusion Principle.

Chemical Stability and Inertness

Chemical stability, often observed in elements with fully filled electron shells, arises from low reactivity when the valence orbitals are complete. This concept, analogous to the inert or noble gases in our universe, is crucial in predicting which elements, based on their electron configuration, will be least reactive.

Ionic Bonding and Compound Formation

Ionic bonding involves the electrostatic attraction between oppositely charged ions formed by the loss or gain of electrons. The formation of compounds such as XY, XY?, and others relies on balancing these charges, which is directly influenced by the electron configuration and reactivity of the elements involved. Understanding this concept is key to predicting the stoichiometry of resultant ionic compounds.

Transcript

00:01 We are asked to consider that we are in another universe with different laws.

00:05 Electrons, which i will refer to as e-, are described by four quantum numbers.

00:23 We'll call them p, q, r, and s.

00:34 Rules are p equals one, two, three, four, five, dot, dot, dot.

00:42 Q takes on a positive odd integer, odd integer, and q is always less than or equal to p.

01:11 R takes on all even integers from negative q to plus q.

01:35 And s is plus one -half or minus one -half.

01:44 Okay, sketch what the first four periods look like.

01:56 Okay, so i think what they want here is p, q, r, and s.

02:15 One, two, three, and four.

02:24 Q can be, these can be odd integers.

02:27 This could be one, this could be one, this could be one and three, this could be one and three.

02:34 R can be zero, zero, zero, zero, and plus even integers, two and minus two.

02:54 And here we can have the same thing, zero, zero, minus two, zero, and plus two.

03:08 Okay, and s can be, they can all be plus one -half or minus one -half, all the way down.

03:38 Okay, what else am i asked to do here? sketch the first four periods of the periodic table.

03:51 Okay, so let's move down to our first four periods, and i will have eight, one, two, three, four, five, six, seven, eight.

04:17 So i can have one and two, and i'll have three and four, and then i will have five.

05:06 Okay, and then, okay, so there's my first question, that's a.

05:26 Now let's do b.

05:30 B asks us to, back to my problem, what are the atomic numbers of the first four elements expected to be least reactive? and i'll go with two, four, 12, and 20.

06:33 Here's my answer for b.

06:39 For part c, there's a bunch of parts of this, so i'm just going to focus on getting that done.

06:48 Give an example, first four rows of x, y, x, y, two, x, two, y, and x, y, three.

07:08 And let me put those down here instead.

07:15 X, y, x, y, two, x, two, y, x, y, three, and x, two, y, three.

07:36 Okay, that doesn't look very hard.

07:40 So x, y, i'll take maybe three and my plus one charge.

07:56 Let me see here.

08:05 Elements that have a minus one are, and a plus one will be, a plus two, and a plus three, this will have a minus two.

08:34 There, so that should be good for this.

08:36 So our example for our x, y could be three and four, excuse me, three and 11.

08:52 For x, y, two, that's going to be, how about six and 11.

09:05 X, two, y, i think i will take five and 10.

09:18 X, y, three, i think i will do, how about seven and 11.

09:29 And then my last one, x, two, y, three, will be maybe a seven and an 18...

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