His Fraudulency

Joe Biteme, properly styled His Fraudulency, continues to infest the White House, and hopium is still being dispensed even as our military appears to have joined the political establishment in knuckling under to the fraud.

All realistic hope lies in the audits, and perhaps the Lindell lawsuit (that will depend on how honestly the system responds to the suit).

One can hope that all is not as it seems.

I’d love to feast on that crow.

The Lindell Reports

It sounds worse that most of us imagined. And we have good evidence (if placed before a judge who understands probability, combinatorics, and statistics (three closely-connected branches of mathematics).

The question is, now that we have this, what’s next?

Can we get more states to do forensic audits? It will be tougher in states where the auditors themselves ended up in their positions of authority through cheating!

Even if not, it’s good to go into whatever comes next with the certitude that we were and are right about…

Joe Biden Didn’t Win. And neither did Hoe, and neither did half the craptastic Dems out there. RINOs might have won the general because at that point voters had a choice between a definite Dem and a maybe-not-as-bad “Republican.” But how many got in due to a corrupted primary?

We have to do our best to force this to stick and force “them” to pay attention to it!

Justice Must Be Done.

The prior election must be acknowledged as fraudulent, and steps must be taken to prosecute the fraudsters and restore integrity to the system.

Nothing else matters at this point. Talking about trying again in 2022 or 2024 is hopeless otherwise. Which is not to say one must never talk about this, but rather that one must account for this in ones planning; if fixing the fraud is not part of the plan, you have no plan.

Lawyer Appeasement Section

OK now for the fine print.

This is the WQTH Daily Thread. You know the drill. There’s no Poltical correctness, but civility is a requirement. There are Important Guidelines,  here, with an addendum on 20191110.

We have a new board – called The U Tree – where people can take each other to the woodshed without fear of censorship or moderation.

And remember Wheatie’s Rules:

1. No food fights
2. No running with scissors.
3. If you bring snacks, bring enough for everyone.
4. Zeroth rule of gun safety: Don’t let the government get your guns.
5. Rule one of gun safety: The gun is always loaded.
5a. If you actually want the gun to be loaded, like because you’re checking out a bump in the night, then it’s empty.
6. Rule two of gun safety: Never point the gun at anything you’re not willing to destroy.
7. Rule three: Keep your finger off the trigger until ready to fire.
8. Rule the fourth: Be sure of your target and what is behind it.

(Hmm a few extras seem to have crept in.)

(Paper) Spot Prices

Last week:

Gold $1763.90
Silver $24.48
Platinum $985.00
Palladium $2712.00
Rhodium $21,150.00

This week, 3PM Mountain Time, markets have closed for the weekend.

Gold $1780.60
Silver $23.83
Platinum $1034
Palladium $2736
Rhodium $20,200

This might be a good time to buy silver. On the other hand it could drop even m0re.

Electrons Get Quanta

If you’ll recall, last time I mentioned that in 1911 van den Broek suggested that an atom’s place in the periodic table depended on the positive charge of the nucleus; when that charge was expressed as a positive-signed multiple of e, you had a simple integer number which is that atom’s atomic number. I then said it was merely an idea for about two years, and then I left you hanging.

I’m going to pick up that thread, but I’m going to do it my way: I’m going to back up a bit and follow another thread to that same place.

As of 1900, chemists were pretty sure they were missing eight elements on the periodic table. Because they didn’t know how many lanthanides (“rare earths”) actually existed (some guesses ran as high as 25) and simply had no idea what was going on there, they didn’t know how many they were missing. (We now know that lanthanum through lutetium is fifteen elements inclusive; chemists back then knew twelve in that range, and suspected there were more.)

Remember in 1900 they didn’t know about atomic number. They did have the periodic table, and it had holes in it that were clearly missing elements, but the lanthanides didn’t seem to fit into that scheme at all so they were a big question mark.

In 1901, europium–a lanthanide whose atomic weight was between samarium and gadolinium–was discovered, and then in 1902-03 actinium was discovered during investigations of the radioactive decay chains. (From the radioactive decay series, astatine, francium and protactinium were not known yet as of 1911, but the first two were “known” holes in the table, below iodine and cesium, and protactinium was probably suspected–it’s hard to tell because back then chemists didn’t realize the actinides were like the lanthanides. My extensive discussion last week was based largely on current knowledge.)

1906 saw the discovery of lutetium, at the time the heaviest of the rare earths.

So in 1911, van den Broek came up with the concept of the atomic number. And the periodic table was pretty “tidy” right up through barium, but after barium were the lanthanides. So I believe they were able to assign every element up to barium atomic numbers, with barium at Z=56. There was a gap at Z=43. Then with an unknown number of lanthanides, it would be impossible to assign an actual number to the first known element after the lanthanides, tantalum, but we knew what group tantalum was in, so we could basically restart counting from there, identifying more holes. Two spaces to the right, under that hole for Z=43, was another hole. Then a hole under iodine and a hole under cesium, as previously mentioned.

Protactinium was discovered in 1913, so we may not have realized it at the time but everything from radium (directly below barium) on up was known.

In 1913 the picture became a lot clearer. Henry Moseley (a student of Rutherford’s), in 1913 was doing x-ray spectroscopy on a variety of elements and measuring the wavelengths. He noticed a fairly simple mathematical relationship between the atomic number (where known) and at least one of the x-ray wavelengths. From this he formulated Moseley’s law. (I’d quote the law here, but although the formula is simple, explaining what the symbols meant would be a royal pain.)

So now the guesswork was gone. Moseley could zap even a rare earth metal with his x ray device, and calculate its atomic number. Lanthanum was 57. Lutetium was Z=71. We had, without realizing it, already nearly completed the list in between: Cerium (58), praseodymium (59), neodymium (60), samarium (62), europium (63), gadolinium (64), terbium (65), dysprosium (66), holmium (67), erbium (68), thulium (69), ytterbium (70), and lutetium (71). Only #61 was missing. {Yes I am enough of a geek to known those by heart.)

So now that numbers could be assigned to every element and not just the first 56, we knew we were missing #43 (right below manganese), #61 (a rare earth), #72, #75 (below #43), #85 and #87. Uranium came in at #92 and was the last element.

Moseley’s law was consistent with the Bohr model of the atom, which was put forward that year (just two years after the Rutherford model).

And the Bohr model is our main topic today, but I will finish Moseley’s story first. Sadly, it won’t take long.

It sure looked like Moseley was destined for bigger and better things, and he had certainly earned himself a Nobel Prize for putting the atomic number on a solid footing. But World War I broke out the next year and Moseley volunteered. He was sent to Gallipoli in modern day Turkey and was killed on August 10, 1915. The Nobel Prize committee gave no award for physics in 1916. We can only speculate, but it seems as if they intended to give that award to Moseley but as they do not give posthumous awards, had to change their plans.

The Bohr model of the atom is actually considered a modification of the prior Rutherford model, which was unsatisfactory for a number of reasons. So it’s technically the “Bohr-Rutherford” model, but most just call it the Bohr model, after the Danish physicist Neils Bohr (1885-1962).

Why was the Rutherford model unsatisfactory? Chief among the issues was that if it were accurate, no atom would last more than about ten billionths of a second. Since I am writing this, and you will soon be reading this, and you and I are both made up of atoms that haven’t collapsed yet, there’s clearly a disconnect.

The Rutherford model supposed that the negatively charged, light electrons orbited the much more massive and very tiny positively charged nucleus. It didn’t discuss orbital periods of the electrons, or anything like that, so it wasn’t very specific. But that wasn’t the big issue.

The problem is that any electric charge that is being accelerated will emit electromagnetic energy. And electrons in orbit about a nucleus are constantly being accelerated. Remember that an object in motion will continue moving at that speed and direction unless acted on by an outside force (this goes back to part 1). An outside force, of course, will cause an acceleration. Since the electrons are following a curved path, they are being accelerated.

Calculations at the time based on Maxwell’s equations showed that it would take about ten billionths of a second for an orbiting electron to radiate away all of its kinetic energy, causing it to spiral in and plow into the nucleus.

How to solve this problem?

Well, there was a sketchy tool in the physicist’s tool kit that essentially functioned by forbidding certain values of energy, or momentum. If this tool could be applied here, then an electron in an orbit would be unable to drop downward, unless it took a big step downward all at once. And there’d be a minimum orbital energy it could not drop below.

That tool was quantum theory. It’s not the same quantum theory that we have today. As I hinted, it basically functioned as an overlay on classical physics, forbidding certain values of some parameters. It had been used by Max Planck to explain the black body spectrum in 1900, and it had been invoked by Albert Einstein to explain the photoelectric effect in 1905 (for which he eventually won the Nobel prize–for this, not for relativity!).

Energy came in fixed quanta, and these quanta’s sizes were always related somehow to Planck’s constant, which is:

h = 6.62607015×10⁻³⁴ J⋅Hz⁻¹

Or equivalently (since a hertz is a “per second”):

h = 6.62607015×10⁻³⁴ J⋅s

This turns out to have the same dimensions as angular momentum. A joule is a kg⋅m²/s², or as a dimension rather than units, m⋅d²/t². Multiply that by time to match Planck’s constant and it’s m⋅d²/t. Angular momentum is speed, times mass, times the distance from the central point around which angular momentum is being measured, or (d/t⋅m⋅d) which is also m⋅d²/t.

However h is defined in terms of full revolutions, and angular momentum operates in radians, so we really need h/2π, a number that turns up so often, it has it’s own symbol, ħ, pronounced “H-bar” and often known as the “reduced Planck constant.” It’s equal to 1.054571817…×10⁻³⁴ J⋅s. Or, since we are talking about atoms here, the preferred units are in terms of electron volts, so the reduced Planck constant is 6.582119569…×10⁻¹⁶ eV⋅s

So if the angular momentum of electrons in an atom were restricted to multiples of ħ, it could keep the main descriptive feature of the Rutherford model (electrons orbiting about the nucleus) while solving the problem of having them spiral into the nucleus, radiating energy all the while. The lowest possible orbit would be the one where the angular momentum was equal to ħ, the next one up (higher energy), 2ħ, and so on.

Well, it’s a fine idea, but does it actually make things look the way they really are?

Let’s work with hydrogen. One electron, one proton. No other electrons to cause complications because they repel the first electron.

Assuming a circular orbit (so that the requisite cross product becomes equal to multiplying distance by velocity), the angular momentum of the electron is going to equal its mass, times its velocity in orbit, times its distance from the nucleus:

m_evr = nħ

The n is the integer multiplier and is now known as the principal quantum number.

Well, we know one of these, the mass. But we can actually express the velocity needed to maintain a circular orbit, in terms of distance and the attractive force between the proton and the electron (which we know), so that gets us down to one unknown. And we can eventually work our way down to figuring that when n is 1, the orbital radius is 0.0529 nanometers (billionths of a meter) for a hydrogen atom (one electron orbiting one proton).

OK, so by analogy with orbital mechanics, the lowest energy orbit is indeed this n = 1 orbit. What could make the electron move out of that orbit?

The hydrogen atom could actually hit another hydrogen atom, transferring kinetic energy to the electron, enough that it could jump to n=2. Thus a hot hydrogen gas, where the kinetic energy of the atoms is higher, could result in electrons being “jumped up” to higher orbits. So, basically, heat can do it.

Or the electron could absorb a photon with enough energy to make the jump.

And if in a higher orbit, how could an electron drop? It could do so by emitting a photon. But it would be a photon that contains precisely the energy difference between the two orbits! .

Remember that E = h ν for light (that last letter being Greek “nu” not a “vee”). So if we know the energy difference, we should be able to figure out the frequency, ν of the photon, then get to its wavelength in nanometers. For wavelengths between 400 and 770 nanometers, the photon will be visible to our eyes and will have a certain exact color.

The lowest orbit has the minimum energy. Just like with astrodynamic orbits, the energy is set to zero at a distance of infinity, and becomes more and more negative the closer the orbit gets to the nucleus, so the energy of the minimum orbit (n=1) is -13.6 eV. The second orbit (n=2) is at -3.4 eV, the third (n=3) is -1.51 eV, and so on, approaching but never equaling zero. So an electron in the third orbit can shed a photon and drop all the way down from -1.51 eV to -13.6 eV, a difference of 12.1 eV. This corresponds to a wavelength of 102.57 nm. That’s an ultraviolet wavelength.

But how about dropping from n=3 to n=2? That difference is about 1.9 eV. And that corresponds to a wavelength of 656.3 nm, which is visible light.

That number no doubt leaped out at someone. And when they computed the numbers for jumping from n=4 to n=2, then n=5 to n=2, and so on, those numbers looked familiar, too.

They were the wavelengths of light in the hydrogen emission spectrum. This is known as the Balmer series, all the lines you get from dropping from some higher n down to 2.

The series of lines corresponding to dropping down to n=1 is called the Lyman series, and as previously indicated, they’re all ultraviolet.

So now we have an explanation of the hydrogen emission spectrum.

Maybe there was something “real” behind this quantum buggery!

The Bohr atom model stopped here. It explained hydrogen very well, but it couldn’t, by itself, cope with more than one electron. However its underlying principles do hold for other cases.

What Moseley had done was identify, via his X ray work, the transition down to n=1, which in heavier atoms is in the x-ray band. This gets progressively more energetic as the charge in the nucleus increases, such that one can actually tell what the nuclear charge is from the x ray wavelength. So this, too, validated the Bohr model in principle, at least insofar as the Bohr model assumes quantum effects are in play.

I’m going to carry this story through (in a grossly oversimplified way) to the present day, except I won’t delve too deeply into the quantum mechanical aspects of it–quantum theory turns out to be seriously weird but this wouldn’t begin to become apparent until about 1925. So far (as of the 1910s), this bowdlerized version where it just arbitrarily restricts what can happen in an otherwise classical physics realm was working pretty well (this is now called “old quantum theory”).

The n=1, n=2, n=3 and so on principal quantum numbers were named electron shells. It became apparent as time went on, though, that each of these shells contained subshells, according to a simple rule: The 1st shell consisted of one subshell, the second shell had two subshells, and so on. The subshells got labeled s, p, d, and f. This arose from quantum mechanical considerations.

Each subshell can only hold a certain number of electrons. An s subshell could hold 2 electrons, a p subshell 6 electrons, a d subshell 10 electrons, and an f subshell 14 electrons. We’ve never dealt with a fifth subshell, but it would probably be labeled g, with 18 electrons. Each goes up four electrons. This, too, arose from quantum mechanical considerations.

The subshells are in turn divided into orbitals holding 2 electrons each, but I won’t tread there. (And again, quantum mechanical considerations).

So, the following subshells exist: 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, and so on.

Electrons are added to the lowest energy shell that isn’t already full. That’s whether you’re creating an ion by adding extra electrons, or just trying to get a large atom up to its normal complement.

Let’s take oxygen as an example. It has eight protons in its nucleus, it will want eight electrons in its shells.

So the first two electrons go into the 1s subshell. Then the 2s subshell gets the next two electrons. Finally, the four remaining electrons go into the 2p subshell, which could accept another two electrons if they were available.

Now let us consider iron, Z=26. The first eight electrons go like oxygen’s. The next two fill up the remainder of the 2p subshell, after which we move on to the 3s subshell, which takes two more electrons (12 so far). 3p takes up another six electrons (18 so far). You might expect that now we will move to the 3d subshell…but that turns out to be wrong. The 3d subshell’s energy is actually slightly higher than the 4s subshell, so we will fill the 4s before the 3d. Electrons 19 and 20 go into the 4s subshell, then the last six electrons do go into the 3d subshell. If we were to continue, the next subshell to fill would be the 4p subshell.

So we’re seeing at the end a sequence where we fill a 2 electron s subshell, a 10 electron d one, then a six electron p one. If we were to carry on to lead (Z=82), we’d encounter our first f subshell, 4f, right after the 6s subshell but before the 5d subshell; lead takes us into the 6p subshell.

The numbers 2, 6, 10, and 14 might be tickling your brain trying to be noticed. If not, perhaps their successive sums will: 2, 8 (2+6), 18 (2+6+10) and 32 (2+6+10+14).

These are the lengths of the rows on the periodic table. In fact, if you look at the table, the left hand side is a “tower” two elements wide–corresponding to the s subshell. The left side is a block six elements wide–corresponding to the p subshell. The central skinny part is ten elements wide, and corresponds to the d subshell. Looking at the two rows that are “footnoted” below the main body of the table, those are usually depicted as 15 units wide, but they are supposed to tuck into a square in the third column, so one of those 15 squares really belongs to the d block. The other 14 are the f subshell. (By the way, chemists argue over whether the first or last of the fifteen is the one in the d-block; they seem to have recently decided to go with the last one of the fifteen.)

So the very shape of the periodic table reflects the shells and subshells, which in turn derive from quantum principles.

The periodic table is on a firm footing now. Atomic number is on a secure footing, We now even understand those elements whose atomic weights aren’t close to integers. We just don’t know why they aren’t exact integers yet.

Obligatory PSAs and Reminders

China is Lower than Whale Shit

Remember Hong Kong!!!

中国是个混蛋 !!!
Zhōngguò shì gè hùndàn !!!
China is asshoe !!!

China is in the White House

Since Wednesday, January 20 at Noon EST, the bought-and-paid for His Fraudulency Joseph Biden has been in the White House. It’s as good as having China in the Oval Office.

Joe Biden is Asshoe

China is in the White House, because Joe Biden is in the White House, and Joe Biden is identically equal to China. China is Asshoe. Therefore, Joe Biden is Asshoe.

But of course the much more important thing to realize:

Joe Biden Didn’t Win

乔*拜登没赢 !!!
Qiáo Bài dēng méi yíng !!!
Joe Biden didn’t win !!!