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fluxsci · 7 years ago

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Elemental Flow - The Orbital Primer pt. 2 (5)

This is it! We have finally reached the conclusion of the orbital arc...or at least the second to last lesson. I’m sure it felt like the Frieza Saga, but I believe that I managed to explain the entirety of orbitals in a concise, but accurate way. Of course, I’ll leave it to you to tell me how I can improve to make this a better story for you. Because, like electrons, we all have to work together here.

In any event, let’s march on and be done with these orbitals. Ah…I can already hear the cheers from the Chemistry 101 students reading this.

Be sure to check out Part 4 for this one. You can’t understand where this one begins without seeing where the other one ends (hence ‘pt. 2’).

Now, it is time to explain the last quantum number.

Spin Quantum Number (s)

Electrons are trying to get rid of their energy in any way possible. Orienting themselves in a way that lowers energy is a good starting point, but they still have plenty of internal energy. In fact, electrons have their own, internal angular momentum, separate from the orbital angular momentum (l).

This was determined after a 1922 experiment by German physicists Otto Stern and Walther Gerlach. The aptly named Stern-Gerlach Experiment involved firing a beam of silver atoms* through a inhomogenous, or uneven, magnetic dipole and observing the results on a detecting wall at the end. The result, surprisingly, was that the beam was deflected in only two directions, landing flush against the wall in two bands.

But how could that be? There’s no way that there should be two, specific places in which the atoms ended up.

If you think about it, if you threw twenty bar magnets past two huge magnets and looked at where they ended up, they would all be stuck on the wall in random places. After all, you have no idea what direction those magnets were when you threw them or how much attraction or repulsion one magnet had than another one, so you should have no idea exactly how they will come out. Shouldn’t it have been the same for these atoms?

In order to explain the significance of this inconsistency, I’ll need to diverge for a second into the physical quantity of momentum.

Gaining Momentum

Given that we know, from classical linear momentum calculation that there must a velocity, some speed over some time from some position which is usually produced by some force (say that ten times fast), and a mass, or the amount of matter an object has. This tells you how much, in numerical form, an object moves. In fact, you likely already knew the definition of “momentum” without knowing how to put it in words. Classical angular momentum is almost completely the same. The only difference is that an axis is involved, around which your mass rotates.

Thus, the two relative quantities are the moment of inertia and angular velocity. The latter is simply the rate at which rotation occurs. On the other hand, the moment of inertia, also known as the angular mass, is used to depict how much torque, or rotational force, you need to move an object a certain distance around an axis with respect to a certain position. The classic example of this is the tightrope walker.

If it was super easy to cause the one walking on a tightrope to flip around the rope (if gravity didn’t exist), then you would say that their moment of inertia is low. But when one walks across a rope you usually see them stick their arms out or hold a long rod. That single act increases the moment of inertia because you have changed the center of the mass, where the force acts. That is, more rotational force would be needed to rotate the walker. Now, Matthew, why did you go through the effort of explaining momentum here? Patience, viewer! The science will wrap together in a nice ribbon. Just in time for Christmas.

Magnets Start Small

I mentioned, from the now legendary Part 2, that electrons, as charged particles, can generate a magnetic field just by moving. It so happens that we know that electrons are “orbiting” the nucleus, and therefore, they must be exhibiting some sort of magnetic field as it is repeatedly revolving in this closed loop. But we never talked about what that field is doing. It wouldn’t make sense for the magnetic field to just disregard the electron and there is definitely no reason for the electron to not feel the force of the magnetic field.

Image via SchoolPhysics

By the way, if you orient your right-hand’s four fingers so that they are going along the path of the electron and then point out your thumb, that gives you the direction of the magnetic field. Every time. It’s called the Right-Hand Rule.

What would happen if you were to hold your hand on a ball lying on a table and then push your hand forward? The ball would roll in the direction your hand moves. It’s the same with electrons – they experience a rotational force, torque, from the magnetic field. The rotating electron creates another effect, according to electrodynamics. It now becomes a natural magnetic dipole, which is an object that generate magnetic fields that experience torque in such magnetic fields due to the presence of two opposite poles. In many ways, their magnetic effects are just tiny bar magnets. Electrons, too, have a “north” and “south” pole, or, more specifically, two poles at which their magnetic fields are strongest.

Image via Live Science

This is a dipole. You’ve seen bar magnets before.

So, let’s do a roundup of what we just learned.

Electrons generate magnetic fields which creates torque on them causing them to rotate and become similar to bar magnets. You should already recognize, then, where the concept of an electron’s angular momentum comes from. Indeed, electrons exhibit their own magnetic moment, from the rotational force, and, coupled with their motion, must create angular momentum!

This is the origin of the theoretical “spin” that electrons have. Although we, realistically, don’t know if the electrons are spinning or not, this is just a name we give conventionally. You will learn why our convention fails us, especially when it comes to quantum mechanics, later.

But, I digress. With all of that said…how did the electrons only end up in two places in the Stern-Gerlach Experiment?

A Discrete Solution

Stern and Gerlach were smart men. They knew, from Bohr’s prior experimentation of the electron, that it must be quantized. So when they crafted this experiment, they expected a quantized result. That is exactly what they saw. But just because they were correct in their hypothesis doesn’t mean their foundation was solid – a lesson for all of you upcoming scientists.

Image by Bill Watterson

Although that’s a result that you could hypothesize based on an expectation gained after seeing the ice in a glass of water melt, the foundation is all wrong.

The quantum mechanical theory of the time wasn’t correct. Their conclusion that the result was due to the quantization of the electron was not the reason for the quantized result.

It was because of the electron’s angular momentum was directed in two specific direction. We call these half-spins, since one beam was split evenly into two. Basically, the momentum on the electrons directed the beam either upward or downward according to the direction of their rotational moment.

A side-note: all elementary particles that hold these spins equal to ½ are called fermions, whereas if their spin value was 1 (what the value would be if the one beam went straight through without any division), it would be called a boson, a word you’ve likely heard before if you’re into physics. These are the two categories in which all particles in the universe reside.

A Return To Form

So...how about another summary?

The Principle Quantum Number (n) determines the energy level, and thus, the electron’s shell. It is conventionally shown with a number from 1 to 5. The Orbital Quantum Number (l) determines where the electrons are with respect to the nucleus. It shows the sub-shell and is typically denoted with a letter (s, p, d or f) according to its number (0, 1, 2 and 3). The Magnetic Quantum Number (m) tells how many subshells there are. It is determined by looking at the subshell and taking the range from -l to l. Lastly, the complex Spin Quantum Number (s) determines whether the electron’s “spin” is +1/2 or -1/2.

Lastly, there’s the Pauli Exclusion Principle, watching over these Quantum Numbers to make sure they behave themselves. No two electrons can have the same quantum mechanical state within the same atom. It was the aforementioned spin quantum number that proved this; remember that the electrons in the Stern-Gerlach did not simply mix – there was a distinction between +1/2 and -1/2. Furthermore, given that the Principle only works with differing quantum mechanical states, only fermions follow this Principle.

Image via futurespaceprogram

This opens up a very important piece of orbital theory.

That spin quantum number shows a great deal, indeed, folks. Because that Pauli Exclusion Principle makes it so that each subshell can only have two electrons – one with the positive spin and one with the negative spin.

And that, my friends, will guide you into the Aufbau Principle…which we will discuss next time.

The next lesson will end the Orbital Arc...I hope you’re ready. Because afterward, things will really pick up.

Please ask questions if you are lost somewhere in these five parts. And share amongst all of your friends – not just the ones interested in science. We can all learn. We just need to light the fire.

*If you understood everything up to this point, you might be able to reason why silver atoms were used. I want to ask you why and give you these three hints to help you: 1) Use the periodic table 2) Orbital Quantum Number 3) Electrons and Protons

#ElementalFlow #Flux #orbitals #chemistry #physics

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fluxsci · 7 years ago

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Elemental Flow - The Orbital Primer pt. 1 (4)

Image by Randall Munroe via xkcd

|| by matthew

This comic gave me a good laugh, despite not being directly related to quantum mechanical orbitals...

In any event, we are back again! I know how much you were looking forward (or perhaps dreading) this part. Well, if not looking forward to, perhaps still trying to reason how all of this is going on within every element in your body and facing a slight existential crisis. All I have to say, in that case, is to try not to worry about it, and, of course, prepare for another dive into the boundary of quantum mechanics and chemistry.

I, again, recommend that you check out the previous parts of the Elemental Flow series, especially Part 2. Familiarizing yourself with the quantum mechanics of electrons before this lesson will make this a smooth experience.

Quantum Numbers

What do the letters “s”, “p”, “d”, “f”, Aufbau, spin, and shapes have in common?

You might be scratching your head and wondering, “Why is he asking me this when I know he’s going to tell me.” And you’re right. Let’s break out our handy dandy…periodic table. And notebook, if you have one (I got you, 90s kids).

Image via Science Notes

Orbitals are organized according to their energy levels. Naturally, every element on the periodic table must exist at a separate energy state in nature than each other (otherwise, what you learned in Part 1 and Part 2 would be meaningless – electrons have no need to configure themselves in different ways if every atom exists at the same energy level). Therefore, there must be a different orbital for each element. And, indeed, there is. The periodic table shows that, at the bottom of each element, there is a different electron configuration for each element. This exclusivity in configuration is called the Pauli Exclusion Principle.

Attentive readers might have already noticed the letters at the bottom of the elements on the periodic table – “s”, “p”, “d”, and “f”.

These labels are only descriptors of one of four quantum numbers.

If you are lamenting the word “quantum” after Part 2 of the Elemental Flow series, don’t fret. A quantum number is a quantity within a quantum mechanical system. Since electrons are quantum mechanical systems, they hold specific quantities. That’s all.

Electrons have four such quantities. We call them the principal quantum number, or n, the orbital quantum number, or l, the magnetic quantum number, or m, and the spin quantum number, or s.

The Quantum Dive – Breaking the Shells

1) Principal Quantum Number (n)

The first, n, is the number that labels the energy level of an electron. Since we know, from Part 1, that the electrons with the lowest energy are the ones closest to the nucleus, we can tell that the lower the value of n, the lower the energy level. In chemistry, the energy level of an electron is described as its electron shell.

These shells are labeled from K to O starting from their innermost shell to their outermost shell, according to their principal quantum number. To be clear, an n of 1 is referred to as the K shell, n = 2 is L, n = 3 is M, n = 4 is N and n = 5 is O. While they do have this alphabetical label, when describing shells, more people recognize the numeric value of n. However, they can help you organize when we talk about the subsequent quantum numbers.

2) Orbital Quantum Number (l)

Next up, l. This quantum number tells about the orbital’s angular momentum, or the momentum brought about by rotation of electrons around some center – the nucleus.

Before I move on from here, I did want to explain this number more carefully.

For those familiar with astronomy, this quantum number is also called the azimuthal quantum number, as an azimuth is a certain angular measurement within a sphere.

Image via UOregon

Within our three-dimensional world, we can describe the position of anything in relation to anything else. As you can see, the azimuth and altitude give the direction of a star in this spherical system. North is usually used as the starting point for an angular calculation when comparing the horizontal position of a star and the altitude is given as angle from the observer in the center to the position on the sphere that the star is located.

But how does this relate to an electron? Take a look at this:

Image by tonfilm via vvvv

The observer is the nucleus, or, in this image, where the x, y, and z axes (representing each of our three dimensions) connect. The star is the point P, or the electron, with some x, y, and z coordinate. The angle between north, or the x-axis, and the point is defined as the azimuth. Lastly, the altitude angle would be the angle between the z-axis and the position of the point.

If the electron was just a point, or particle, then this would be a simple case of calculating the ordinary angular momentum.

But it isn’t just a particle, is it?

Image by Yuta Aoki via Wikimedia

The wave nature of electrons.

The angular momentum is harder to calculate in this system than it is in ordinary physics, due to the Wave-Particle Duality of the electron (discussed in Part 2). The electron is traveling quickly on a wave-like pattern. At any given time, we are unsure of where the electron may be. Instead of treating the electron like a particle, it is treated like a standing wave. More simply put, its wave functionality, constant and uninterrupted as it is, is used to determine its angular momentum. Therefore, the orbital angular momentum, is calculated completely differently than the classical angular momentum, which will be discussed when we reach the spin quantum number.

Perhaps the actual mathematics can be shown in a separate lesson if the interest is great enough? For now, recognize that, by solving this equation for the angular momentum, you receive non-negative integer values, or 0, 1, 2, 3, etc.

Aha! A new possibility reveals itself. If you were to believe that electrons were like their classical systems, you would probably say that it’s impossible for an object that’s moving to have 0 momentum. After all, if you’re walking down the street, you have momentum; how could an electron which is constantly revolving around the nucleus have 0 momentum? But quantum mechanically, a system with 0 angular momentum or, in other words, l = 0, simply orbits the nucleus in its wave-like pattern along the xy plane without any z altitude. The electron only has an azimuth, no altitude.

When I said in the last part that you had already learned about orbitals, this is what I meant. Because an electron orbiting the nucleus on an xy plane looks oddly familiar…

Image via Wikispaces

The Bohr Model of Hydrogen

Is that...? Why, yes it is! The Bohr Model! He did come up with the initial idea of orbitals. was that dastardly scientist was right!?

Not so fast.

First, let’s clean up this image. Since we’re not concerned with the electron’s decrease in energy state (like we were in part 2 when this was being explained), let’s look at the hydrogen atom at its lowest energy state.

Image via Chemistry LibreTexts

The electron is still on the n = 1 orbital and orbiting the nucleus like above. Only the n = 2 and n = 3 orbitals have been removed.

Bohr was only correct when it comes to things with one electron and an angular momentum of 0. This is because Bohr’s elementary model only observes the energy between the nucleus and the electrons only, not the energy created between the repulsion of electrons. The image above shows the only case in which the Bohr model is correct - with the hydrogen atom. Hydrogen only has one electron and its nucleus, meaning this fits Bohr’s model. Furthermore, as per the aforementioned Pauli Exclusion Principle, there are no other elements like hydrogen in nature.

To wrap up the second and most complicated quantum number, we make note of the fact that we can’t really know what the xy-axis is as it electrons see it.

To conceptualize what I’m saying, think of the image above as the wheels on a gyroscope.

Of course, in a quantum mechanical system, there is more discrete and fast motion, but this is a fantastic example. Now, if the revolving electron in the Bohr model was taking any of the wheels in the above gyroscope, you can understand why it would be hard to tell exactly where the electron would be, let alone where its x and y axes are.

But what you do know is that the electron is somewhere within the sphere made by the rotating gyroscope wheels.

This might sound familiar to you who remember or re-read Part 2 because this is the exact conclusion you derive from the Electron Cloud model that Schrodinger developed!

Image via Ask A Mathemtician/Physicist

I love it when science comes together...You gotta admit, that’s pretty cool.

With all of that said, the purpose of the orbital quantum number is to tell you the shape of the electron subshell. Like the principal quantum number, these have an alphabetical naming system too…and it’s one you’ve already seen! That is: s, p, d and f. l = 0 to l = 3 represents s to f. Unlike the principal quantum number, however, it is conventional to use s, p, d and f rather than the numeric orbital quantum number value.

With that said, if the principal quantum number, n, is equal to 1 and the orbital quantum number, l, is equal to 0, you have a 1s system, which is the electron configuration of the hydrogen atom (check the bottom of the hydrogen element on your periodic table).

Now, I think after all of that, it’s good to keep ourselves organized.

To recap, the principal atomic number tells us the electron shell or energy level of the element, and the orbital quantum number tells us the electron subshell. There can be multiple subshells in one shell. And each individual electron configuration is called an orbital.

Image by thomji via Chemistry Stack Exchange

3) Magnetic Quantum Number (m)

Before we wrap up with this image, there’s something important in it that will help you understand the magnetic quantum number.

You might have noticed above that there are three different p orbitals in the above image. That is due to the different ways an orbital can orient itself within space as the amount of electrons in the system increases. This is what Bohr did not account for in his model; when more electrons enter the system, in order to keep energy as low as possible, the system must orient itself differently within the three dimensions.

The magnetic quantum number is a handy way of telling us how many ways a subshell can orient itself. I say it’s handy because there’s a simple equation to tell you how.

For every value of l, there is a range of values of m from -l to l, including zero.

So, if our system is a d orbital, which is l = 2, there would be 5 ways the subshells could orient themselves, given by the m values -2, -1, 0, 1 and 2.

That’s all there is to that. See? Not so bad.

Intermission

Okay, okay. Break time. We don’t want to overcook your brains with chemistry and quantum theory. Fortunately, what we are going over is, theoretically, all there is to orbitals (without the droll mathematics, of course). And, as you already know, this leads to some amazing science. After all, after learning about electron shells, the next step can only be how elements combine to reduce energy even further!

Are you enjoying learning about how these microscopic particles work and seeing how something so complex can create something as simple as a drop of water and/or something as ubiquitous as air?

Let me know. I would love to talk science with you guys.

As always, thank you for joining me, and I will see you again very soon.

#elementalflow #flux #orbitals #scienceeducation #quantummechanics

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fluxsci · 7 years ago

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Elemental Flow - Valentia Orbitalis (3)

Image via MicroMountain

And we’re back with some more. This time, finally, we discuss orbitals. What if I told you that you already know what they are? For those of you who have already studied chemistry, you’ve possibly already started to put together the pieces from the last two lessons. For the rest of you, we have laid the groundwork for orbitals already by discussing what they are in detail. Orbitals are nothing more than the position of electron in the space of an atom.

I should stop before I get ahead of myself. Because it’s been so long since we’ve talked about electrons, I think it’s only proper to begin with a summary of the past lessons. Of course, if you want to understand these at a higher level, please check out part 1 and part 2.

In the Name of Energy

Low energy means no problems. The first lesson on electrons focused on their orientation and how they exist in a way that decreases their energy. The second furthered that discussion, showing that microscopic particles exhibit both particle-like behavior and wave-like behavior, changing the number of possible places that electrons can exist within the three dimensions, again, to minimize energy. In both lessons, we have discussed that modeling exactly where the electron is is difficult, but telling where it might be in a “cloud” of possible positions is far easier.

I don’t exaggerate when I say that, if you understand those two things, you understand most of orbital theory. But, of course, I’ll show you what I mean.

Elementary Table

First, we should establish a familiarity with the periodic table.

Image via Science Notes

Don’t be scared. Take a deep breath. This massive organization of scientific data should not scare you.

This table, like most periodic tables should, gives us all of the information required to talk about the elements. The key given explains what is within each box. To further explain, the number in the top left, or the atomic number, represents the number of protons within the atom. Given no excess in positive or negative charge, the atomic number can also be taken to refer to the number of electrons within an atom as well. The number in the top right, or the atomic mass or weight, is given as the size of an atom. Since the nucleus of any atom makes up most of the weight, you will usually see a reference to the mass number given before any particle. The mass number, unlike the atomic number, is the combined amount of protons and neutrons in any element.

Image via IPod Physics

Elements will always have the same amount of protons, which is why the atomic number is defined as the number of protons. However, an element will not always have the same number of electrons or the same number of neutrons.

You might have heard the term “isotope” before. Isotopes are the variations of an elements, given by differing numbers of neutrons. Some isotopes are less stable than others and, the less stable they are, the less likely that they are occur less in nature.

Image via TutorCircle

As you can see, protium, the hydrogen with one proton only, is the most commonly occurring, and, as such, the mass number of hydrogen is usually written as 1. Isotopes of hydrogen can have a mass number of 2 or 3.

But now we get to the interesting and most relevant part of the table: the electron shells and configurations shown at the bottom.

Sharing Shells

Remember when I said in the first lesson that reactions between elements exist in a give-and-take relationship? It’s finally time to tie the neat bow on the present that I had been preparing for you since the beginning. Let’s jump right in.

It is the electron shell that determines how many electrons an atom gives up. The theory of electron shells came from the idea that Niels Bohr had about electrons needing to be a certain distance away from the nucleus.

The outermost electron shell is called the valence shell. This is the shell that interacts with the valence shells of other elements. We have determined that the preferred number of valence electrons for any element in the valence shell is eight. This is according to the amount of electrons within elements in the noble gas category (the elements on the rightmost column of the periodic table). The reason for that is due to a unique characteristic of noble gases – they are almost completely nonreactive. If you put a noble gas next to any element, without any further additions, nothing would happen.

While the outermost shell is important, however, I would like to turn your attention to the inner shells – where the orbitals truly shine…in the next lesson. Don’t be too upset with me. You’ll appreciate this given the amount there is to tell you. Keep that periodic table handy.

And feel free to review and ask questions in preparation for the next lesson.

#flux #orbital theory #orbitals #science education #chemistry #physics #ElementalFlow

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fluxsci · 7 years ago

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Elemental Flow - Two Natures (2)

Circle Wave by Dave Whyte via [https://dribbble.com/shots/1696376-Circle-wave]

|| by matthew It’s interesting how the deeper you dive into the atom, the more you find. There really is a whole universe in these atoms. As such, I recommend that you take a look at the previous lesson in the Elements’ Flow series in order to really understand where I will be going in this one.

Before I jump right in, I recommend that you actively participate in this lesson. Grab a notepad and pen or use your word processor of choice and take notes. This one is very involved and you may have questions that I encourage you to answer. They will help not only you, but me as well, and you might even inspire another chapter of the storyline.

Without further ado, enjoy…and keep an extra box of tissues nearby; this one’s is a tear-jerker.

What Are They?

Imagine, for a moment, a situation where there are many electrons surrounding a nucleus. As we previously discussed, Schrödinger created a model where electrons are a certain length and orientation away from the nucleus, yet close enough to experience its attractive force while maintaining a respectable distance away from other electrons – a tough balancing act for sure. With respect to this model, you might expect them orient themselves around a nucleus in any way that reduces their energy.

But why do they move at all? Why would they not just orient themselves in the spots that satisfy those three conditions and then simply vibrate in place to get rid of any excess energy that enters their system? On a macroscopic scale, magnets do this: they don’t bounce around – they either snap in place or repel each other.

The reason that electrons can’t just settle is because these, like other microscopic particles, have a hidden second nature that they must abide by.

I imagine that this is an area where most college chemistry professors avoided, much to all of our dismay, because it explains quite a bit about why electrons do what they do. They must have thought that everyone understood beginner level Quantum Mechanics. Common mistake, I suppose (sarcasm). If you’re a part of the 99% that doesn’t know what I’m talking about, strap in. This will probably be a bumpy ride.

Bohring Beginning

Quantum Mechanics has the capacity to either make you worry about how difficult it is, excite you over its mythos and the scientists responsible for its inception, or terrify you about the microscopic world that composed everything you know and love. Or a combination of the three.

In the quest for the “hidden nature”, I say we dive into a few of the key figures that wanted to model the electron. Let’s begin with Niels Bohr and his model of the electron.

Image via [https://www.universetoday.com/46886/bohrs-atomic-model/]

Shortly after Rutherford’s model, which you saw in the last lesson, Bohr edited the model to be more consistent with his findings.

He noticed that, during the reduction of energy in the electrons, they would release light.

But, alone, that is not such a big deal – light is a form of energy. The problem was the strange way that light was coming from the atoms. Let’s take a brief divergence into the physics of light to figure the phenomenon out.

From Light Comes Color

Light, as we can see it, is the mixture of energies on the visible spectrum. That might sound complex, but it’s actually quite simple to understand, given that you see it in effect after the sun comes out after a nice rainstorm.

Image via [http://clipart-library.com/images/kc85abK9i.jpg]

White light, when refracted, or bended, through a substance (water in the case of a rainbow) splits into seven memorable colors: red, orange, yellow, green, blue, indigo and violet. They are split according to the size of their wave, or wavelength, with red light having the highest wavelength (around 700 nanometers) and violet having the lowest (around 400 nanometers). These wavelengths are inversely-proportional to the amount of energy, meaning as wavelength grows, energy drops.

Image via [https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/902/2015/02/23224709/CNX_Psych_05_02_Wave.jpg]

There’s even a nice formula for this. I’ll show it below, but don’t worry about this for now. It won’t be on the test.

You can that if you put in bigger and bigger numbers in the wavelength symbol, lambda, energy gets smaller and smaller. And there’s another constant! Don’t worry, we’ll get to Planck when we talk about quantum mechanics. He is the founder of the field, after all.

Image via [http://astronomyonline.org/Science/Frequency.asp]

Discrete Discovery

So, what was the strange discovery Bohr made?

He noticed specific colors coming from the electrons when he measured the system. If the electrons could truly be anywhere around the nucleus, Bohr would have seen the full visible spectrum of colors like what you see in a rainbow. In quantum mechanical terms, this electron is quantized, meaning that it only releases discrete, or distinct, energy levels, not continuous ones, like that of a rainbow.

Continuous on the top, discrete on the bottom.

Image by Dmitry Karpenko & Vahe Ganapetyan via [https://www.reefll.com/svet_v_rifovom_akvariume]

This led Bohr to think that the electrons must be an exact distance away from the nucleus and each other. When higher-energy electrons decrease in energy level, they go to another exact distance from the nucleus that is lower than the one they were. The transition to lower orbits creates a specific color of light, caused by the energy that they give off.

As reasonable as these discoveries seem, science isn’t always so easy to get right the first time, no matter how many years one has spent on the topic. Important lesson.

First, electrons do not just infinitely continue to expand outward from the nucleus according to their energy state. You might imagine that if it gets too far away, it would just break free of the attractive electric force of the nucleus. That is absolutely true, and, there is such a concept called a “free electron”, which is defined as just that.

Secondly, Bohr seems to think here that electrons are traveling on an orbit like planets around a star, making the model completely two-dimensional. Think about that for a moment. Are school buses in children’s drawings really as flat as they look on a piece of paper? Realistically, they’re three-dimensional; school buses carry rows and rows of children. This limits the electrons in his model to only expand outward, overlapping with the first problem.

To explain the exertion of light by transitioning electrons, Bohr had to apply research of the legendary Albert Einstein just about two decades earlier. Einstein made a name for himself by publishing a set of papers that included a discovery of the photon.

The photon is defined as light’s quantum, or the discrete and fundamental unit of energy of light. Einstein found that the quantum had no rest mass, meaning that, when the photon is not in motion (at rest), it has no mass. That mind-blowing discovery revolutionized physics for good.

Nevertheless, it was odd that an electron mirrored the photon in that it behaved as though it was quantized. Why would an electron, a particle with mass, share qualities with a photon, a particle without mass? Perhaps there were more similarities between these particles than just this?

Electromagnetic Forces of Nature

Light has been debated since the times of the legendary Sir Isaac Newton. Despite his own experiment of splitting light into its seven colors with a prism (yes, that was him), Newton believed that it was a particle because of how light created clear shadows.

Image drawn by John Adam Houston

See? Even great scientists can miss things. You’ll remember that the only reason that we get the rainbow of colors is due to refraction.

The kicker is that particles do not refract. Only waves do.

Experiments done over hundreds of years following Newton have yielded similar results. The most notable experiments were done by James Clerk Maxwell in the 1800s, who developed a set of equations for electromagnetic waves that we still use to this day. Of course, Einstein would rebel in the early 1900s and move on to experimentally prove that light was not only a wave, but also a particle.

So light is massless, and behaves like waves and particles. It’s crazy to insist that an electron could be similar, right?

Louis de Broglie, a scientist of France, didn’t think so. He saw where Bohr’s experiments left him and, unsatisfied with his model, tried to take it a step further theorizing that microscopic particles with mass also behaved like waves.

Using the aforementioned equations of Maxwell and Einstein’s discovery of the dual nature of light, de Broglie was set to make history. He knew that, as a charged particle, an electron would likely be under the influence of both an electric field and a magnetic field making their wave pattern electromagnetic. Electromagnetic waves, are defined as oscillations, or regular movements back and forth (like a pendulum), that are caused by both electric and magnetic fields.

Remember that equation we talked about in the last part – Coulomb’s Law? It defined the electrostatic “power” of charged particles. The relationship between particles, whether they were attracted to or repulsed by each other, would create an electric field!

The strength of the field from any individual charge is determined by the strength of that charge.

Image via [http://electricity-automation.com/img/electricity/fieldLines.jpg]

Magnetic fields are created, simply, whenever charges move.

Image via [http://www.schoolphysics.co.uk/age16-19/Atomic%20physics/Electron%20physics/text/Electron_motion_in_electric_and_magnetic_fields/index.html]

Beautiful Curves

With this knowledge, de Broglie only needed to validate his theory by comparing it to Bohr’s findings while improving upon them to eliminate the previously-mentioned shortcomings in Bohr’s model.

Fortunately, it is theoretically easy to do all three. Bohr found that the electrons must be in defined orbits – otherwise they would not be exhibiting discrete energy in the form of photons when they went from a higher to a lower energy state. That means electrons must exist such that their orbits are uninterrupted and stable. We define waves that are constant and not under any interference standing waves. The electrons must also be in phase with their orbits, meaning that they stay on a consistent path over time.

This is what that looks like:

Image via [http://hyperphysics.phy-astr.gsu.edu/hbase/Bohr.html]

The frequency of the waves, or, how many humps there are, is purely determined by how much energy the electrons have. In fact, the only possible way that one can have an exact orbit as more and more electrons are added is if the electrons are at an energy level that allows them to be a standing wave. If electrons were to become excited and the energy used to excite them was not enough to bring them to a standing wave, it would not move to a higher energy state.

Also, notice that n = 1 looks exactly like Bohr’s model, a simple circular orbit. Bohr’s model was only correct for the case where there is only one electron present – the hydrogen atom!

Lastly, wrapping it up nicely, the waves from this model move into three dimensions, supplanting the limited 2D model of Bohr.

Image by Andrew D. Hwang via [https://math.stackexchange.com/questions/2383454/what-will-be-the-form-of-the-equation-of-a-standing-wave-in-circular-form-as-sho]

This is how electrons move, creating the wave-particle duality of all things composed of microscopic particles. We know that electrons are absurdly fast, as well, so, by observation, we can never know where on the path electrons are at any time. This is what ultimately inspired Schrödinger to create the electron cloud model that we use today. Despite the messiness of that model, electrons on it are moving in these same wave-like patterns. Schrödinger’s concern, unlike de Broglie’s, was to create a mathematic model to figure out the probability of finding an electron in a certain position, which he was successful in doing, beginning orbital theory.

So, in closing, at an atomic level, your body is behaving like both a wave and a particle. I hope that doesn’t keep you up at night. If it does, just stare at this image that is strikingly similar to the above model. I promise it will calm you down.

You deserve it after making it through this one.

Image via [https://www.pinterest.com/pin/678636237570753011/]

#science #quantum mechanics #flux #electrons #einstein #bohr #schrodinger #ElementalFlow

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fluxsci · 7 years ago

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Elemental Flow - Charged Relationship of Give and Take (1)

|| by matthew

How does one personify the relationship between an individual element and another? Sure, you could use the word “electrostatic” or explain it by going into depth about electronegativity, but those aren’t immediately relatable. If I were to put it into more understandable words, I would say that it’s a game of sharing. Sharing that happens the same way almost every single time according to both size and state of matter. Some reactions occur naturally just by distance. Some may only occur in the present of some outside energy source like heat.

Reactions between the elements, thus, play a game of give and take. But give and take what?

The Necessity of Negativity

The only way to properly answer that question is to explain the importance of the negatively-charged electrons.

Image via [http://www.chemistryjokes.com/jokes/stupid-electrons/]

While any atom's core is made up of protons and neutrons, two of the most elementary particles in existence, electrons surround that core, attracted to its positively-charged protons. Yes, the phrase “likes repel and opposites attract” is certainly true of subatomic particles and is a fundamental truth of chemistry. However, I digress: electrons are also crucial in the communication between that element and any other. Think of it this way: electrons are the invitation to the party that every particle in the universe wants to be a part of. The particles show off their 'status' by how many electrons they own. Kind of like the guy that doesn’t stop bragging about how many girls are into him. Yeah, we all know that guy.

The guy is a jerk, but he still gets whatever he wants because he’s got the social pull. Well, believe it or not, atoms are the same way. But we will come back to this in the next piece.

You may have heard the terms “valence shell” and “orbital”. Yes, I can already hear the collective cry of pain from those who are familiar with the beginning lessons of chemistry in college or some advanced high-school programs. Don’t worry. I will make this…less painless than your professors tried to.

In order to properly understand, we have to start with a philosophy that holds true for every system in the universe. That is, that there is always a desire to be at the lowest energy possible. Everything you see in the world follows this principle. It is why when a car crashes, sound is released in response to how fast the car was going. That is an example of a transfer from kinetic energy, the energy of motion, to sound energy. Energy represents stability of a system. The lowest energy state represents the most stable state. In other words, if a system could not release energy, for whatever reason, it would be considered unstable.

Orbitals are an extension of that philosophy. These are the representation of energy states in any given element, which are “filled” by our party-invitations, the electrons.

But if an electron is randomly encircling the nucleus of an atom, why would there be different energy states? What causes electrons to occupy different orbitals?

Mathematical Attraction

When you are an electron, you are naturally the most attracted to the nucleus of an atom, where both positively charged particles reside. But you could imagine, if an atom with a large atomic number, or the number of protons in the nucleus, were to be surrounded by an equally large number of electrons in close proximity, you should generally expect that all of the negative charge near each other would increase the total energy of each electron – remember, likes repel, meaning electrons do not like electrons. This is according to the electric force, that very cumbersome thing that I mentioned in the first paragraph. In chemistry and physics, this is referred to as Coulomb’s Law.

Image by Melanie Fine via [http://chemin10.com/periodic-trends-and-coulombs-law/]

We will go through the terms of this equation in full.

First, most notably is k, the Coulomb Constant. A constant, if you are unaware, is a fixed value, usually represented by a letter or sign. Basically, this constant, k, will always represent a value of 9 x 10^9 N*m^2/C^2. (N is newton, a unit of force, m is meter, a unit for distance and C is coulomb, a unit for charge).

Next, we have both q values. These represent the quantity of the charges between the two particles being compared.

Last is r, or the distance between the two particles.

Now, these values, after being determined experimentally, can be put into the above equation and an electric force can be quantified, but the important part here is the sign of the force, or whether it is positive or negative. If the force is positive, the two particles repel each other, and if it is negative, the two attract each other. Electrons that are near each other have positive electric force, meaning they repel, and their energies rise when near each other. The question, then, is what would electrons in close proximity do?

If you answered that they try to reduce their energy, you are 100% correct.

The higher the repulsion force, the more likely they are to distance themselves in order to lower that total energy. This creates a situation where electrons are not only attracted to the positively-charged nucleus, but repelled by lower-energy electrons. This fits intimately with the concept of orbitals – electrons randomly “orbiting” the nucleus at different energy states.

Image via [http://byjus.com/chemistry/rutherfords-model-of-atoms-and-its-limitations/]

The Atomic Balancing Act

The quotations I put around “orbiting” are important, as electrons do not really orbit in your conventional sense. In actuality, they occupy a certain space around the nucleus and can be anywhere in that space or at any time. So, yes, if you didn’t know, that classic image of an atom founded by Ernest Rutherford is completely wrong. In actuality, it looks like this:

Image via [http://coutsd.weebly.com/schrodinger-electron-cloud-model.html]

Brought to you by Schrödinger. Yes, the same one with the cat and the box. Or was there a cat in that box...?

In any event, to further explain why an electron occupies a space rather than orbiting in a conventional sense, we need to discuss energy once again. When an electron is farther away from the nucleus, it has a large amount of “stored energy”, or potential energy. This potential energy is the energy that propels the electron towards the nucleus. As it moves, the potential energy converts to the energy of motion, or kinetic energy.

High potential energy up there, high kinetic energy on his way down...And zero energy when he hits the ground...Splat.

Image by Ms. Lintan (http://mslintan.tumblr.com/) via [http://mslintan.tumblr.com/post/51478270140]

If you were wondering why an electron just doesn’t smash into the nucleus, it is because the amount of kinetic energy is far larger than the potential energy at the center. In fact, the kinetic energy is infinite at the center; therefore, the momentum of the electron is infinite at the center. At that point, it’s impossible for the electron to attach to anything – it’s got far too much energy!

Wait…too much energy? We can’t have that, now can we?

Therefore, to minimize net energy, there must be a certain distance where the electron is placed so that it still experiences attraction from the nucleus and does not experience a near infinite kinetic energy. This balance is tentative, causing the electron to move in an unpredictable manner, but still maintain a certain area.

If you guessed that this sounds a lot like orbitals, congratulations, you’ve mastered energy states! According to the distance that the electrons occupy, the orbitals of the atom can look different. The electron cloud above represents the orbital configuration that one would see in a lithium atom…But we have tons more…Enjoy this sneak peek at what is coming next.

Image by Donald A. McQuarrie via “Quantum Chemistry”

#science #chemistryjokes #scienceeducation #atoms #electrons #orbitals #Flux #ElementalFlow

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fluxsci · 7 years ago

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The Elemental Flow Summary

The Elemental Flow Summary #Flux #Science #Atoms #Orbitals

Image via Vivax Solutions The Elemental Flow arc is long past us, but our objective is to make sure you understand what you’ve learned…It’s one thing to say that you’ve been taught. It’s another to say that you can remember – a general flaw brought about by time constraints in school. The Motivations for Electrons Electrons behave in a simple manner. There is only one factor that motivates it –…

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#electrons #ElementalFlow #flux #orbitals #Science

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fluxsci · 7 years ago

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Elemental Flow - The Aufbau Ribbon (6)

The modern masters promise very little; they know that metals cannot be transmuted, and that the elixir of life is a chimera. But these philosophers, whose hands seem only made to dabble in dirt, and their eyes to pore over the microscope or crucible, have indeed performed miracles. They penetrate into the recesses of nature, and show how she works in her hiding places. They ascend into the heavens: they have discovered how the blood circulates, and the nature of the air we breathe. They have acquired new and almost unlimited powers; they can command the thunders of heaven, mimic the earthquake, and even mock the invisible world with its own shadows.

- Mary Shelley (Frankenstein)

Did you notice that the scale of what we discuss is getting bigger? Yet there’s always going to be a ribbon to tie things up with…That’s the beauty of science having its gentle fingers on every pulse.

The ribbon around everything that we’ve discussed in the last 5 chapters is the Aufbau Principle. It basically describes the order of how electrons organize according to everything that we’ve learned. Specifically, electrons seek stability according to the rules of the Pauli Principle, which states that there can only be two electrons in any one orbital.

In addition, the Aufbau principle, from the German word “build-up” states that electrons must occupy the orbitals of the lowest energy before going to the higher energy orbitals.

That makes sense, right? Electrons have no need nor desire to be at a high energy level; if they can exist in a lower energy state, they will be.

The Build-Up

Before we begin, you might want to keep a periodic table handy.

Image via ScienceNotes

Building from chapter 4 and 5, the organization of each orbital conventionally takes the form of Principle-Orbital-Spin (n-l-s). The Aufbau Principle dictates that we start from lowest to highest energy level. As such, it’s surprisingly trivial to label these orbitals to see just how electrons organize themselves along the periodic table.

The first number, the Principle Quantum Number is what shows the energy level, and thus, the electron shell of an element. If we are trying to occupy the lowest energy states first, we start with 1 – ground state energy. Next, the Orbital Quantum Number, the subshell number. Its lowest value is 0, corresponding to its label - s. Last, the Spin Quantum Number gives you whether one or both electron spins have been filled. The two spins (negative and positive) of each subshell must be filled before moving to the next subshell.

The unnamed Magnetic Quantum Number, the subshell orientation number, is necessary for telling how a subshell is filled by electrons. As a reminder, telling how many orientations there are is as simple as looking at the orbital quantum number and counting the spectrum from negative to positive. For example, if the orbital number is 0, there’s only 1 subshell. If it’s 1, there are 3 (-1, 0, 1).

The n-l-s system dictates that the lowest possible energy state is 1s1. This value is the numerical representation of an orbital. This particular orbital corresponds to hydrogen.

But remember, there are two electrons, spinning oppositely, per subshell. With the addition of the second electron, we hit 1s2. This state corresponds to helium.

Once all subshells’, and, therefore, the entire shell’s electrons have been filled, the next shell can be filled. We know that the next principle number, 2, marks an increase in energy states, which also means that the distance that electrons are from the nucleus increases. Ergo, the more energy electrons have, the more capacity they have to break away from the attractive forces of the nucleus.

With the increase in distance and the addition of even more electrons comes increases in possible electron configurations, resulting in not only new subshells, but also new orientations. Yet each orbital follows the Aufbau Principle. As such, you see an organization like the following picture.

Image via PrintableDiagram

This is an orbital diagram. Each arrow represents an electron and its spin.

Pretty easy, right? But, of course, science has to throw a proverbial wrench in our understanding. Why can’t it just be easy for once…? I know, dear reader, I know.

Attack of the Hund’s

When it comes to elements that have multiple orbitals orientations in a subshell, which is every element with a principle number of 2 or above, each orbital must have one electron spin occupied before it is occupied with the electron with the opposite spin. This is known as the Hund’s Rule. You could likely guess the reason for this now, but, just in case you haven’t understood the only motivation that electrons have yet, it is to reduce energy.

Two electrons grouping together in an orbital is already hard – the negative charges naturally repel each other. To reduce the effects of repulsion, the electrons inhabit the orbitals with similar energy levels first. Each spin direction has such a similar energy level to an electron with the same spin. That means, since Pauli’s Principle prevents two electrons with the same spin from existing in the same subshell, each subshell will be filled with one spin direction before they are filled with the opposite spin.

A respectable analogy is something that you’ve likely experienced. Have you ever been reading a book at a library or bookstore with plenty of empty chairs dispersed around? How would you feel if, then, someone sits right next to you, occupying your space? Doesn’t that just feel wrong? Maybe a little inconvenient? How about if someone sat directly across from you. Now that would just be awkward; imagine you looking up from your riveting novel only to see a pair of peering eyes looking back at you. But, if all of the seats in the socially appropriate places are taken, then there’s less of an issue with people taking the remaining seats. That’s, essentially, how electrons feel. They want to fill the empty, most distant seats before filling in in the inconvenient seats.

Therefore, orbital diagrams will show that electrons fill each orientation with the same upward spin before filling each orientation with the opposite downward spin. The necessity of having similar spin is based off the observed principle that like spins repel less.

For clarity, here is another orbital diagram with 36 elements. Check out boron (B) to Neon (Ne) to understand Hund’s Rule.

Image via Meta-Synthesis

We will need this for the next part, so hold onto it.

Diagonal Rule

There’s one more curve ball that you should be aware of.

Electrons tend to fill orbitals in a unique, but organized way after the 2p subshell in most cases. When you get to the third principle number, you gain yet another subshell – the d subshell.

As we’ve said 1s1 is hydrogen and 1s2 is helium. With each element in the periodic table, the number of electrons within the system grows by one. But when you get to Argon (Ar) and move to Potassium (K), it goes from 3p to 4s. Why would we skip the 3d shell? After all, we went from 1s, to 2s-2p, then 3s-3p. Shouldn’t 3d come next?

There was a little factor that I purposely did not mention until this point. You can actually define the energy of orbitals by adding the principle quantum number and the orbital quantum number – n + l. This is called the Madelung Rule, which gives the order that orbitals are filled in. So, if we take hydrogen, for example, with an n of 1 and an l of 0, or s, we see that it has an energy level of 1, which is the lowest. Hydrogen and helium, technically, both fit into this 1s category, but we know that helium has two electrons, while hydrogen has only one. Therefore, helium has more energy in the system.

To belabor the point, it would be as if you had a solitary magnet on the table. It won’t move on its own until you put something of a similar pole near it, in which case it will move away. Electrons experience a similar reaction to each other, and therefore, the element itself is more energetic the more electrons there are.

But, returning to potassium (K), which has an n of 4 and an l of 0, it has an energy level lower than Scandium (Sc), which has an n of 3 and an l of 2. Potassium, which occupies the 4s orbital, has an energy level of 4, while scandium has an energy level of 5. Therefore, the 4s level is filled first.

This staggering creates a well-known diagonal. In fact, we can easily tell how to fill orbitals by following this Diagonal Rule.

Image via HyperPhysics

It’s simply amazing how we manage to organize something as chaotic as an electron. I suppose, however, that this is how they organize; we are just observers in this game, of which we are a sentient and thinking part.

There’s one more amazing thing that these orbitals reveal about the periodic table. It explains the Noble Gases.

The Noble Story

Time for another callback. Remember in chapter 3, when I mentioned noble gases and valence electrons? I said that noble gases were almost completely nonreactive.

Look at this periodic table.

Image via Chemistry LibreTexts

This puts a little more attention on the electron configuration. Do me a favor: take a look at the noble gas group, or the column to the right.

Their orbitals are completely filled! There is not one spin arrow that is unaccompanied. You might have noticed that beryllium (Be) and magnesium (Mg) also fit this criterion. However, recall that every principle quantum number over 2 has a p or higher orbital. Those two elements, and all other elements in Group 2, don’t fill the p orbital, like neon and argon do in their respective rows.

Noble gases are nonreactive because there are no electrons required to complete their electron shells. Therefore, an element paired with a noble gas will lead to no result; there is no response to the phone call, as it were. Without space free for more electrons, there’s almost no way for elements to communicate.

If you look at your complete periodic table and the image of the orbital diagram used in the Diagonal Rule section, you can see this is the case for Argon (Ar) and Krypton (Kr) as well. Yes, Superman is from a very noble planet indeed.

Conclusion

At last, the Elemental Flow Arc comes to its end. Now that you know what electrons are, in terms of how they move and organize themselves in an element, you are well equipped to understand how elements combine. In fact, I’ve already given you the answer to that. But, I suppose we will see soon, as we move with the flow eternal.

#flux #elementalflow #orbitals #electrons #scienceeducation #science

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