The **4 Quantum Numbers** provide us the coordinates to find the theoretical location of an electron.

Quantum Theory

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## Introduction to Quantum Mechanics

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Now, quantum mechanics represents the mathematical or theoretical description of matter and its electrons on the atomic scale. It's a way of us describing the behavior of electrons within any given atom. Now, if we were to take a mathematical approach to it, we'd have to use short schrodinger's wave equation. So if we take a look, we can see that this equation is pretty complicated, We have sign there, we have delta. But don't worry, this type of equation isn't necessary for this level of chemistry. So we're gonna bypass the mathematical approach in describing the behavior of electrons. Instead, we're going to take more of a theoretical approach and that means that we're gonna have to understand the quantum numbers. Now, some people may hate the quantum numbers. We're gonna go piece by piece and understand how the four quantum numbers themselves help to explain the location and therefore the behavior of any particular electron within a given atom.

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## Introduction to Quantum Mechanics

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remember, The quantum numbers are theoretical approach and understanding the behavior of electrons. They represent a set of values to describe the energy levels and ultimately the location of a specific electron. Now, within an atom, we have what we first call our shell. The shell is the orbit that the electrons take as they travel around the nucleus. Now, within this shell, we find what are called sub shells. These sub shells are the regions where a group of electrons in an atom are located within the same shell. The sub shells use the variables of S, P, D and F. Now, within these sub shells, we have our orbital's. This is the region within a sub shell where specific electrons can be found. So if we take a look here at our quantum view, we have first are shell and within our shall we have our sub shell here in blue and within our sub shall we have our orbital in red and within a given orbital is where you find your electrons thes electrons spin will learn either clockwise or counterclockwise, so we'll see what that entails later on. Now this quantum view connects directly to our quantum numbers. So with our quantum numbers, we have our principal quantum number are angular momentum Quantum number are as a mutual quantum number. So both terms are interchangeable. The magnetic quantum number in our spin quantum number with the principal quantum number. This deals with the energy and size off a show, and it uses the variable end. Next, we have our angular momentum. Quantum number also called her as a mutual quantum number. It deals with the shape oven orbital within a sub shop. It uses the variable l Next we have our magnetic quantum number here. This just gives us the orientation of electrons in a set off orbital's. But more specifically, it gives us the location of electrons within a set of orbital's. It uses the variable M sabal. And then finally we have our spin quantum number, and from the name it tells us the spin off an electron in an orbital, and it uses the variable m sub s. Now, all four quantum numbers together ultimately gives us the location of us an exact electron within an atom. Looking at all four quantum numbers together, we start off first with the atom and within the atom. We look at its shell, one particular shell. Within that shop, we find our sub shop within our sub shell. We have our orbital's, and within a specific orbital is where we locate finally, the electron of interest. So this is the basic breakdown for the quantum numbers. We start off macro view looking at an Adam overall. And as we start looking at all the quantum numbers together, it gets us, Mawr and Mawr and Mawr specific in terms of an electron that we seek. All right, so that's the way we use the quantum numbers to understand the behavior of electrons and ultimately, the locations.

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## Introduction to Quantum Mechanics Example 1

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now here, it says if the path of an electron within an orbital can be seen as an ellipse sees which quantum number would best describe this image? All right, so they're saying that the electron is traveling in an Ellipse, sees so in ellipses can be seen as something like this. So they're talking about the specific shape that the electron create as it moves along its path. So we're talking about ah shape. Now we know that if we're talking about a shape that has to deal with the angular momentum quantum number another name for the angular momentum quantum number would be the ASM youthful quantum number. So that would mean that option B would be are correct answer.

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