Introduction to Quantum Mechanics - Video Tutorials & Practice Problems
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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 psi in 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 gonna 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, but we're going to go piece by piece and understand how the 4 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 a theoretical approach in understanding the behavior of electrons. They represent a set of values that 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 subshells. These subshells are the regions where a group of electrons in an atom are located within the same shell. The subshells use the variables of s, p, d, and f. Now within these subshells we have our orbitals. This is the region within a subshell where specific electrons can be found. So if we take a look here at our quantum view, we have first our shell, and within our shell we have our sub shell here in blue, and within our sub shell we have our orbital in red. And within a given orbital is where you find your electrons. These electrons spin will learn either clockwise or counterclockwise, 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, our angular momentum quantum number, our azimuthal quantum number, so both terms are interchangeable, the magnetic quantum number and our spin quantum number. With the principal quantum number this deals with the energy and size of a shell, and it uses the variable n. Next, we have our angular momentum quantum number also called our azimuthal quantum number. It deals with the shape of an orbital within a sub shell. It uses the variable l. Next, we have our magnetic quantum number. Here, this just gives us the orientation of electrons in a set of orbitals, but more specifically it gives us the location of electrons within a set of orbitals. It uses the variable m sub l. And then finally we have our spin quantum number, and from the name it tells us the spin of an electron in an orbital, and and it uses the variable m sub s. Now all 4 quantum numbers together ultimately gives us the location of us an exact electron with an atom. Looking at all 4 quantum numbers together, we start off first with the atom, and within the atom we look at its shell, one particular shell. Within that shell we find our sub shell. Within our sub shell we have our orbitals, 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 atom over all, and as we start looking at all the quantum numbers together it gets us more and more and more specific in terms of an electron that we seek. Alright? So that's the way we use the quantum numbers to understand the behavior of electrons and ultimately their 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 ellipsis, Which quantum member would best describe this image? Alright. So they're saying that the electron is traveling in an ellipsis. So an ellipsis 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 a shape and 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 azimuthal quantum number. So that would mean that option b would be our correct answer.
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