Wave Function - Video Tutorials & Practice Problems

On a tight schedule?

Get a 10 bullets summary of the topic

This section deals with the basics of quantum mechanics. Don't worry too much about it, but this is some good general information.

Definition of an Atomic Orbital:

These funny orbital shapes represent the 3-D plots of the equations that describe the probability of finding electrons at any given place as their energy states increase.

1

concept

The probability of finding electrons in a given place.

Video duration:

6m

Play a video:

Hey everyone. So in this video we're gonna take a look at wave functions. But before we get to them, let's talk about the importance of quantum mechanics. So why is exactly quantum mechanics and important topic? Well we need to understand is the smaller an object gets, the more likely it can behave as either a particle or a wave. And this comes with great complications in terms of determining the location of that particle, how it's moving etcetera. Now, quantum mechanics is what states that electrons, because they're so small, behave both as particles and as waves. And with quantum mechanics we have the Heisenberg uncertainty principle which states that we cannot simultaneously know an electron speed and position. So we might know the speed in which an electron is traveling but we won't know its position or we may know its position but not know how fast it's moving. So because of this issue we more focus on the probability on an electron's location. And this is where wave functions come in handy. So we're gonna say equations called wave functions correspond to the energy state of an electron. And to symbolize this wave function, we use the symbol of sai so wave functions is corresponded by this image of a sigh and we're gonna say the relative probability of finding an electron can be derived from the way function. And we do this by squaring our side. Okay, so here again we don't know both the speed and position of an electron. So we're talking about the probability of finding an electron location instead. Now we're gonna say here that the three D plot of the y squared. So relative probability is called an atomic orbital. So, coming from general chemistry, we know that an orbital is the probable location of any defined electron. So this is our chance of finding electrons. Words where it's going to be high. Now, remember from general chemistry we talked about different types of orbital's. So we have as orbital's which are spherical in nature like one S and two S. And then we have p orbital's which look like dumbbells. But an easy way to remember the shape of a p orbital soapy here. Peanut also starts with a P these kind of look like peanuts. Okay, so that's a good way to help you remember the shape of a p orbital. Now, remember when we talk about these different orbital's their find within different energy levels. So we're looking at let's say the carbon atom, we can talk about how can we display its orbital diagram Remember for carbon, its atomic number is six, which means it has six electrons. So that means that the electron configuration is one S 22 us two to P two. Now let's start filling out each one of these orbital's. First of all, remember an S orbital has only one orbital, its shape is spherical in nature. Remember that each one of these orbital these boxes can house a max of two electrons. And following what we call the exclusion principle. We're not gonna go too much into those things. These are simple things that we learned in gen can remember the electrons in there have to be have opposite spins. So we have one electron spinning up and then we have one electron spinning down. Now the order doesn't really matter which one you write first, they just have to have opposite spins. Once we filled up the one s we move on to to us us has more energy and we moved from lower energy orbital to higher energy orbital's following off balls principle. So here we go, one up, one down now, the two piece, there's three of them, there's X, Y and Z. Okay, they all have the same energy since they're all two P orbital's the only difference is the position in which they lie on the X axis, the y axis and Z axis, but they're all the same energy because of this. You could technically start filling them up at PZ if you want, but traditionally we fill them out starting with P X. And we're going to say here following our half half spin rule. So Hunt's rule, we have felt first we have to fill in two electrons, so one up one up, You could also do one down 1 down. That would also work as well. But traditionally start out with the one spinning up first. Now, if we look at this, this is how we complete the orbital diagram for the carbon atom. So this tells us that in the first show, which only houses the one s orbital, we have a maximum of two electrons possible and in the second show, we have both two s and two p orbital's. This in theory can hold up to eight electrons. It doesn't hold it for carbon because carbon just doesn't have enough electrons. It only has four total electrons within our second show. And then here we have our little meme. In terms of remember we had schrodinger's cat. Remember with shorting just cat it was the possibility of being both alive and dead. So quantum mechanics states that I am simultaneously half alive, half dead. So this kind of goes in relationship to electrons where the electron could be in this position or it might not be. So there's a half chance of it being there or not. So this kind of goes hand in hand with that concept. So, just remember, we can't know both the speed and position of an electron, but we can talk about the probability the most likely location of an electron and that most likely location of electron can be defined as orbital's

Atomic Orbital Interference

Instead of colliding into each other, wave functions have the ability to interfere with each other upon meeting.

The type of interference determines if a new bond will be created between the two orbitals.

2

concept

Constructive vs. destructive interference.

Video duration:

3m

Play a video:

Hey everyone. So in this video we're gonna take a look at wave functions. But before we get to them, let's talk about the importance of quantum mechanics. So why is exactly quantum mechanics and important topic? Well we need to understand is the smaller an object gets, the more likely it can behave as either a particle or a wave. And this comes with great complications in terms of determining the location of that particle, how it's moving etcetera. Now, quantum mechanics is what states that electrons, because they're so small, behave both as particles and as waves. And with quantum mechanics we have the Heisenberg uncertainty principle which states that we cannot simultaneously know an electron speed and position. So we might know the speed in which an electron is traveling but we won't know its position or we may know its position but not know how fast it's moving. So because of this issue we more focus on the probability on an electron's location. And this is where wave functions come in handy. So we're gonna say equations called wave functions correspond to the energy state of an electron. And to symbolize this wave function, we use the symbol of sai so wave functions is corresponded by this image of a sigh and we're gonna say the relative probability of finding an electron can be derived from the way function. And we do this by squaring our side. Okay, so here again we don't know both the speed and position of an electron. So we're talking about the probability of finding an electron location instead. Now we're gonna say here that the three D plot of the y squared. So relative probability is called an atomic orbital. So, coming from general chemistry, we know that an orbital is the probable location of any defined electron. So this is our chance of finding electrons. Words where it's going to be high. Now, remember from general chemistry we talked about different types of orbital's. So we have as orbital's which are spherical in nature like one S and two S. And then we have p orbital's which look like dumbbells. But an easy way to remember the shape of a p orbital soapy here. Peanut also starts with a P these kind of look like peanuts. Okay, so that's a good way to help you remember the shape of a p orbital. Now, remember when we talk about these different orbital's their find within different energy levels. So we're looking at let's say the carbon atom, we can talk about how can we display its orbital diagram Remember for carbon, its atomic number is six, which means it has six electrons. So that means that the electron configuration is one S 22 us two to P two. Now let's start filling out each one of these orbital's. First of all, remember an S orbital has only one orbital, its shape is spherical in nature. Remember that each one of these orbital these boxes can house a max of two electrons. And following what we call the exclusion principle. We're not gonna go too much into those things. These are simple things that we learned in gen can remember the electrons in there have to be have opposite spins. So we have one electron spinning up and then we have one electron spinning down. Now the order doesn't really matter which one you write first, they just have to have opposite spins. Once we filled up the one s we move on to to us us has more energy and we moved from lower energy orbital to higher energy orbital's following off balls principle. So here we go, one up, one down now, the two piece, there's three of them, there's X, Y and Z. Okay, they all have the same energy since they're all two P orbital's the only difference is the position in which they lie on the X axis, the y axis and Z axis, but they're all the same energy because of this. You could technically start filling them up at PZ if you want, but traditionally we fill them out starting with P X. And we're going to say here following our half half spin rule. So Hunt's rule, we have felt first we have to fill in two electrons, so one up one up, You could also do one down 1 down. That would also work as well. But traditionally start out with the one spinning up first. Now, if we look at this, this is how we complete the orbital diagram for the carbon atom. So this tells us that in the first show, which only houses the one s orbital, we have a maximum of two electrons possible and in the second show, we have both two s and two p orbital's. This in theory can hold up to eight electrons. It doesn't hold it for carbon because carbon just doesn't have enough electrons. It only has four total electrons within our second show. And then here we have our little meme. In terms of remember we had schrodinger's cat. Remember with shorting just cat it was the possibility of being both alive and dead. So quantum mechanics states that I am simultaneously half alive, half dead. So this kind of goes in relationship to electrons where the electron could be in this position or it might not be. So there's a half chance of it being there or not. So this kind of goes hand in hand with that concept. So, just remember, we can't know both the speed and position of an electron, but we can talk about the probability the most likely location of an electron and that most likely location of electron can be defined as orbital's