Hey everyone. So, in this video we're going to take a look at wave functions. But before we get to them, let's talk about the importance of quantum mechanics. So, why is quantum mechanics an important topic? Well, what we need to understand is that 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, etc. Quantum mechanics states that electrons, because they are so small, behave both as particles and as waves. With quantum mechanics, we have the Heisenberg uncertainty principle which states that we cannot simultaneously know an electron’s speed and position. So, we might know the speed at 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. Because of this issue, we more focus on the probability of an electron’s location, and this is where wave functions come in handy. So, we're going to say equations called wave functions correspond to the energy state of an electron. And to symbolize this wave function, we use the symbol of Psi. Okay. Wave functions are corresponded by this image of a Psi. And we're going to say the relative probability of finding an electron can be derived from the wave function, and we do this by squaring our Psi. 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's location instead. Now, we're going to say here that the three-dimensional plot of the y squared, so relative probability, is called an atomic orbital. 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 where it's going to be high. Remember from general chemistry we talked about different types of orbitals. So, we have s orbitals, which are spherical in nature like 1s and 2s, and then we have p orbitals, which look like dumbbells. But an easier way to remember the shape of a p orbital, so p here, p knot, 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 orbitals, they're found within different energy levels. So, when we're looking at, let's say, the carbon atom, we could talk about how can we display its orbital diagram. Remember for carbon, its atomic number is 6, which means it has 6 electrons, so that means its electron configuration is 1s^{2}, 2s^{2}, 2p^{2}. Now, let's start filling out each one of these orbitals. First of all, remember an s orbital has only 1 orbital, its shape is spherical in nature. Remember that each one of these orbitals, these boxes, can house a maximum of 2 electrons. Following what we call the Pauli exclusion principle, we're not going to go too much into those things. These are simple things that we learned in general chemistry. Remember the electrons in there have to have opposite spins. So we'd have 1 electron spinning up and then we have 1 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 1s we move on to 2s. 2s has more energy and we move from lower energy orbitals to higher energy orbitals following Aufbau's principle. So, here we go 1 up, 1 down. Now the 2ps, there are 3 of them: x, y, and z. Okay. They all have the same energy since they're all 2p orbitals. The only difference is the position in which they lie on the x-axis, the y-axis, and the 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 px. And we're going to say here, following our half-spin rule, so Hund's rule, we half-fill first, we have to fill in 2 electrons. So one up, one up. You could also do 1 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 shell, which only houses the 1 s orbital, we have a maximum of 2 electrons possible. And in the second shell, we have both 2s and 2p orbitals. This, in theory, can hold up to 8 electrons. It doesn't hold 8 for a carbon because carbon just doesn’t have enough electrons. It only has 4 total electrons within our second shell. And then here we have our little, meme in terms of remember we had Schrödinger’s cat. And remember with Schrödinger's 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 like goes hand in hand with that concept. So just remember we can't know both the speed and location of an electron, but we could talk about the probability, the most likely location of an electron. And that most likely location of an electron can be defined as orbitals.

- 1. A Review of General Chemistry5h 5m
- Summary23m
- Intro to Organic Chemistry5m
- Atomic Structure16m
- Wave Function9m
- Molecular Orbitals17m
- Sigma and Pi Bonds9m
- Octet Rule12m
- Bonding Preferences12m
- Formal Charges6m
- Skeletal Structure14m
- Lewis Structure20m
- Condensed Structural Formula15m
- Degrees of Unsaturation15m
- Constitutional Isomers14m
- Resonance Structures46m
- Hybridization23m
- Molecular Geometry16m
- Electronegativity22m

- 2. Molecular Representations1h 14m
- 3. Acids and Bases2h 46m
- 4. Alkanes and Cycloalkanes4h 19m
- IUPAC Naming29m
- Alkyl Groups13m
- Naming Cycloalkanes10m
- Naming Bicyclic Compounds10m
- Naming Alkyl Halides7m
- Naming Alkenes3m
- Naming Alcohols8m
- Naming Amines15m
- Cis vs Trans21m
- Conformational Isomers13m
- Newman Projections14m
- Drawing Newman Projections16m
- Barrier To Rotation7m
- Ring Strain8m
- Axial vs Equatorial7m
- Cis vs Trans Conformations4m
- Equatorial Preference14m
- Chair Flip9m
- Calculating Energy Difference Between Chair Conformations17m
- A-Values17m
- Decalin7m

- 5. Chirality3h 39m
- Constitutional Isomers vs. Stereoisomers9m
- Chirality12m
- Test 1:Plane of Symmetry7m
- Test 2:Stereocenter Test17m
- R and S Configuration43m
- Enantiomers vs. Diastereomers13m
- Atropisomers9m
- Meso Compound12m
- Test 3:Disubstituted Cycloalkanes13m
- What is the Relationship Between Isomers?16m
- Fischer Projection10m
- R and S of Fischer Projections7m
- Optical Activity5m
- Enantiomeric Excess20m
- Calculations with Enantiomeric Percentages11m
- Non-Carbon Chiral Centers8m

- 6. Thermodynamics and Kinetics1h 22m
- 7. Substitution Reactions1h 48m
- 8. Elimination Reactions2h 30m
- 9. Alkenes and Alkynes2h 9m
- 10. Addition Reactions3h 18m
- Addition Reaction6m
- Markovnikov5m
- Hydrohalogenation6m
- Acid-Catalyzed Hydration17m
- Oxymercuration15m
- Hydroboration26m
- Hydrogenation6m
- Halogenation6m
- Halohydrin12m
- Carbene12m
- Epoxidation8m
- Epoxide Reactions9m
- Dihydroxylation8m
- Ozonolysis7m
- Ozonolysis Full Mechanism24m
- Oxidative Cleavage3m
- Alkyne Oxidative Cleavage6m
- Alkyne Hydrohalogenation3m
- Alkyne Halogenation2m
- Alkyne Hydration6m
- Alkyne Hydroboration2m

- 11. Radical Reactions1h 58m
- 12. Alcohols, Ethers, Epoxides and Thiols2h 42m
- Alcohol Nomenclature4m
- Naming Ethers6m
- Naming Epoxides18m
- Naming Thiols11m
- Alcohol Synthesis7m
- Leaving Group Conversions - Using HX11m
- Leaving Group Conversions - SOCl2 and PBr313m
- Leaving Group Conversions - Sulfonyl Chlorides7m
- Leaving Group Conversions Summary4m
- Williamson Ether Synthesis3m
- Making Ethers - Alkoxymercuration4m
- Making Ethers - Alcohol Condensation4m
- Making Ethers - Acid-Catalyzed Alkoxylation4m
- Making Ethers - Cumulative Practice10m
- Ether Cleavage8m
- Alcohol Protecting Groups3m
- t-Butyl Ether Protecting Groups5m
- Silyl Ether Protecting Groups10m
- Sharpless Epoxidation9m
- Thiol Reactions6m
- Sulfide Oxidation4m

- 13. Alcohols and Carbonyl Compounds2h 17m
- 14. Synthetic Techniques1h 26m
- 15. Analytical Techniques:IR, NMR, Mass Spect6h 50m
- Purpose of Analytical Techniques5m
- Infrared Spectroscopy16m
- Infrared Spectroscopy Table31m
- IR Spect:Drawing Spectra40m
- IR Spect:Extra Practice26m
- NMR Spectroscopy10m
- 1H NMR:Number of Signals26m
- 1H NMR:Q-Test26m
- 1H NMR:E/Z Diastereoisomerism8m
- H NMR Table21m
- 1H NMR:Spin-Splitting (N + 1) Rule17m
- 1H NMR:Spin-Splitting Simple Tree Diagrams11m
- 1H NMR:Spin-Splitting Complex Tree Diagrams8m
- 1H NMR:Spin-Splitting Patterns8m
- NMR Integration18m
- NMR Practice14m
- Carbon NMR4m
- Structure Determination without Mass Spect47m
- Mass Spectrometry12m
- Mass Spect:Fragmentation28m
- Mass Spect:Isotopes27m

- 16. Conjugated Systems6h 13m
- Conjugation Chemistry13m
- Stability of Conjugated Intermediates4m
- Allylic Halogenation12m
- Reactions at the Allylic Position39m
- Conjugated Hydrohalogenation (1,2 vs 1,4 addition)26m
- Diels-Alder Reaction9m
- Diels-Alder Forming Bridged Products11m
- Diels-Alder Retrosynthesis8m
- Molecular Orbital Theory9m
- Drawing Atomic Orbitals6m
- Drawing Molecular Orbitals17m
- HOMO LUMO4m
- Orbital Diagram:3-atoms- Allylic Ions13m
- Orbital Diagram:4-atoms- 1,3-butadiene11m
- Orbital Diagram:5-atoms- Allylic Ions10m
- Orbital Diagram:6-atoms- 1,3,5-hexatriene13m
- Orbital Diagram:Excited States4m
- Pericyclic Reaction10m
- Thermal Cycloaddition Reactions26m
- Photochemical Cycloaddition Reactions26m
- Thermal Electrocyclic Reactions14m
- Photochemical Electrocyclic Reactions10m
- Cumulative Electrocyclic Problems25m
- Sigmatropic Rearrangement17m
- Cope Rearrangement9m
- Claisen Rearrangement15m

- 17. Ultraviolet Spectroscopy51m
- 18. Aromaticity2h 31m
- 19. Reactions of Aromatics: EAS and Beyond5h 1m
- Electrophilic Aromatic Substitution9m
- Benzene Reactions11m
- EAS:Halogenation Mechanism6m
- EAS:Nitration Mechanism9m
- EAS:Friedel-Crafts Alkylation Mechanism6m
- EAS:Friedel-Crafts Acylation Mechanism5m
- EAS:Any Carbocation Mechanism7m
- Electron Withdrawing Groups22m
- EAS:Ortho vs. Para Positions4m
- Acylation of Aniline9m
- Limitations of Friedel-Crafts Alkyation19m
- Advantages of Friedel-Crafts Acylation6m
- Blocking Groups - Sulfonic Acid12m
- EAS:Synergistic and Competitive Groups13m
- Side-Chain Halogenation6m
- Side-Chain Oxidation4m
- Reactions at Benzylic Positions31m
- Birch Reduction10m
- EAS:Sequence Groups4m
- EAS:Retrosynthesis29m
- Diazo Replacement Reactions6m
- Diazo Sequence Groups5m
- Diazo Retrosynthesis13m
- Nucleophilic Aromatic Substitution28m
- Benzyne16m

- 20. Phenols55m
- 21. Aldehydes and Ketones: Nucleophilic Addition4h 56m
- Naming Aldehydes8m
- Naming Ketones7m
- Oxidizing and Reducing Agents9m
- Oxidation of Alcohols28m
- Ozonolysis7m
- DIBAL5m
- Alkyne Hydration9m
- Nucleophilic Addition8m
- Cyanohydrin11m
- Organometallics on Ketones19m
- Overview of Nucleophilic Addition of Solvents13m
- Hydrates6m
- Hemiacetal9m
- Acetal12m
- Acetal Protecting Group16m
- Thioacetal6m
- Imine vs Enamine15m
- Addition of Amine Derivatives5m
- Wolff Kishner Reduction7m
- Baeyer-Villiger Oxidation39m
- Acid Chloride to Ketone7m
- Nitrile to Ketone9m
- Wittig Reaction18m
- Ketone and Aldehyde Synthesis Reactions14m

- 22. Carboxylic Acid Derivatives: NAS2h 51m
- Carboxylic Acid Derivatives7m
- Naming Carboxylic Acids9m
- Diacid Nomenclature6m
- Naming Esters5m
- Naming Nitriles3m
- Acid Chloride Nomenclature5m
- Naming Anhydrides7m
- Naming Amides5m
- Nucleophilic Acyl Substitution18m
- Carboxylic Acid to Acid Chloride6m
- Fischer Esterification5m
- Acid-Catalyzed Ester Hydrolysis4m
- Saponification3m
- Transesterification5m
- Lactones, Lactams and Cyclization Reactions10m
- Carboxylation5m
- Decarboxylation Mechanism14m
- Review of Nitriles46m

- 23. The Chemistry of Thioesters, Phophate Ester and Phosphate Anhydrides1h 10m
- 24. Enolate Chemistry: Reactions at the Alpha-Carbon1h 53m
- Tautomerization9m
- Tautomers of Dicarbonyl Compounds6m
- Enolate4m
- Acid-Catalyzed Alpha-Halogentation4m
- Base-Catalyzed Alpha-Halogentation3m
- Haloform Reaction8m
- Hell-Volhard-Zelinski Reaction3m
- Overview of Alpha-Alkylations and Acylations5m
- Enolate Alkylation and Acylation12m
- Enamine Alkylation and Acylation16m
- Beta-Dicarbonyl Synthesis Pathway7m
- Acetoacetic Ester Synthesis13m
- Malonic Ester Synthesis15m

- 25. Condensation Chemistry2h 9m
- 26. Amines1h 43m
- 27. Heterocycles2h 0m
- Nomenclature of Heterocycles15m
- Acid-Base Properties of Nitrogen Heterocycles10m
- Reactions of Pyrrole, Furan, and Thiophene13m
- Directing Effects in Substituted Pyrroles, Furans, and Thiophenes16m
- Addition Reactions of Furan8m
- EAS Reactions of Pyridine17m
- SNAr Reactions of Pyridine18m
- Side-Chain Reactions of Substituted Pyridines20m

- 28. Carbohydrates5h 53m
- Monosaccharide20m
- Monosaccharides - D and L Isomerism9m
- Monosaccharides - Drawing Fischer Projections18m
- Monosaccharides - Common Structures6m
- Monosaccharides - Forming Cyclic Hemiacetals12m
- Monosaccharides - Cyclization18m
- Monosaccharides - Haworth Projections13m
- Mutarotation11m
- Epimerization9m
- Monosaccharides - Aldose-Ketose Rearrangement8m
- Monosaccharides - Alkylation10m
- Monosaccharides - Acylation7m
- Glycoside6m
- Monosaccharides - N-Glycosides18m
- Monosaccharides - Reduction (Alditols)12m
- Monosaccharides - Weak Oxidation (Aldonic Acid)7m
- Reducing Sugars23m
- Monosaccharides - Strong Oxidation (Aldaric Acid)11m
- Monosaccharides - Oxidative Cleavage27m
- Monosaccharides - Osazones10m
- Monosaccharides - Kiliani-Fischer23m
- Monosaccharides - Wohl Degradation12m
- Monosaccharides - Ruff Degradation12m
- Disaccharide30m
- Polysaccharide11m

- 29. Amino Acids3h 20m
- Proteins and Amino Acids19m
- L and D Amino Acids14m
- Polar Amino Acids14m
- Amino Acid Chart18m
- Acid-Base Properties of Amino Acids33m
- Isoelectric Point14m
- Amino Acid Synthesis: HVZ Method12m
- Synthesis of Amino Acids: Acetamidomalonic Ester Synthesis16m
- Synthesis of Amino Acids: N-Phthalimidomalonic Ester Synthesis13m
- Synthesis of Amino Acids: Strecker Synthesis13m
- Reactions of Amino Acids: Esterification7m
- Reactions of Amino Acids: Acylation3m
- Reactions of Amino Acids: Hydrogenolysis6m
- Reactions of Amino Acids: Ninhydrin Test11m

- 30. Peptides and Proteins2h 42m
- Peptides12m
- Primary Protein Structure4m
- Secondary Protein Structure17m
- Tertiary Protein Structure11m
- Disulfide Bonds17m
- Quaternary Protein Structure10m
- Summary of Protein Structure7m
- Intro to Peptide Sequencing2m
- Peptide Sequencing: Partial Hydrolysis25m
- Peptide Sequencing: Partial Hydrolysis with Cyanogen Bromide7m
- Peptide Sequencing: Edman Degradation28m
- Merrifield Solid-Phase Peptide Synthesis18m

- 32. Lipids 2h 50m
- 34. Nucleic Acids1h 32m
- 35. Transition Metals5h 33m
- Electron Configuration of Elements45m
- Coordination Complexes20m
- Ligands24m
- Electron Counting10m
- The 18 and 16 Electron Rule13m
- Cross-Coupling General Reactions40m
- Heck Reaction40m
- Stille Reaction13m
- Suzuki Reaction25m
- Sonogashira Coupling Reaction17m
- Fukuyama Coupling Reaction15m
- Kumada Coupling Reaction13m
- Negishi Coupling Reaction16m
- Buchwald-Hartwig Amination Reaction19m
- Eglinton Reaction17m

# Wave Function - Online Tutor, Practice Problems & Exam Prep

Quantum mechanics reveals that electrons exhibit both particle and wave characteristics, complicating their position and speed determination. The Heisenberg uncertainty principle states we cannot know both simultaneously, leading to a focus on probability through wave functions, denoted as Ψ. The probability of finding an electron is derived by squaring Ψ, resulting in atomic orbitals. Constructive and destructive interference of wave functions leads to bonding and antibonding molecular orbitals, respectively, influencing electron probability and chemical bonding.

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.

### The probability of finding electrons in a given place.

#### Video transcript

## 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.

### Constructive vs. destructive interference.

#### Video transcript

Let's keep going. So now let's talk about one more thing, in terms of quantum mechanics. And that is what I was hinting at earlier with the fact that these particles don't just act as particles. They don't just bump into each other. They act more like waves and to a certain extent. So, as waves, they have the ability to interfere with each other. So it's right in that word, Interfere. And what that means is that instead of colliding, they may actually interfere constructively or destructively.

So what does that mean? Well, think about it like this. Instead of thinking that these two orbitals are like balls and, like, they will hit each other and bounce off of each other. No. That's not how they act at all. Instead, think of these orbitals as waves, as regions of waves. And once these orbitals overlap with each other, they can either amplify each other or they can basically cancel each other out. You could also think about it for example, like a pool of water and I make two different splashes in two different places. Some of the waves are going to come together and make bigger waves. Right? But also, some of the waves are going to come together and actually cancel each other out. Maybe you've noticed that there will be some regions that are really big waves and some regions that have not that many waves. Okay? That's the difference between constructive and destructive interference.

So when I have constructive interference, the waves come together and they make waves of greater amplitude. Alright? With destructive interference, that means that these orbitals come together, but they wind up cancelling each other out in some way and actually making no net wave at the end.

Now what do these waves represent? I know you're thinking where is Johnny going with this? Well, when you increase the amplitude of your wave, what you're doing is you're increasing the chances of finding an electron that's in a certain place. Okay? So notice that I have this region of overlap right here. Okay? That is between the two. When I have constructive interference, what that means is that now the chances of finding electrons in this space right here are higher. Okay? When I have destructive interference, then what that means is that the chances of finding electrons in the middle are lower. Okay? And that's what I've drawn here at the top and the bottom. When they constructively interfere, that's what we call a bonding molecular orbital. And that's the whole idea behind a chemical bond. A chemical bond isn't just some random stick floating out in space. What it is, is that there's a higher mathematical probability of finding electrons in that region right here. And that's what we call a bond. So anytime you think of a bond now, think that's where electrons are likely to be. Okay?

Now the opposite is true when they destructively interfere. When they destructively interfere, that's called an anti-bonding orbital. What happens is that the chances of finding an electron in the middle actually go straight to zero. Remember that I said that Psi Square is the orbital or the relative probability. So, basically what we're saying is that there's no relative probability of finding electrons right in between there. By the way, just so you guys know, any area that has a probability of zero is called a node. That's just something random that you might need to know, just some terminology that you guys need to understand.

## Do you want more practice?

More sets### Here’s what students ask on this topic:

What is the Heisenberg Uncertainty Principle and how does it relate to wave functions?

The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know both the exact position and exact momentum of an electron. This principle is crucial in quantum mechanics because it highlights the limitations of measuring subatomic particles. Wave functions, denoted as Ψ, are mathematical descriptions that provide the probability of finding an electron in a particular location. By squaring the wave function (Ψ²), we obtain the probability density, which helps us understand where an electron is likely to be found. This probabilistic approach is necessary due to the inherent uncertainties described by the Heisenberg Uncertainty Principle.

How do wave functions describe the behavior of electrons in atoms?

Wave functions (Ψ) describe the behavior of electrons in atoms by providing a mathematical representation of the electron's quantum state. These functions are solutions to the Schrödinger equation and correspond to specific energy levels of electrons. When we square the wave function (Ψ²), we obtain the probability density, which indicates the likelihood of finding an electron in a particular region around the nucleus. This probabilistic approach helps us understand the distribution of electrons in atomic orbitals, such as s, p, d, and f orbitals, each with distinct shapes and energy levels.

What is the significance of constructive and destructive interference in wave functions?

Constructive and destructive interference in wave functions are significant because they influence the formation of molecular orbitals and chemical bonds. Constructive interference occurs when wave functions overlap and amplify each other, leading to a higher probability of finding electrons in the overlapping region. This results in bonding molecular orbitals, which stabilize the molecule. Destructive interference happens when wave functions overlap and cancel each other out, reducing the probability of finding electrons in the overlapping region. This creates antibonding molecular orbitals, which destabilize the molecule. Understanding these interferences helps explain the nature of chemical bonds and molecular stability.

What are atomic orbitals and how are they related to wave functions?

Atomic orbitals are regions around an atom's nucleus where there is a high probability of finding an electron. They are derived from wave functions (Ψ), which are solutions to the Schrödinger equation for electrons in atoms. By squaring the wave function (Ψ²), we obtain the probability density, which describes the likelihood of finding an electron in a specific region. Atomic orbitals come in different shapes and energy levels, such as s (spherical), p (dumbbell-shaped), d, and f orbitals. These orbitals help us understand the electron configuration and chemical behavior of atoms.

How does the concept of nodes relate to wave functions and electron probability?

Nodes are regions in an atomic or molecular orbital where the probability of finding an electron is zero. They are directly related to wave functions (Ψ) because nodes occur where the wave function changes sign, resulting in Ψ² being zero. In atomic orbitals, nodes can be radial (spherical) or angular (planar). The presence and number of nodes help determine the shape and energy of the orbital. Understanding nodes is crucial for visualizing electron distribution and predicting chemical reactivity, as they indicate areas where electrons are unlikely to be found.