Atomic Orbitals

1. Atomic Orbitals SCH4U0 Tabone

2. Orbital Shapes • In previous lessons we alluded to the fact that the different orbitals (subshells) have their own distinct shapes • Now we are going to discuss these shapes • However, before we can do that we must discuss our views about electrons • Typically we view them as particles • Now we view them as waves as well • How does this affect our model of the atom (in respect to orbitals)?

3. Heisenberg Uncertainty Principle • The Heisenberg Uncertainty Principle is a core foundation of quantum theory and greatly influences our view of electrons in orbitals • The principle states that the product of the uncertainty in position and momentum of a particle must be greater than a constant • There are a few important consequences of this

4. Heisenberg Uncertainty Principle • The more accurately we try to determine the position of a particle, the less accurately we know its momentum • We know where it IS but not where it is GOING • The more accurately we try to determine the momentum of a particle, the less accurately we know its position • We know where it is going and how fast it is moving, but not where it is • This can be illustrated fairly simply

5. Uncertainty • If we take a laser and pass it through a slit, we can continuously decrease the size of the slit • This will lower our uncertainty in the position of the photons • Eventually, as we continue to decrease our uncertainty in where the photons are, our uncertainty in their position must start to increase • This causes the beam to widen

6. What Does This Mean? • For us, this means that we have no accurate way of simultaneously knowing every property of the electrons in the atom • If we want to model the atom showing the exact positions and momentums of the electrons, we can’t • So how do we model the atom? • We use Schrödinger’s wave equation • Or at least a certain interpretation of it

7. Schrödinger’s Wave Equation • Schrödinger was able to make an equation that describes the position of all the electrons in an atom • It was based on the wave nature of matter • It is also extremely complicated to solve for any atom other than hydrogen

8. Schrödinger’s Wave Equation • What we need to know about this equation is how it is interpreted • The equation is viewed as representing all of the possible configurations (or states) the atom can be in • Each state is assigned a probability • The exact state in which an atom currently is can only be known through experiment • So we say that an atom has a probability of existing in any of the possible states at any given time, and we don’t really know which is true until we try and observe it

9. Schrödinger’s Cat • This can be illustrated using a simple setup with a cat in a box • This was first suggested as a thought experiment by Schrödinger to show why the probabilistic interpretation of his equation was incorrect • But in reality it underlines why the probabilistic interpretation works • The key point to remember is that radioactivity is a probabilistic quantum process • There is a finite chance that particles will “jump” out of the nucleus in a given increment of time

10. Schrödinger’s Cat Hammer Fuzzy Cat Geiger Counter Poisonous Gas Radioactive Material

11. Schrödinger’s Cat • There is a 50% chance the radioactive material will decay in 1 hour and a 50% chance that it will not • Meaning that at the end of the hour there is an equal chance that the cat is alive or dead – and we do not know which is true • So we say that at the hour mark the cat is both alive and the dead • The state condenses into one or the other when we open the box and make an observation

12. Electron Clouds • So what does this mean about electrons in atoms? • Since we cannot know where an electron is at any given time, we instead determine probable locations for the electron • We sum these probable locations up and view the electron instead as a cloud of electron density

13. Atomic Orbitals • If we analyze the electron clouds of different orbitals we can see that they all have characteristic shapes • s-orbitals

14. Atomic Orbitals • p-orbitals

15. Atomic Orbitals • d-orbitals

16. Electron Density Graphs • When electron density is graphed against distance from the nucleus, some interesting trends are seen • Orbitals of the same type have an increasing number of nodes as their energy level increases • 1s has no node, 2s has 1 node, 3s has 2 nodes, etc... • 2p has no node, 3p has 1 node, 4p has 2 nodes, etc... • A node is an area with little to no electron density

17. Electron Density Graphs Electron Density

18. Orbitals

19. Electron Density Graphs • Similarly, if we compare orbitals within the same energy level there is a pattern • As the ℓ number increases, the # of nodes decreases • 3s has 2 nodes, 3p has 1 nodes, 3d has 0 node • This same trend is shown in every energy level • The highest energy orbital always has 0 nodes

20. Electron Density Graphs

21. Quantum Tunnelling • Using the probabilistic approach to viewing matter, every particle has a probability of existing anywhere • But most of these probabilities are extremely small • This can be used however to transport particles through and across barriers • Ex: an alpha particle (helium nucleus) within a larger nucleus (like Ra) has a small probability of existing outside of the nucleus • This is how radioactive decay occurs Ra-226  Rn-222 + He

22. Quantum Tunnelling • Quantum tunnelling is also the phenomenon behind touch screens • The electrons in the screen have a small probability of being located in the sensors below the screen. • As the screen is pushed and the screen moves closer the sensors beneath, the probability increases • Eventually the probability is large enough that a significant (though small) number of electrons “jumps” from the screen to the sensors and starts an electric current