1. Arrangement of Electrons in Atoms 4-2 The Quantum Model of the Atom

2. Electrons as Waves  Last section we learned that light can behave as both a particle and a wave. What about electrons?  Louis De Broglie stated that electrons could be considered waves confined to a space around an atomic nucleus.  Electron waves can exist, but only at specific frequencies corresponding to specific frequencies.

3. Electrons as Waves  Experiments showed that electrons (like light) could be bent, or diffracted. Also, electron beams could interfere with each other.  Diffraction – bending of light when passed through a crystal.  Interference – overlapping of waves, reducing energy in some areas.

4. Heisenberg Uncertainty Principle  The position and momentum of a moving object can not simultaneously be measured and known exactly.  Due to the duel nature of matter and energy  Only important with small scale objects

5. Chapter 4 Section 2 The Quantum Model pages 104-1105 Heisenbery Uncertainty Principle Animation

6. The Schrödinger Wave Equation  Erwin Schrödinger developed an equation, which treated electrons in atoms as waves.  Solutions to wave equation are known as wave functions.  Don’t worry about wave functions, we do a little more with it in AP  Coupled with Heisenberg Uncertainty Theory, lead to Quantum Theory  Quantum Theory – describes mathematically the wave properties of electrons and other very small particles.

7. The Schrödinger Wave Equation  Most Important Idea: We can only know the probability of finding an electron, not its exact location.  Orbital – a 3-dimensional region around the nucleus that indicates the probable location of an electron.  Fig 4-11

8. Review  Energy is quantized ( found in specific amounts)  Electrons have wavelike behavior  Impossible to know electron position and momentum.  Can predict the probability of electron location  Called the Quantum-mechanical model

9. Probability and Orbital  The density of an electron cloud is called the electron density.  Higher density – more likely to find electron  Lower density – less likely to find electron  An orbital is the region where a given electron is likely found.

11.  There are different types of orbitals….s, p, d, f which we will talk about more later.

12. Orbitals and Energy   To describe orbitals, scientists use quantum numbers.  Quantum Number – specify the properties of atomic orbitals and the properties of electrons in orbitals.

13. Principal Quantum Number  indicates the main energy level occupied by the electron.  Sometimes considered the shell.  n are positive integers (n = 1, n=2, n=3, …)  As n increases, energy and distance from nucleus increases.  n = 1 is the lowest energy level, closest to the nucleus.  More than one electron can have the same value of n.  The total number of orbitals that exist in a given shell is equal to n 2.

14. Angular Momentum Quantum Number (l)  indicates the shape of an orbital  Also considered the sublevel.  The number of orbital shapes possible is equal to n  l can have values of 0 and all positive integers less than or equal to n-1  If n = 1, l = 0: (l = n – 1 = 1 –1 = 0)  If n = 2, l = 1 and 0: (l = n – 1 = 2 – 1 = 1)

15.  Each orbital is assigned a letter, which corresponds to a shape  s orbital – see figure 4-25 pg 144

16.  p orbital- see figure 4-26 in book

17.  d orbital – see figure 4-27 in book

18.  Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel.  Ex. 1s sublevel is the s orbital is in the first main energy level  Ex. 2p sublevel is the set of p orbitals in the second energy level  Ex. 3d sublevel is the set of d orbitals in the third energy level

19. Magnetic Quantum Number (m l )  indicates the orientation of an orbital around the nucleus  m l = +/- l and every integer in between  Ex. If n = 1, l = 0, m l = 0  This means there is a single s orbital in the first energy level  If n = 2, l = 1, m l = -1, 0, +1  In the second energy level there are three p orbitals

20.  If n = 4, l = 2, m l = -2, -1, 0, +1, +2  In the fourth energy level there are five d orbitals.  If n = 4, l = 0, m l = 0  In the fourth energy level there is 1 s orbital

21. Spin Quantum Number (m s )  indicates the spin states of an electron in an orbital, either +1/2, or –1/2. Electrons spin on an internal axis either clockwise or counterclockwise. A single orbital can hold a maximum of two electrons, which must have opposite spins. o

22. Summary of Energy Levels, Sublevels, and Orbitals Principal Energy Level SublevelsOrbitals n = 11s1s (one) n = 22s, 2p2s (one) + 2p (three) n = 33s, 3p, 3d 3s(one) + 3p(three)+3d(five ) n = 44s, 4p, 4d, 4f 4s(one)+4p(three)+4 d(five)+4f(seven)

23. Max Number of Electrons in Each Sublevel Sublevel# of OrbitalsMax # of Electrons s12 p36 d510 f714