From the previous chapters…

1. From the previous chapters… • A while back, we talked about what an atom looks like • Dense central core • Core comprises protons, neutrons • Protons with + charge • Should ring a bell… • Electrons? Remember them? (neg charge) • They have mass (they’re Catholic?) albeit small • Occupy most of the SPACE around nucleus

2. How are they arranged? • An atom has a dense central core, called the nucleus, and is composed of protons and neutrons. (marbles in Fenway Park) • Electrons surround the nucleus, occupy most of the volume of an atom, but have very little mass (relative to protons/neutrons) • An atom has no net charge, positively charged protons are balanced by electrons

3. Electrons—how are they arranged? • Arranged in roughly spaced concentric shells. Called electron configurations. • Outer shells of electrons are called valence electrons (we will discuss this at some length for the rest of the semester). • Unfortunately we now must delve into some physics, a necessary and very worthwhile discussion… • Foreshadowing…we put electrons into orbitals, very specific ones. • These orbitals dictate a lot of the behavior we see in atoms.

4. How do we KNOW this? • Recall that we’ve discussed the idea of ‘closer to the + charged nucleus = more energy to remove’. • Successive electron removal tougher (fewer e-s, same +) • Nuclear atraction , electron repulsions . • SO!! Let’s strip an electron and see what we get! • If we examine the energies to remove an electron, a clear picture emerges. • Recall we brought this up earlier…ionization energy.

5. Stripping sodium bare! Note in the graph on the right, the lower the ‘dot’, the lower the amount of energy Note there are two jumps, from electons 1—2, and from 10—11 ‘smooth’ progression from 2—10. Suggests distinct ‘levels’ Kind of like floors in a building.

6. Jumps are more obvious numerically Lithium!! Look at that! From 0.86 to 12.1 aJ (attojoules, a ridiculously small unit, just pay attention to the gap

7. Same song, different verse…potassium Again, note the ‘jumps’ from 1—2, 10—11, 18—19. Suggests the electrons occupy different ‘floors’ within an atom. ALSO note that sodium and potassium BOTH have a jump after electron #1 Group 1 anybody? Go back to the previous graphic…note these jumps and how they pertain to GROUPS

8. Valence and Core electrons • Valence electron—electrons that occupy the outermost shell of an atom • Sodium and potassium—one electron • Etc from groups 2, 3 and so on. • Core electrons—the REST. • Don’t interact in bonding at all • Takes WAY TOO MUCH energy to get rid of them • Gives rise to what we refer to as Lewis dot formulas.

9. Lewis Dot Formulas • Simple…a chemical symbol with its valence electrons

10. The electromagnetic spectrum

11. Describing forms of EM Radiation • All EM radiation can be described using frequency (n) and wavelength (l) • Wavelength—distance between crests of a wave • Frequency—number of crests per unit time (usually measured in sec)

12. A Forrest Gump simple EQ.! • Nothing else this semester will be this simple—relating freq and wavel. • What’s nu? C over lambda. • nl = c or n = c / l • c is the speed of light (2.998 x 108 m/s)

13. OK, maybe too simple… • Let’s relate that equation to something useful, like energy. • E = hc/l What’s that h? It’s Planck’s constant, 6.626 x 10-34J·s (really freaking small!)

14. Discrete Energy units.

15. So an atom has discrete energy levels called ‘shells’, which occur at a specific distance from the nucleus and electrons can occupy the ‘space’ in these shells So, remember the structure of the atom? The simple one…

16. Can these ‘lines’ be explained? • Absolutely—An equation, called the Rydberg Equation calculates the wavelengths of the visible lines in the hydrogen line spectrum. • When n > 2, this equation becomes… R = 1.0974 x 107 m-1

17. Recap of dirt simple equations… • What’s nu? C over lambda. • n = c / l (c = 2.998 x 108 m/s) • Relation of energy to wavelength • E = hc/l or, since n = c / l E = hn • Calculating wavelength from line spectrum R = 1.0974 x 107 m-1

18. Extending the Rydberg Eq. • Rydberg is too specific, only calc’s. for n = 2 (where n = principle quantum number). • A more useful and general equation is given by ⇩ relates the energy transition from ANY initial level to any FINAL level.

19. Summary of atomic spectra • The origin of atomic spectra is the movement of electrons between energy levels (floors 1-5) • Energy is absorbed…an electron is excited, and moves from a low energy level to high • Energy is emitted…an electron relaxes, the electron moves from high to low energy states

20. Spectra—Discreet/Continuous Above—continuous spectrum (from sunlight), bottom, line spectrum from JUST Hydrogen (note, lines indicate discreet energy transitions)

21. Atomic Orbitals—we’re now in Ch 5. • Several mathematical relationships (when combined) describe the behavior of electrons in an atom • The math need not concern us—though we need to know what it tells us. • DeBroglie—light has wave and particle behavior • Schroedinger’s wave eq.s predict: • Wave functions (or an energy state of an atom) • the allowed energy of an electron AND • the probability of finding an electron in a particular region in space

22. More on the math • From Scrodinger • Also determined that three quantum numbers are needed to describe the 3-D coordinates of an electron’s motion. • Those numbers are n, l, and ml. • (note, the second/third “numbers” are L and mL

23. Atomic Orbitals, cont. • The region in space where an electron is most likely found is called an orbital • The way to visualize this region is to draw a picture that represents a 90% probability of finding an electron within • Using a set of four numbers (quantum numbers)…we can describe the location of electrons that surround an atom

24. Principal Quantum Number, n • Most informative quantum number—shows energy of electron (↑ n  higher energy (less attraction to the nucleus) • n is only an integral value, 1, 2, 3… • n also  number of different orbital types in a subshell • n2 total # of orbitals within n subshell

25. Second Quantum Number, l • Also very important, determines the SHAPE of the atomic orbital. • Has values from 0, to a maximum of n-1 • For n = 3, l can be either 0, 1, or 2 • These subshells are commonly given letter designations, s, p, d, f, g, etc…

26. More on second Q# • When l = 0,  s orbital • When l = 1,  p orbital • Energies of these subshells (or orbitals) are always s < p < d < f… (s is lowest energy, the most stable, greatest attraction to nucleus • Another note, as n increases, the orbitals become larger, and the number of different orbitals increases

27. Third Quantum Number, ml • Can have any integral value from –l to l. • For l = 3, then ml could be –3, -2, -1, 0, 1, 2, 3 • This gives the number of different types of orbitals (easier to see this…) • For n = 3, l = 1 (when l= 1, => p orbital), then ml = -1, 0, +1…three different types

28. Quantum number summary • n tells us the size of an atomic orbital • Size corresponds to energy • how many subshells there are (= to n) • n2 gives total number of orbitals within n shell • l tells us the shape of an atomic orbital • ml tells us how many orbitals there are (based on l, of course)

29. Visual representation of orbitals • recall that my artistry bites…so here’s what orbitals look like without me confusing things.

30. There is a fourth quantum number, ms, which is either ± ½. That’s the seat at the bottom. This is based on the Pauli Exclusion principle, which states that no two electrons may have the same 4 quantum #’s Another way to see this

31. Quantum Numbers: ml The magnetic quantum number (ml): • Determines the orientation in space of the orbitals of any given type in a subshell. • Can be any integer from –l to +l • The number of possible values for mlis (2l + 1), and this determines the number of orbitals in a subshell.

32. Notice: ones orbital in each principal shell threep orbitals in the second shell (and in higher ones) fived orbitals in the third shell (and in higher ones)

33. Example 7.10 Considering the limitations on values for the various quantum numbers, state whether an electron can be described by each of the following sets. If a set is not possible, state why not. (a) n= 2, l= 1, ml= –1 (c) n= 7, l= 3, ml= +3 (b) n= 1, l= 1, ml= +1 (d) n= 3, l= 1, ml= –3 Example 7.11 Consider the relationship among quantum numbers and orbitals, subshells, and principal shells to answer the following. (a) How many orbitals are there in the 4d subshell? (b) What is the first principal shell in which f orbitals can be found? (c) Can an atom have a 2d subshell? (d) Can a hydrogen atom have a 3p subshell?

34. The 1s Orbital • The 1s orbital (n = 1, l = 0, ml = 0) has spherical symmetry. • An electron in this orbital spends most of its time near the nucleus. Spherical symmetry; probability of finding the electron is the same in each direction. The electron cloud doesn’t “end” here … … the electron just spends very little time farther out.

35. The Three p Orbitals Three values of mlgives three p orbitals in the p subshell.

36. The Five d Orbitals Five values of ml(–2, –1, 0, 1, 2) gives five d orbitals in the d subshell.

37. The Stern-Gerlach Experiment Demonstrates Electron Spin These silver atoms each have 24 +½-spin electrons and 23 –½-spin electrons. The magnet splits the beam. These silver atoms each have 23 +½-spin electrons and 24 –½-spin electrons. Silver has 47 electrons (odd number). On average, 23 electrons will have one spin, 24 will have the opposite spin.

38. Electron Spin: ms • The spin refers to a magnetic field induced by the moving electric charge of the electron as it spins. • The magnetic fields of two electrons with opposite spins cancel one another; there is no net magnetic field for the pair. • The electron spin quantum number (ms)explains some of the finer features of atomic emission spectra. • The number can have two values: +½ and –½.

39. CUMULATIVE EXAMPLE Which will produce more energy per gram of hydrogen: H atoms undergoing an electronic transition from the level n= 4 to the level n= 1, or hydrogen gas burned in the reaction: 2 H2(g) + O2(g)  2 H2O(l)?