5Kinds of EM waves G a m m a R a y s There are many (page 276) different l and nRadio waves, microwaves, x rays and gamma rays are all examplesLight is only the part our eyes can detectGammaRadioRayswaves
6The speed of light in a vacuum is 3.00 x 108 m/s = c c = ln What is the wavelength of light with a frequency 5.89 x 105 Hz?What is the frequency of blue light with a wavelength of 484 nm?
7In 1900Matter and energy were seen as different from each other in fundamental waysMatter was clearly composed of particles.Energy could come in waves, with any frequency (belief at the time).However, Max Planck found that the cooling of hot objects couldn’t be explained by viewing energy emitted in any frequency.Sometimes referred to as the “ultraviolet catastrophe”!
8Energy is Quantized Planck found DE came in chunks with size hn DE = nhνwhere n is an integer.and h is Planck’s constanth = x J sthese packets of hν are called quantum
9Einstein is nextSaid electromagnetic radiation is quantized in particles called photonsEach photon has energy = hν = hc/lCombine this with E = mc2you get the apparent mass of a photonm = h / (lc)
10Which is it? Is energy a wave like light, or a particle? Yes Concept is called the Wave -Particle duality.What about the other way, is matter a wave?
11Matter as a waveUsing the velocity v instead of the frequency ν (because the object is not traveling at the speed of light) we getDe Broglie’s equation l = h/mv…can calculate the wavelength of an object
12Example CalculationsThe laser light of a CD is 7.80 x 102 m. What is the frequency of this light?What is the energy of a photon of this light?What is the apparent mass of a photon of this light?What is the energy of a mole of these photons?
13What is the wavelength?of an electron with a mass of x kg traveling at 1.0 x 107 m/s?Of a softball with a mass of 0.10 kg moving at 125 mi/hr?Yes, we can calculate these…but really all we need is the relationshipThe more massive the particle, the shorter the wavelength.Particles have very small wave properties…whereas light has very large wave properties.
14How do they know?When light passes through, or reflects off, a series of thinly spaced lines, it creates a rainbow effectbecause the waves interfere with each other.
27Which did it do? It made the diffraction pattern The electron is a waveLed to Schrödingers equation
28What will an electron do? An electron does go though both, and makes an interference pattern.It behaves like a wave.Other matter has wavelengths too short to notice.
29Spectrum The range of frequencies present in light. White light has a continuous spectrum.All the colors are possible.A rainbow.
30Hydrogen spectrum 656 nm 434 nm 410 nm 486 nm Emission spectrum because these are the colors it gives off or emitsCalled a line spectrum.There are just a few discrete lines showing656 nm434 nm410 nm486 nm
31What this meansOnly certain energies are allowed for the hydrogen atom.Can only give off certain energies.Use DE = hn = hc / lEnergy in the atom is quantized
32Niels Bohr Developed the quantum model of the hydrogen atom. He said the atom was like a solar systemThe electrons were attracted to the nucleus because of opposite charges.Didn’t fall in to the nucleus because it was moving around
33The Bohr Ring AtomHe didn’t know why but only certain energies were allowed.He called these allowed energies ENERGY LEVELS.Putting energy into the atom moved the electron away from the nucleusFrom ground state to excited state.When it returns to ground state it gives off light of a certain energy
35The Bohr Model n is the energy level Z is the nuclear charge, which is +1 for hydrogen.E = x J (Z2 / n2 )n = 1 is called the ground statewhen the electron is removed, n = ¥E = 0 due to no interaction with the nucleus
36We are worried about the change When the electron moves from one energy level to another in a hydrogen atom...DE = Efinal - EinitialDE = x J Z2 (1/ nf2 - 1/ ni2)P. 286 in the text shows a great example…And on p. 287 Sample Problem 7.4 and p Sample Problem 7.5!
37Energy of Electron Transition Let’s try #45 on page 322.
38Energy of Electron Transition What wavelength of light is required for transitioning an electron?Try #49 p. 322
39ExamplesCalculate the energy need to move an electron from its ground state to the third energy level.Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom.Calculate the energy released when an electron moves from n= 5 to n=3 in a He+1 ion (note: the Z value changes)!
40When is it true?Only for hydrogen atoms and other mono- electronic species.Why the negative sign?To increase the energy of the electron you move it further from the nucleus.the maximum energy an electron can have is zero, at an infinite distance.
41The Bohr Model Doesn’t work…or …it only works for hydrogen atoms electrons don’t move in circlesthe quantization of energy is right, but not because they are circling like planets.
42The Quantum Mechanical Model A totally new approachDe Broglie said matter could be like a wave.De Broglie said they were like standing waves.The vibrations of a stringed instrument
44What’s possible?You can only have a standing wave if you have complete waves.There are only certain allowed waves.In the atom there are certain allowed waves called electrons.1925 Erwin Schroedinger described the wave function of the electronHigh degree of math, but what is important are the solutions…
45Schrödinger’s Equation The wave function is a F(x, y, z)Actually F(r,θ,φ)Solutions to the equation are called orbitals.These are not Bohr orbits but regions of space where finding the position of an electron is high.Each solution is tied to a certain energyThese are the energy levels
46There is a limit to what we can know We can’t know how the electron is moving or how it gets from one energy level to another.The Heisenberg Uncertainty PrincipleThere is a limit to how well we can know both the position and the momentum of an object.
47What does the wave Function mean? Nothing!?! But it helps to explain what we are able to observe about the atom!It is not possible to visually map it.The square of the function is the probability of finding an electron near a particular spot.Best way to visualize it is by mapping the places where the electron is likely to be found.
49Defining the size of the orbital… The size that encloses 90% of the total electron probability position.NOT at a certain distance, but a most likely distance.The first solution for the shape of the probability position is a sphere.Subsequent solutions are complex geometric shapes!
50Quantum Numbers There are many solutions to Schrödinger’s equation Each solution can be described with quantum numbers that describe some aspect of the solution.Principal quantum number (n)=size and energy of an orbitalHas integer values >0
51Quantum numbers Angular momentum quantum number “l” Describes the shape of the orbitalHas integer values from 0 to n-1l = 0 is called sl = 1 is called pl =2 is called dl =3 is called fl =4 is called gEtc. but not in this course!!!
58Quantum numbers Magnetic quantum number (m l) integer values between - l and + ltells the 3-D orientation of the orbital around the x,y, and z axes.Electron spin quantum number (m s)Can have 2 valueseither +1/2 or -1/2The electron is either spinning clockwise or counter clockwise…or up or down, etc.
59Polyelectronic Atoms More than one electron Contains three energy contributions:The kinetic energy of moving electronsThe potential energy of the attraction between the nucleus and the electrons.The potential energy from repulsion of electrons
60Polyelectronic atoms Can’t solve Schrödinger’s equation exactly Difficulty is repulsion of other electrons.Solution is to treat each electron as if it were effected by the net field of charge from the attraction of the nucleus and the repulsion of the electrons.Effective nuclear charge = Zeff
61We examine the effect of the nucleus on this single e-! Sodium Atom+1111 electrons+1110 otherelectronse-e-ZeffWe examine the effect of the nucleus on this single e-!
62Effective Nuclear charge Can be calculated fromE = x J (Zeff2 / n2 ) andDE = x J Zeff2 (1/ nf2 - 1/ ni2)Complicated…so we will have a qualitative understanding of the Zeff based on:The number of protons attracting the e- (the “z” value).The effective repulsions of the other e-.
63The Periodic TableDeveloped independently by German Julius Lothar Meyer and Russian Dmitri Mendeleev (1870’s)They didn’t know much about the atom.Simply placed elements in columns based on similar properties.Mendeleev predicted properties of missing elements...BRILLIANT!
64Aufbau Principle Aufbau is German for building up. As the protons are added one by one to the nucleus, the electrons also fill up “hydrogen- like” orbitals.Fill up in order of energy from low to high!This is the Aufbau Principle!
65Orbitals available to a Hydrogen atom 7p6s6p6d6f5s5p5d5f4s4p4d4fIncreasing energy3s3p3d2s2pOrbitals available to a Hydrogen atom1s
66With more electrons, repulsion changes the energy of the orbitals. Increasing energy1s2s3s4s5s6s7s2p3p4p5p6p3d4d5d7p6d4f5fWith more electrons, repulsion changes the energy of the orbitals.
67Increasing energy He with 2 electrons 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 3d4d5d7p6d4f5fHe with 2 electrons
68Increasing energy1s2s3s4s5s6s7s2p3p4p5p6p3d4d5d7p6d4f5fThe order of filling follows simple physics laws and creates “orbital energy overlap”!
69DetailsValence electrons- the electrons in the outermost principal quantum levels of an atom.Core electrons- the inner electronsHund’s Rule- The lowest energy configuration for an atom is the one have the maximum number of unpaired electrons in the orbital.C 1s2 2s2 2p2
70Fill from the bottom up following the arrows 2s 2p3s 3p 3d4s 4p 4d 4f5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f1s22s22p63s23p64s23d104p65s24d105p66s2
71However, I prefer to use the periodic table to generate the electron configurations!!!
72DetailsElements in the same column have the same electron configuration (families).Put in columns because of similar properties.Similar properties because of electron configuration.Noble gases have filled energy levels.Transition metals are filling the d orbitals
73The Shorthand Write the symbol of the noble gas before the element Then the rest of the electrons.Aluminum - full configuration1s22s22p63s23p1Ne is 1s22s22p6so Al is [Ne] 3s23p1
74The Shorthand Sn- 50 electrons The noble gas before it is Kr Takes care of 36Next 5s2Then 4d10[ Kr ]5s24d105p2Finally 5p2[ Kr ]4d105s25p2
75Exceptions Ti = [Ar] 4s23d2 V = [Ar] 4s23d3 Cr = [Ar] 4s13d5 Mn = [Ar] 4s23d5Half filled orbitalsScientists aren’t certain why it happens (still debating)same for Cu [Ar] 3d10 4s1
76More exceptions Lanthanum La: [Xe] 5d1 6s2 Cerium Ce: [Xe] 5d1 4f16s2 Promethium Pr: [Xe] 4f3 6s2Gadolinium Gd: [Xe] 4f7 5d1 6s2Lutetium Pr: [Xe] 4f14 5d1 6s2We’ll just pretend that all except Cu and Cr follow the rules…otherwise, the question will drive your response!
77More PolyelectronicWe can use Zeff to predict properties, if we determine it’s pattern on the periodic table.Can use the amount of energy it takes to remove an electron for this.Ionization Energy- The energy necessary to remove an electron from a gaseous atom.
78Remember this E = -2.18 x 10-18 J(Z2/n2) was true for Bohr atom. Can be derived from quantum mechanical model as wellfor a mole of electrons being removedE =(6.02 x 1023/mol)2.18 x J(Z2/n2)E= 1.13 x 106 J/mol(Z2/n2)E= 1310 kJ/mol(Z2/n2)
80This gives us Ionization energy = 1310 kJ/mol(Zeff2/n2) So we can measure ZeffThe ionization energy for a 1s electron from sodium is 1.39 x 105 kJ/mol .The ionization energy for a 3s electron from sodium is 4.95 x 102 kJ/mol .This marked difference demonstrates shielding within the atom!
81ShieldingElectrons on the higher energy levels tend to be farther out.Have to “look through” the other electrons to see the nucleus.They are less attracted by the nucleus.lower effective nuclear chargeIf shielding were completely effective,Zeff = 1Why isn’t it?
82PenetrationThere are levels to the electron distribution for each orbital2s
83Graphically2sPenetrationRadial ProbabilityDistance from nucleus
84Graphically3sRadial ProbabilityDistance from nucleus
88Penetration effectThe outer energy levels penetrate the inner levels so the shielding of the core electrons is not totally effective.From most penetration to least penetration the order isns > np > nd > nf (within the same energy level)This is what gives us our order of filling… electrons prefer s and p
89How orbitals differThe more positive the nucleus, the smaller the orbital.A sodium 1s orbital is the same shape as a hydrogen 1s orbital, but it is smaller because the electron is more strongly attracted to the nucleus.The helium 1s is smaller as wellThis effect is important for discussion of shielding and trends!
94Periodic TrendsIonization energy the energy required to remove an electron form a gaseous atomHighest energy electron removed first.First ionization energy (I1) is that required to remove the first electron.Second ionization energy (I2) - the second electronetc. etc.
95Trends in ionization energy for MgI1 = 735 kJ/moleI2 = 1445 kJ/moleI3 = 7730 kJ/moleThe effective nuclear charge increases as you remove electrons.It takes much more energy to remove a core electron than a valence electron because there is less shielding
96Explain this trend For Al I1 = 580 kJ/mole I2 = 1815 kJ/mole
97Across a Period Generally from left to right, I1 increases because there is a greater nuclear charge with the same shielding.As you go down a group I1 decreases because electrons are further away and there is more shielding
98It is not that simpleZeff changes as you go across a period, so will I1Half-filled and filled orbitals are harder to remove electrons fromhere’s what it looks like
102Atomic Size First problem…where do you start measuring? The electron cloud doesn’t have a definite edge.They get around this by measuring more than 1 atom at a time
103Atomic Size}RadiusAtomic Radius = half the distance between two nuclei of a diatomic molecule
104Trends in Atomic Size Influenced by two factors Shielding More shielding is further awayCharge on nucleusMore charge pulls electrons in closer
105Group trends H Li Na K Rb As we go down a group Each atom has another energy levelSo the atoms get biggerHLiNaKRb
106Periodic Trends Na Mg Al Si P S Cl Ar As you go across a period the radius gets smaller.Same energy levelMore nuclear chargeOutermost electrons are closerNaMgAlSiPSClAr
107RbKOverallNaLiAtomic Radius (nm)KrArNeH10Atomic Number
108Electron AffinityThe energy change associated with adding an electron to a gaseous atomHigh electron affinity gives you energy-exothermicMore negativeIncrease (more - ) from left to rightgreater nuclear charge.Decrease as we go down a groupMore shielding
109Ionic Size Cations form by losing electrons Cations are smaller than their atom of origination.(Metals form cations)Cations of representative elements have noble gas configuration.
110Ionic size Anions form by gaining electrons Anions are bigger than their atom of origination.(Nonmetals form anions)Anions of representative elements have noble gas configuration.
111Configuration of Ions Ions “always” have noble gas configuration Na is 1s22s22p63s1Forms a 1+ ion - 1s22s22p6Same configuration as neonMetals form ions with the configuration of the noble gas before them - they lose electrons
112Configuration of IonsNon-metals form ions by gaining electrons to achieve noble gas configuration.They end up with the configuration of the noble gas after them.
113Group trends Li+1 Na+1 K+1 Rb+1 Cs+1 Adding energy level Ions get bigger as you go downLi+1Na+1K+1Rb+1Cs+1
114Periodic Trends N-3 O-2 F-1 B+3 Li+1 C+4 Be+2 Across the period nuclear charge increases so they get smaller.Energy level changes between anions and cationsN-3O-2F-1B+3Li+1C+4Be+2
115Size of Isoelectronic ions Iso - sameIso electronic ions have the same # of electronsAl+3 Mg+2 Na+1 Ne F-1 O-2 and N-3all have 10 electronsall have the configuration 1s22s22p6 Ne
116Size of Isoelectronic ions Positive ions have more protons so they are smallerN-3O-2F-1NeNa+1Al+3Mg+2
118ElectronegativityThe tendency for an atom to attract electrons to itself when it is chemically combined with another element.How electron “greedy” it is!Large electronegativity means it pulls the electron strongly toward itself.Atoms with a very high Zeff should also have a high EN!
119Group Trend The further down a group more shielding Less attracted (Zeff)Low electronegativity.
120Periodic Trend Metals are at the left end Low ionization energy- low effective nuclear chargeLow electronegativityAt the right end are the nonmetalsMore negative electron affinityHigh electronegativityExcept noble gases
121Ionization energy, electronegativity Electron affinity INCREASE
124The information it hides Know the special groupsThe number and type of valence electrons determine an atom’s chemistry.You can get the electron configuration from it.Metals lose electrons have the lowest IENon metals- gain electrons most negative electron affinities
125The Alkali MetalsDoesn’t include hydrogen- it typically behaves as a non-metalMoving down…decrease in IEIncrease in radiusDecrease in melting pointBehave as reducing agentsDemo Time!!!
126Reducing ability Lower IE< better reducing agents Cs>Rb>K>Na>Liworks for solids, but not in aqueous solutions.In solution Li>K>NaWhy?It’s the water -there is an energy change associated with dissolving
127Hydration Energy Li+(g) → Li+(aq) is exothermic for Li+ -510 kJ/mol for Na kJ/molfor K kJ/molLi value is so large due to its high charge density…a lot of charge on a very small atom!Li loses its electron more easily because of this in aqueous solutions.
128The reaction with water Na and K react explosively with water (generate a great deal of H2 quickly).Li doesn’t.Even though the reaction of Li has a more negative DH than that of Na and K.Na and K melt (lower melting points)DH does not tell you speed of reaction…more in Chapter 12.