Chapter 12: Phenomena
Phenomena: Different wavelengths of electromagnetic radiation were directed onto two different metal sample (see picture). Scientists then recorded if any particles were ejected and if so what type of particles as well as the speed of the particle. What patterns do you see in the results that were collected? K Wavelength of Light Where Particles Ejected Speed of Exp. Intensity Directed at Sample Ejected Particle Ejected Particle
-7 - 4 푚 1 5.4×10 m Medium Yes e 4.9×10 푠
-8 - 6 푚 2 3.3×10 m High Yes e 3.5×10 푠 3 2.0 m High No N/A N/A 4 3.3×10-8 m Low Yes e- 3.5×106 푚 Electromagnetic 푠 Radiation 5 2.0 m Medium No N/A N/A Ejected Particle -12 - 8 푚 6 6.1×10 m High Yes e 2.7×10 푠 7 5.5×104 m High No N/A N/A Fe Wavelength of Light Where Particles Ejected Speed of Exp. Intensity Directed at Sample Ejected Particle Ejected Particle 1 5.4×10-7 m Medium No N/A N/A
-11 - 8 푚 2 3.4×10 m High Yes e 1.1×10 푠 3 3.9×103 m Medium No N/A N/A
-8 - 6 푚 4 2.4×10 m High Yes e 4.1×10 푠 5 3.9×103 m Low No N/A N/A
-7 - 5 푚 6 2.6×10 m Low Yes e 1.1×10 푠
-11 - 8 푚 7 3.4×10 m Low Yes e 1.1×10 푠 Chapter 12: Quantum Mechanics and Atomic Theory Chapter 12: Quantum Mechanics and Atomic Theory
o Electromagnetic Radiation o Quantum Theory o Particle in a Box Big Idea: The structure of atoms o The Hydrogen Atom must be explained o Quantum Numbers using quantum o Orbitals mechanics, a theory in o Many-Electron Atoms which the properties of particles and waves o Periodic Trends merge together.
2 Electromagnetic Radiation
Spectroscopy: The analysis of electromagnetic radiation emitted/absorbed by substances.
Electromagnetic Radiation: Consists of oscillating (time-varying)electric and magnetic fields that 8 푚 travel through space at 2.998 × 10 푠 (c = speed of light) or just over 660 million mph.
Note: All forms of radiation transfer energy from one region of space into another.
Examples of Electromagnetic Radiation: • Visible light • Radio Waves • X-Rays
3 Chapter 12: Quantum Mechanics and Atomic Theory Electromagnetic Radiation
Wavelength (λ): Is the peak-to-peak distance. Note: Changing the wavelength changes the region of the spectrum (i.e. x-ray to visible).
Amplitude: Determines brightness of the radiation.
Frequency (ν): The number of cycles per 1 second (1 퐻푧 = 1 푠).
4 Chapter 12: Quantum Mechanics and Atomic Theory Electromagnetic Radiation
5 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
If white light is passed through a prism, a continuous spectrum of light is found. However, when the light emitted by excited hydrogen atoms is passed through a prism the radiation is found to consist of a number of components or spectra lines.
6 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Black Body: An object that absorbs and emits all frequencies of radiation without favor. Heated Black Bodies
푾 푻흀 = ퟐ. ퟗ푲풎풎 푰 = ퟓ. ퟔퟕ × ퟏퟎ−ퟖ 푻ퟒ 풎풂풙 풕풐풕 풎ퟐ푲ퟒ
Note: λmax is the most prevalent wavelength, not the longest wavelength. 7 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Theory Scientists used classical physics arguments to derive an expression for the energy density (Rayleigh Jens Law). 푇 퐸푛푒푟𝑔푦 퐷푒푛푠𝑖푡푦 ∝ 휆4 The Problem With Explaining Black Body Radiation Using Classical Mechanics Classical mechanics put no limits on minimum wavelength therefore at very small 휆, 퐸 would be a huge value even for low temperatures.
8 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Max Plank: Proposed that the exchange of energy between matter and radiation occurs in quanta, or packets of energy. His central idea was that a charged particle oscillating at a frequency 휈, can exchange energy with its surroundings by generating or absorbing electromagnetic radiation only in discrete packets of energy. Quanta: Packet of energy (implies minimum energy that can be emitted). Charged particles oscillating at a frequency, 휈, can only exchange energy with their surroundings in discrete packets of energy.
9 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Photoelectric Effect: Ejection of electrons from a metal when its surface is exposed to ultra violet radiation.
10 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Findings of the Photoelectric Effect 1) No electrons are ejected unless the radiation has a frequency above a certain threshold value characteristic of the metal. 2) Electrons are ejected immediately, however low the intensity of the radiation. 3) The kinetic energy of the ejected electrons increases linearly with the frequency of the incident radiation. Albert Einstein Proposed that electromagnetic radiation consists of massless “particles” (photons) Photons are packets of energy Energy of a single photon = ℎ · 휈
11 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Work Function (횽): The minimum amount of energy required to remove an electron from the surface of a metal.
If 퐸푝ℎ표푡표푛 < Φ no electron ejected
If 퐸푝ℎ표푡표푛 > Φ electron will be ejected
12 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
With what speed will the fastest electrons be emitted from a surface whose threshold wavelength is 600. nm, when the surface is illuminated with light of − wavelength 4.0 × 10 7 푚?
13 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
H atoms only emit/absorb certain frequencies.
What is causing these properties? Electrons can only exist with certain energies. The spectral lines are transitions from one allowed energy level to another.
14 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Finding energy levels of H atom
∆퐸 = 퐸푢푝푝푒푟(2) − 퐸푙표푤푒푟 1 = ℎ휈푒푚𝑖푡푡푒푑
15 1 1 휈푒푚𝑖푡푡푒푑 = 3.29 × 10 퐻푧 2 − 2 (Found experimentally) 푛1 푛2
Note: In this equation n2 is always the large number which corresponds to the higher energy level.
15 1 1 −34 15 1 1 −ℎ 3.29 × 10 퐻푧 2 − 2 = − 6.626 × 10 퐽 ∙ 푠 3.29 × 10 퐻푧 2 − 2 푛2 푛1 푛2 푛1 Note: The negative sign appeared because a negative sign was taken out of parenthesis.
−18 1 1 -2.178 × 10 퐽 2 − 2 =퐸푢푝푝푒푟(2) − 퐸푙표푤푒푟(1) 푛2 푛1 Energy level of H atom 1 퐸 = −2.178 × 10−18퐽 n= 1, 2, 3, … 푛2 Energy level of other 1e- systems 푍2 퐸 = −2.178 × 10−18퐽 n= 1, 2, 3, … 푛2 15 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory Student Question What is the wavelength of the radiation + emitted by a 퐿𝑖2 ion when an electron transitions between 푛 = 4 to the 푛 = 2 levels? 8 푚 Helpful Hint: c = 2.998×10 푠
a) -1.664×1024 m b) -5.399×10-8 m c) 1.621×10-7 m d) 4.864×10-7 m e) None of the Above
16 Chapter 12: Quantum Mechanics and Atomic Theory m s Quantum Theory
Constructive Interference: When the peaks of waves coincide, the amplitude of the resulting wave is increased.
Destructive Interference: When the peak of one wave coincides with the trough of another wave the resulting wave is decreased.
17 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
When light passes though a pair of closely spaced slits, circular waves are generated at each slit. These waves interfere with each other.
Where they interfere constructively, a bright line is seen on the screen behind the slits; where the interference is destructive, the screen is dark.
18 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory Student Question Imagine an alternate universe where the value of Planck constant is 6.62607×10-9 J·s. In that universe, will the following require quantum mechanics or classical mechanics to adequately describe it? A bacterium with a mass of 3.0 pg, 9.0 μm long, 휇푚 moving at 6.00 푠 .
a) classical b) quantum c) You could use either
19 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Particles have wave like properties, therefore, classical mechanics are incorrect.
Classical Mechanics: Particles have a defined trajectory. Location and linear momentum can be specified at every moment.
Quantum Mechanics: Particles behave like waves. Cannot specify the precise location of a particle.
Note: For the hydrogen atom, the duality means that we are not going to be able to know the speed of an electron orbiting the nucleus in a definite trajectory.
20 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Theory
Wavefunction (흍): A solution of the Schrödinger equation; the probability amplitude.
Note: This gives you a representation of the particle’s trajectory.
Examples : 휓 = sin(푥)
Probability Density (흍ퟐ): A function that, when multiplied by volume of the region, gives the probability that the particle will be found in that region of space.
Note: This value must be between 0 and 1
21 Chapter 12: Quantum Mechanics and Atomic Theory Particle in a Box
Particle in a 1-D Box Boundary Conditions 푥 = 0휓 = 0 푥 = 퐿휓 = 0 What is the wavefunction? sin(푥) (sin(0) = 0 푎푛푑 sin(휋) = 0) 1 2 Τ2 푛휋푥 휓 푥 = 푠𝑖푛 퐿 퐿
Note: n is a quantum number. Quantum numbers are integers or ½ integers that label a wavefunction.
1Τ2 Note: The term 2 is there for normalization in order to get 2 퐿 휓 = 1
22 Chapter 12: Quantum Mechanics and Atomic Theory Particle in a Box
What are the allowed energy levels?
Get the allowed energy levels from Schrödinger’s equation
2 1 ℏ 2 Τ2 푑2 푛휋푥 ℏ2 푑2휓 − 2 sin =퐸휓 − +푉 푥 휓=퐸휓 2푚 퐿 푑푥 퐿 2푚 2 푑푥 풏흅풙 Take 1st derivative of 풔풊풏 Note: V(x)=0 for the particle in a box 푳 푑 푑 푛휋푥 푑 푛휋 푛휋푥 ℏ2 푑2휓 푠𝑖푛 = 푐표푠 − =퐸휓 푑푥 푑푥 퐿 푑푥 퐿 퐿 2푚푑푥2 풏흅풙 1 Take 2nd derivative of 풔풊풏 ℏ2 푑2 2 ൗ2 푛휋푥 푳 − 2 sin =퐸휓 2푚푑푥 퐿 퐿 푑 푛휋 푛휋푥 2휋 2 푛휋푥 cos =− sin 푑푥 퐿 퐿 퐿 퐿
23 Chapter 12: Quantum Mechanics and Atomic Theory Particle in a Box
Plug 2nd derivative back into wavefunction 1 1 2 Τ2 2 Τ2 ℏ 2 푛휋 푛휋푥 2 푛휋푥 2푚 퐿 퐿 sin 퐿 = 퐸 퐿 sin 퐿
Cancel out 2 2 ℏ 푛휋 2푚 퐿 = 퐸
Simplify ℎ ℏ = 2휋 2 ℎ 2 2 2 2푛 휋 ℎ2푛2 퐸 = 2 휋 = 2푚퐿2 8푚퐿2
24 Chapter 12: Quantum Mechanics and Atomic Theory The Hydrogen Atom
Atomic Orbitals: A region of space in which there is a high probability of finding an electron in an atom.
Note: The wavefunctions’ of electrons are the atomic orbitals.
The wavefunction of an electron is given in spherical polar coordinates 푟 = distance from the center of the atom 휃 = the angle from the positive z-axis, which can be thought of as playing the role of the geographical “latitude” 휑 = the angle about the z-axis, the geographical longitude
25 Chapter 12: Quantum Mechanics and Atomic Theory The Hydrogen Atom
Wavefunction of an electron in a 1-electron atom
휓 푟, 휃, 휙 = 푅 푟 푌 휃, 휙
푅(푟) = Radial Wavefunction 푌(휃, 휑) =Angular Wavefunction
26 Chapter 12: Quantum Mechanics and Atomic Theory The Hydrogen Atom
General wavefunction expression for a hydrogen atom:
+1
-1
0
+2
-1
+1
-2
0
27 Chapter 12: Quantum Mechanics and Atomic Theory The Hydrogen Atom
Schrödinger Equation for the H-atom
ℏ2 1 푑 푑휓 푑 푑휓 1 푑2휓 − sin 휃 푟2 + sin 휃 + + 푉 푟 휓 = 퐸휓 2휇푟2 sin 휃 푑푟 푑푟 푑휃 푑휃 sin 휃푑휙2 2 푉 푟 = −푒 +푒 = −푒 4휋휀∘푟 4휋휀∘푟 푉(푟) = Columbic potential energy between the proton and electron 휇 = Reduced mass (proton and electron)
Scientists have solved for the energy of the H-atom 4 ℎ푅 −18 1 푚푒푒 15 퐸 = − 2=−2.178×10 2 푅 = 3 2 = 3.290 × 10 퐻푧 푛 푛 8ℎ 휀∘ 푛 = principle quantum number can be 1, 2, 3, … ℎ = planks constant 6.62608×10-34J·s
28 Chapter 12: Quantum Mechanics and Atomic Theory The Hydrogen Atom
Pictured: The permitted energy levels of a hydrogen atom. The levels are labeled with the quantum number 푛 which ranges from 푛 = 1 (ground state) to 푛 = ∞.
29 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Numbers
Principle Quantum Number (푛) Related To: Size and Energy Allowed Values: 1,2,3,… (shells)
Note: The larger the 푛, the larger the size, the larger the orbital, and the larger the energy.
Note: When identifying the orbital, the 푛 value comes in front of the orbital type.
Example: 3p 푛 = 3
30 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Numbers
Angular Momentum Quantum Number (푙) Related To: Shape Allowed Values: 0,1,2, … , 푛 − 1 (subshells)
Value Orbital What are the possible 푙 values of l Type given the following 푛 values? 0 s 1) 푛 = 1 1 p 2) 푛 = 2 2 d 3) 푛 = 3 3 f What type of orbital is associated with the following quantum numbers? 1) 푛 = 1 and 푙 = 0 2) 푛 = 2 and 푙 = 1 3) 푛 = 3 and 푙 = 0
31 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Numbers
Magnetic Quantum Number (푚푙) Related To: Orientation in space
(specifies exactly which orbital [ex: 푝푥 ]) Allowed Values: 푙, 푙 − 1, … , 0, … , −푙 (orbitals)
What are the possible values of 푚푙 given the following 푛 and 푙 values? 1) 푛 = 1 and 푙 = 0 2) 푛 = 2 and 푙 = 1 3) 푛 = 2 and 푙 = 0
32 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Numbers
Note: The quantum number ml is an alternative label for the individual orbitals: in chemistry, it is more common to use x, y, and z instead.
33 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Numbers
A summary of the arrangements of shells, subshells, and orbitals in an atom and the corresponding quantum numbers.
34 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Numbers Student Question The following set of quantum numbers is not
allowed: 푛 = 3, 푙 = 0, 푚푙 = −2. Assuming that the 푛 and 푚푙 values are correct, change the 푙 value to an allowable combination.
a) 푙 = 1 b) 푙 = 2 c) 푙 = 3 d) 푙 = 4 e) None of the Above
35 Chapter 12: Quantum Mechanics and Atomic Theory Quantum Numbers
Electron Spin Quantum Number (푚푠) Related To: Spin of the electron Allowed Values: +½ (spin up ↑) or -½ (spin down ↓)
36 Chapter 12: Quantum Mechanics and Atomic Theory Orbitals
What does an s-orbital (푙 = 0) look like? 푛 = 1 and 푙 = 0
2푒−푟Τ푎∘ 푅 푟 = 3Τ2 (radial wavefunction) 푎∘ 1 푌 휃, 휙 = (angular wavefuction) 2휋1Τ2 2푒−푟Τ푎∘ 1 푒−푟Τ푎∘ 휓 푟, 휃, 휙 = = 3Τ2 2휋1Τ2 3 1Τ2 푎∘ 휋푎∘ −2푟Τ푎 2 푒 ∘ 휓 푟, 휃, 휙 = 3 휋푎∘
37 Chapter 12: Quantum Mechanics and Atomic Theory Orbitals
The three s-orbitals (풍 = ퟎ) of lowest energy
The simplest way of drawing an atomic orbital is as a boundary surface, a surface within which there is a high probability (typically 90%) of finding the electron. The darker the shaded region within the boundary surfaces, the larger the probability of the electron being found there.
38 Chapter 12: Quantum Mechanics and Atomic Theory Orbitals
What do p-orbitals (푙 = 1) look like?
39 Chapter 12: Quantum Mechanics and Atomic Theory Orbitals
What do d-orbitals (푙 = 2) look like?
40 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
The electrons in many-electron atoms occupy orbitals like those of hydrogen but the energy of the orbitals differ.
Differences between the many-electron orbital energies and hydrogen atom orbital energies: The nucleus of the many-electron orbitals have more positive charge attracting the electrons, thus lowering the energy. The electrons repel each other raising the energy.
41 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
The number of electrons in an atom affects the properties of the atom.
Potential Energy for He atom (2 p and 2 e-) Attraction of Attraction of Repulsion electron 1 to electron 2 to between the the nucleus the nucleus two electrons 2푒2 2푒2 푒2 푉 = − − + 4휋휀∘푟1 4휋휀∘푟2 4휋휀∘푟12
푟1 = distance between electron 1 and the nucleus
푟2 = distance between electron 2 and the nucleus
푟12 = distance between the two electrons
Note: H with 1 electron has no electron-electron repulsion and the electron will have the same energy if is the 2s or 2p orbital (all orbitals within one shell degenerate).
42 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
Why do the energies change? Shielding: The repulsion experienced by an electron in an atom that arises from the other electrons present and opposes the attraction exerted by the nucleus.
Effective Nuclear Charge (Zeff): The net nuclear charge after taking into account the shielding caused by other electrons in the atom. Note: s electrons can penetrate through the nucleus while p and d electrons cannot. Amount of Shielding S P D F Distance from nucleus 43 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s
Order of Orbital Filling
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p
44 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
Electron Configuration: A list of an atom’s occupied orbitals with the number of electrons that each contains. In the ground state the electrons occupy atomic orbitals in such a way that the total energy of the atom is a minimum. We might expect that atoms would have all their electrons in the 1s orbital however this is only true for H and He. Pauli Exclusion Principle: No more than two electrons may occupy any given orbital. When two electrons occupy one orbital, the spins must be paired.
Note: Paired spins means ↑ and ↓ electron (↑↓)
45 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
Smallest Subshell l n s 0 1 p 1 2 d 2 3 f 3 4
Writing Electron Configurations Step 1: Determine the number of electrons the atom has. Step 2: Fill atomic orbitals starting with lowest energy orbitals first and proceeding to higher energy orbitals. Step 3: Determine how electrons fill the orbitals.
46 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
Electron Configurations: He Step 1: Step 2: Step 3:
Be Step 1: Step 2: Step 3:
47 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
Electron Configurations: C Step 1: Step 2: Step 3: ______2p ______2p ______2p ↑↓ 2s ↑↓ 2s ↑↓ 2s ↑↓ 1s ↑↓ 1s ↑↓ 1s
Note: Electrons that are farther apart repel each other less.
Note: Electrons with parallel spins tend to avoid each other more.
48 Chapter 12: Quantum Mechanics and Atomic Theory Many-Electron Atoms
Atoms with exceptions to their electron configurations
49 Chapter 12: Quantum Mechanics and Atomic Theory Periodic Trends
Effective Nuclear
Charge:(Zeff) The net nuclear charge after taking into account the shielding caused by other electrons in the atom.
50 Chapter 12: Quantum Mechanics and Atomic Theory Periodic Trends
Effective Nuclear
Charge:(Zeff) The net nuclear charge after taking into account the shielding caused by other electrons in the atom.
Why: Going across the periodic table, the number of core electrons stays the same but the number of protons increases. The core electrons are responsible for most of the shielding, therefore the
Zeff gets larger as you go across a period. Although going down a group adds more core
electrons it also adds more protons therefore Zeff is pretty much constant going down a group.
51 Chapter 12: Quantum Mechanics and Atomic Theory Periodic Trends
Atomic Radii: Half the distance between the centers of neighboring atoms in a solid of a homonuclear molecule.
Why: Going across a period the Zeff increases, therefore the pull on the electrons increases and the atomic radii decrease. Going down a group, more atomic shells are added and the radii increase.
52 Chapter 12: Quantum Mechanics and Atomic Theory Periodic Trends
First Ionization Energy: (I) The minimum energy required to remove the first electron from the ground state of a gaseous atom, molecule, or ion. X(g) → X+(g) +e-
Why: Going across a period the Zeff increases therefore it is harder to remove an electron and the first ionization energy increases. However, going down a group the electrons are located farther from the nucleus and they can be removed easier.
53 Chapter 12: Quantum Mechanics and Atomic Theory Periodic Trends
1st Ionization Energies of the First 20 Elements 2500 He Ne 2000 F Ar ) N 1500 H O Cl mol C P S Be
1000 B Mg Si I (kJ/ I Li Al Ca Na K 500
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Atomic Number Why don’t B and Al fit the 1st ionization energy trend?
54 Chapter 12: Quantum Mechanics and Atomic Theory Periodic Trends
Electron Affinity: (Eea) The energy change associated with the addition of an electron to a gas-phase atom. X(g) + e- → X-(g)
Note: More common definition: the energy released when a electron is added to a gas-phase atom. This definition results in a sign flip for most books.
Why: Going across a period the Zeff increases, therefore, the atom has a larger positive charge and releases more energy when an electron is added to the atom. Going down a group the electron is added farther from the nucleus so less energy is released. When energy is released it has a negative sign, therefore, F has the smallest (largest negative number) electron affinity. This trend does not hold true for the noble gases. Note: This trends has the most atoms that do not obey it. 55 Chapter 12: Quantum Mechanics and Atomic Theory Periodic Trends
Electron Affinity of the First 20 Elements 50 He Be N Ne Mg Ar Ca B 0 Al Li Na K -50 H P
) C -100 O Si
mol -150 S
(kJ/ -200 ea
E -250 -300 F Cl -350 -400 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Atomic Number
56 Chapter 12: Quantum Mechanics and Atomic Theory Take Away From Chapter 12
Big Idea: The structure of atoms must be explained using quantum mechanics, a theory in which the properties of particles and waves merge together.
Electromagnetic Radiation (27) Be able to change between frequency and wavelength 푐 = 휆휈 Be able to assign what area of the electromagnetic spectrum radiation comes from.
Numbers correspond to end of chapter questions. 57 Chapter 12: Quantum Mechanics and Atomic Theory Take Away From Chapter 12
Quantum Theory Know that electromagnetic radiation has both wave and matter properties. (32) Photoelectric effect (particle property) (29,30,31) Know what the work function of a material is Diffraction (wave property) Be able to calculate the energy carried in an electromagnetic wave (21) 퐸 = ℎ휈 Know that matter has both wave and matter properties. Be able to calculate the wavelength of matter. (34,36,37) ℎ 휆 = 푚푣 Know that the Heisenberg uncertainty principle determines the accuracy in which we can measure momentum and position.(53) 1 ℏ ∆푝∆푥 ≥ 2 Numbers correspond to end of chapter questions. 58 Chapter 12: Quantum Mechanics and Atomic Theory Take Away From Chapter 12
Particle in a Box Know that the wavefunction of different systems can be found using boundary conditions. 1Τ2 2 푛휋푥 Particle in a box wavefunction 휓 = 퐿 sin 퐿 Know that the square of the wavefunction tells us the probability of the particle being in a certain location. (70) Know the most likely location of a particle in a box (ex: n = 1 particle most likely in center of box, n = 2 particle most likely on sides of box) Know that the Schrödinger equation allows us to match wavefunctions with allowed energy values. 2 2 Particle in a box 퐸 = 푛 ℎ (57,58,59,61) 8푚퐿2 The Hydrogen Atom Know that when quantum mechanics is applied to 1 electron systems the observed energy and the theoretical energies match. (44,45,46,48,50,51,147) 2 퐸 = −2.178 × 10−18 푍 푛2 Numbers correspond to end of chapter questions. 59 Chapter 12: Quantum Mechanics and Atomic Theory Take Away From Chapter 12
Quantum Numbers (62,66,68,69,78,79) Know that the quantum number 푛 gives the size and energy Allowed values of 푛 = 1, 2, … Know that the quantum number l gives the orbital type (shape) Allowed values of 푙 = 0, 1, 2 , … 푛 − 1
Know that the quantum number 푚푙 gives the orbital orientation (ex: 푝푥)
Allowed values of 푚푙 = −푙, … 0, … 푙 Know that a fourth quantum number was needed to have theory
match experiment, 푚푠
Allowed values of 푚푠 = +½ 푎푛푑 − ½
Numbers correspond to end of chapter questions. 60 Chapter 12: Quantum Mechanics and Atomic Theory Take Away From Chapter 12
Orbitals Know that when atomic orbitals are drawn they represent the area in which e- have a 90% chance of being in. (71) Know the what s, p, and d orbitals look like. Many-Electron Atoms Be able to write both the full and shorthand electron configurations of atoms.(80,81,84,88,96,98) Be able to predict the number of unpaired electrons in a system.(97) Periodic Trends Know the trends of effective nuclear charge, atomic radii, ionization energy, and electron affinity. (13,14,103,104,106,112,114, 119,120,139)
Numbers correspond to end of chapter questions. 61 Chapter 12: Quantum Mechanics and Atomic Theory