CHEMISTRY 161 Chapter 8 Quantum Mechanics

1. Structure of an Atom subatomic particles electrons protons neutrons

17p 18n 17e Cl mass number atomic number 18 neutrons e-e- classical physics predicts that electron falls into nucleus Why are atoms stable?

2. Waves EXP1

Intensity distance, x.. direction of propagation wavelength [m] amplitude v = x/tt = x/v

Intensity time, t.. direction of propagation period [s] T Frequency [s -1 ] [1 Hz = 1 s -1 ] Hertz

Frequency and Wavelength wavelengthfrequencyspeed of radiation meter (m)Hz or s -1 m s -1 LONG WAVELENGTH, LOW FREQUENCY

light can be described as a wave

James Maxwell POSTULATE visible light consist of electromagnetic waves speed of propagation (speed of light) c = 3  10 8 ms -1

light has two components 1.electric field 2.magnetic field

ELECTROMAGNETIC SPECTRUM INCREASING FREQUENCY & ENERGY

Which color has the higher frequency? 1 = orange 2 = blue  = c Wavelength  (nanometers) VISIBLE SPECTRUM

The wavelength of the yellow light from a lamp is 589 nm. What is the frequency of the radiation?

Li NaK different atoms emit distinct light EXP2 3. Postulates

Max Planck h is Planck’s constant h = x J s

energy can be emitted or absorbed only in discrete quantities (little packages) EXP3/4

Emission Nebula

CLASSICAL any amount of energy can be emitted or absorbed NON-CLASSICAL energy can be emitted or absorbed only in discrete quantities (little packages) energy is not continuous QUANTUM smallest amount of energy which can be absorbed/ emitted

Albert Einstein Electromagnetic radiation can be viewed as a stream of particle-like units called photons POSTULATE 3. Properties of Photons

E initial E final ABSORPTION OF A PHOTON atoms and molecules absorb discrete photons (light quanta)

de Broglie Duality of Wave and Corpuscle light has properties of a wave and of a particle

SUMMARY 1. light can be described as a wave of a wavelength and frequency 2. light can be emitted or absorbed only in discrete quantities (quantum - photon) 3. duality of wave and corpuscle

de Broglie wavelength each particle can be described as a wave with a wavelength λ 4. Properties of Electrons

matter and light (photons) show particle and wave-like properties WAVE-PARTICLE DUALITY MASS INCREASESWAVELENGTH GETS SHORTER MASS DECREASES WAVELENGTH GETS LONGER

Wave-likeParticle-like BaseballProtonPhotonElectron WAVE-PARTICLE DUALITY large pieces of matter are mainly particle-like small pieces of matter are mainly wave-like MASS

1. light behaves like wave and particle 2. electron behaves like wave and particle 3. electrons are constituents of atoms 4. light is emitted/absorbed from atoms in discrete quantities (quanta)

E initial E final EMISSION OF A PHOTON atoms and molecules emit discrete photons electrons in atoms and molecules have discrete energies 5. Electrons, Photons, Atoms

EMISSION SPECTRA analyze the wavelengths of the light emitted only certain wavelengths observed only certain energies are allowed in the hydrogen atom

Balmer found that these lines have frequencies related n = 1, 2, 3, 4, 5…

electrons move around the nucleus in only certain allowed circular orbits e-e- THE BOHR ATOM each orbit has a quantum number associated with it QUANTUM NUMBERS n is a QUANTUM NUMBER n= 1,2,3,4……... n = 4 n = 3 n = 2 n = 1

n = 4 n = 3 n = 2 n = 1 THE BOHR ATOM QUANTUM NUMBERS and the ENERGY Z = atomic number of atom A = x J = Ry THIS ONLY APPLIES TO ONE ELECTRON ATOMS OR IONS

BOHR ATOM ENERGY LEVEL DIAGRAM Z=1 HYDROGEN ATOM!

EnEn ENERGY n=1 -A BOHR ATOM ENERGY LEVEL DIAGRAM

n=1 -A n=2 -A/4 EnEn ENERGY BOHR ATOM ENERGY LEVEL DIAGRAM

n=1 -A n=2 -A/4 EnEn n=3 -A/9 n=4 ENERGY BOHR ATOM ENERGY LEVEL DIAGRAM e-e- E photon = h ELECTRON EXCITATION

n=1 -A n=2 -A/4 EnEn 0 n=3 -A/9 n=4 Energy e-e- ELECTRON DE-EXCITATION emission of energy as a photon e-e-

nini nfnf only a photon of the correct energy will do ABSORPTION OF A PHOTON

nini nfnf

nini nfnf

nini nfnf energy is absorbed

nfnf nini EMISSION OF A PHOTON This means energy is emitted!

nini nfnf IONIZATION OF AN ATOM This means energy is absorbed!

EE the ionization energy for one mole is IONIZATION ENERGY = 2.178x J atom -1 x 6.022x10 23 atoms mol -1 =13.12 x 10 5 J mol -1 = 1312 kJ mol -1 = x J for one atom

e-e- THE BOHR ATOM QUANTUM NUMBERS n = 4 n = 3 n = 2 n = 1 absorption emission ionization energy

6. HEISENBERG’S UNCERTAINTY PRINCIPLE  x is the uncertainty in the particle’s position  p is the uncertainty in the particle’s momentum in the microscopic world you cannot determine the momentum (velocity) and location of a particle simultaneously EXP5

THE HEISENBERG UNCERTAINTY PRINCIPLE if particle is big thenuncertainty small EXP5

This means we have no idea of the velocity of an electron if we try to tie it down! Alternatively if we pin down velocity we have no idea where the electron is! So for electrons we cannot know precisely where they are!

we cannot describe the electron as following a known path such as a circular orbit Bohr’s model is therefore fundamentally incorrect in its description of how the electron behaves. we cannot know precisely where electrons are!

Schroedinger (1926) Born (1927)

The probability of finding an electron at a given location is proportional to the square of  22  electron has wave properties EXP VI

 2 – The Bus - Propabilities

orbit of an electron at radius r (Bohr) probability of finding an electron at a radius r (Schroedinger, Born) 

1. Schroedinger defines energy states an electron can occupy  2. square of wave function defines distribution of electrons around the nucleus high electron density - high probability of finding an electron at this location low electron density - low probability of finding an electron at this location atomic orbital wave function of an electron in an atom each wave function corresponds to defined energy of electron an orbital can be filled up with two electrons (box) EXPVII

most atoms have more than two electrons each electron in an atom is different electrons have different ‘labels’ called quantum numbers

QUANTUM NUMBERS 1.principle quantum number 2. angular momentum quantum number 3. magnetic quantum number 4. spin quantum number

1. principle quantum number n n = 1, 2, 3, 4, 5… hydrogen atom: n determines the energy of an atomic orbital measure of the average distance of an electron from nucleus n increases → energy increases n increases → average distance increases

e-e- n = 4 n = 3 n = 2 n = 1 n = K L M N O P ‘shell’ maximum numbers of electrons in each shell 2 n 2 EXP6

2. angular momentum quantum number l = 0, 1, … (n-1) l = s p d f g h define the ‘shape’ of the orbital

1s, 2s, 3s 3s 2s 1s

3. magnetic quantum number m l = -l, (-l + 1), … 0…… (+l-1) +l defines orientation of an orbital in space

2p x, 3p x, 4p x 4p x 3p x 2p x

d orbitals

4. spin quantum number m s = -1/2; + 1/2

ORBITALS AND QUANTUM NUMBERS 1.principle quantum number 2. angular momentum quantum number 3. magnetic quantum number 4. spin quantum number n = 1, 2, 3, 4, 5… l = 0, 1, … (n-1) m l = -l, (-l + 1), … 0…… (+l-1) +l m s = -1/2; + 1/2

 (n, l, m l, m s ) ATOMIC ORBITALS nlmlml orbitalsdesignation 10011s 20012s 1-1,0,+132p x,2p y,2p z 30013s 1-1,0,+133p x,3p y,3p z 2-2,-1,0,+1,+253d xy,3d yz,3d xz, 3d x 2 -y 2,3d z 2 4…………

H Atom Orbital Energies energy level diagram H atom 3s3p3d2s2p1s3s3p3d2s2p1s E energy depends only on principal quantum number orbitals with same n but different l are degenerate

1s1s E 2s2s 2p2p 3s3s 3p3p 3d3d 4s4s 4p4p 5s5s 4d4d MULTI-ELECTRON ATOM orbitals with same n and different l are not degenerate energy depends on n and m l EXAMPLES [Xe]

Periodic Table of the Elements period groupgroup chemical reactivity - valence electrons ns 1 ns 2 ns 2 np 6 ns 2 (n-1)d x

7. PERIODIC TRENDS 3. IONIZATION ENERGIES 4. ELECTRON AFFINITIES 1. ATOMIC RADIUS 2. IONIC RADIUS

ATOMIC RADIUS MAIN GROUPS ATOMIC RADIUS

1s, 2s, 3s 3s 2s 1s

2p x, 3p x, 4p x 4p x 3p x 2p x

ATOMIC RADIUS MAIN GROUPS ATOMIC RADIUS effective nuclear charge

IONIC RADII IONIC RADIUS

cations are smaller than their atoms anions are larger than their atoms Na is 186 pm and Na + is 95 pm F is 64 pm and F - is 133 pm same nuclear charge and repulsion among electrons increases radius one less electron electrons pulled in by nuclear charge O < O – < O 2–

EXAMPLES Which is bigger? Na or Rb Rb higher n, bigger orbitals K or Ca K poorer screening for Ca Ca or Ca 2+ Ca bigger than cation Br or Br - Br smaller than anion

QUESTION The species F -, Na +,Mg 2+ have relative sizes in the order 1F - < Na + <Mg 2+ 2F - > Na + >Mg 2+ 3Na + >Mg 2+ > F - 4Na + =Mg 2+ = F - 5 Mg 2+ > Na + >F -

QUESTION 1F - < Na + <Mg 2+ 2F - > Na + >Mg 2+ 3Na + >Mg 2+ > F - 4Na + =Mg 2+ = F - 5 Mg 2+ > Na + >F - Na + is 95 pm Mg 2+ is 66 pm F - is 133 pm ALL 1s 2 2s 2 2p 6 ALL are isoelectronic

3. IONIZATION ENERGIES M(g)  M + (g) + e - energy required to remove an electron from a gas phase atom in its electronic ground state I 1 > 0 first ionization energy (photon)

M + (g)  M 2+ (g) + e - M 2+ (g)  M 3+ (g) + e - second ionization energy third ionization energy I 2 > 0 I 3 > 0 I 1 > I 2 > I 3

Why? electrons closer to nucleus more tightly held IONIZATION ENERGY first ionization energies decrease d shell insertion

IONIZATION ENERGY

1. closed shells are energetically most stable 2. half-filled shells are energetically very stable DERIVATION OF IONIZATION ENERGIES

noble gases have the highest ionization energy

4. ELECTRON AFFINITIES the energy change associated with the addition of an electron to a gaseous atom X(g) + e –  X – (g) electron affinity can be positive or negative

Why? ELECTRON AFFINITY general trend

1. closed shells are energetically most stable 2. half-filled shells are energetically very stable DERIVATION OF ELECTRON AFFINITIES