Download Figure 7.18 The 3d orbitals

Chapter 7: Quantum Theory and Atomic Structure
E-M RADIATION: LIGHT
Electro-Magnetic radiation includes visible light, microwave, TV, radio, x-ray, etc.
Radiation is a combination of vibrating electric and magnetic fields in repeatable waveforms
Wavelength, λ (lambda): distance from crest to crest
Frequency, (nu): # crests to pass a point in 1 second, units are #/s or Hz
Wave velocity = λ 
All E-M radiation in a vacuum has constant velocity called the speed of light: c = 2.998 x 108 m/s.
Therefore c = λ  (Memorize formula and c)
Long λ => short  & vice-versa
Figure 7.1 Frequency and wavelength
Figure 7.2 Amplitude of a wave
Figure 7.3 Regions of the electromagnetic spectrum (Visible light is a very small portion.)
Sample Problem 7.1a (you do the work here) Note A = Angstrom, an old unit of wavelength. Conversion is 1A
= 1.0 x 10-10 m.
E-M RADIATION
E-M radiation was considered to be a wave/energy phenomenon and not matter
Max Planck developed a new physics when classical physics could not be used to interpret data from
blackbody radiation
Blackbody radiation is emitted by solid bodies that are heated to high T and become incandescent
Classical physics had to assume continuous radiation, and it could not resolve the data that there was
discrete radiation
Planck developed theory of Packets of Energy called quanta
The energy associated with quanta was proportional to the frequency of the radiation:
E = h
h = Planck’s constant 6.626 x 10-34 J.s
Wavelength, Frequency and Energy
If c =, and E = h, then with rearranging and substituting: E = hc/
What is the energy of a photon with a wavelength of 399.0 nm?
(from 4th ed. Figure 7.6 Blackbody radiation)
Figure 7.6 Demonstration of the photoelectric effect
Photoelectric Effect
Photoelectric Effect: electrons are ejected from a metal's surface if it is exposed to uv radiation
Each metal required a characteristic minimum uv frequency to start ejecting e-s
Called Threshold freq, o
- As  increases more e-s ejected with higher vel (more KE)
These data also defied classical physical explanation
Einstein reviewed data, recalled Planck's quanta
The "incident" radiation consists of quanta of energy, E = h, called photons - thus the PHOTOELECTRIC
Effect
In order to eject an e-, a min KE is required, E = ho
If E>ho then excess KE is supplied to the e-, increasing its velocity
Chapter 7: Quantum Theory and Atomic Structure
For Na metal, o = 5.51 x 1014 Hz
Sample Problem 7.2: (you do work here)
Line Spectra
Experiments with "excited" atoms of H produced emission spectra
- always a discrete set of lines at certain wavelengths
White light dispersed by a prism or diffraction grating:
- we see ROYGBIV – a continuous spectrum from 750 nm to 400 nm
When a gas-filled tube is charged with current, only certain EM 's are detected - called a line spectrum
or emission spectrum
The gas particles split into individual atoms
The e-s are excited by the current into a higher energy level.
When they drop down, they emit energy of a certain λ, with energy gaps at distinct intervals
Figure 7.7 The line spectra of several elements (Compare the continuous spectrum of visible light vs. the
discrete or line spectra of the three elements shown.)
Line Spectra and Energy Levels
Hydrogen atomic line spectra – also called emission spectra –
- worked out mathematically (by several scientists) to define the energy of the light emitted &
relationships between the lines
Balmer: red, green & blue lines (656.3, 486.1, 434.0, 410.1 nm)
1/λ = Ry(1/22 - 1/n2)
If n > 2 Ry = Rydberg constant = 1.096776 x 107/m
If n = 3 get red, n = 4 get green, n = 5 get blue, n =6 get violet
Figure 7.8 Three series of spectral lines of atomic hydrogen. Balmer is in the visible region and the other
series, which have names also, are in uv or ir area of E-M radiation.
 The Bohr Model of Hydrogen atom
 1. H atoms have only certain allowable energy levels called stationary states.
 2. Atom does not radiate energy while in a stationary state.
 3. Atoms changes to another stationary state by absorbing or emitting a photon.
Energy=EstateA-EstateB=hn
What line spectra mean
Bohr found En = - Rhc/n2
where R = 1.097 x 107/m, h = 6.626 x 10-34 J.s, c = speed of light
Rhc = 2.178 x 10-18 J (since they are all constants)
Then En= -2.178 x 10-18 J/n2
All E is therefore < 0, and has discrete values only
Nucleus (proton) & e- are so far apart there's no attraction anymore
Negative E is more stable than zero energy
n = 1 is the ground state, all above are excited states
Figure 7.9 Quantum staircase
Figure 7.10 The Bohr explanation of the three series of spectral lines
Chapter 7: Quantum Theory and Atomic Structure
Emission vs. Absorption Spectroscopy
- Instrumental techniques used to obtain information about atomic or molecular energy levels
- Emission: electrons in an atom are excited to a higher energy state and then emit photons as they
return to lower energy states
- Absorption: electrons in an atom absorb photons of certain wavelengths and jump to higher energy
states; photons NOT absorbed are observed!
- See Figure 7.11 in text: why chlorophyll looks green
Figure B7.1 (4th ed.) Flame tests
Practice sample problem 7.3 and its follow-up problem.
A hydrogen atom has an e- excited up to level 4, and it drops back to level 2. (a) determine the wavelength of
the photon emitted and (b) the energy difference.
(a) Use 1/ = Ry(1/22 – 1/42)
 = 4.8617 x 10-7 m
(b) Use E = hc/
E = 4.086 x 10-19 J
Follow-up: Answer the same questions for the e- excited up to level 6.
"Traveling waves" vs. stationary waves or standing waves
Stationary wave:
- fixed at both ends
- has "nodes"
- never moves on those spots
with distance = length/2
Only certain λ's are possible for a standing wave
Figure 7.12 Wave motion in restricted systems
Wave-particle Duality
Einstein remembered for E = mc2, where m = E/c2 = (hc/λ)/c2 = h/λc
This appears to say that a photon of a certain wavelength has mass!
Proved by Arthur Compton in 1922
E-M radiation is both waves & little packets of energy and matter called photons
De Broglie 1923: if light has wave-particle duality, then matter, which is particle-like, must also be wavelike
under certain conditions
Rearranged m = h/c to get λ = h/mv
This is called deBroglie wavelength. It means that all matter exhibits both particle and wave properties
Sample Problem 7.4 (Note the relationship 1 Joule = 1 kg*m2/s2)
Wave-particle Duality
Bohr’s Theory: 1 e- in H atom occupying certain energy states - a certain quanta
Spherical orbitals around the nucleus
Chapter 7: Quantum Theory and Atomic Structure
With de Broglie's hypothesis: e- must have a certain λ to make a complete revolution - like a standing wave
An integral # of complete λ's to fit the sphere's circumference
Circumference = 2  r, therefore nλ = 2  r, n = 1, 2, 3....
Figure 7.14 Summary of the major observations and theories leading from classical theory to quantum theory
Heisenberg Uncertainty Principle:
Uncertainty: (Δx)(mΔv) > h/4
Δx is the location of the electron
mΔv is its momentum
Need Δ because we can’t know both at the same time
Sample Problem 7.4 (4th ed.): An electron moving near an atomic nucleus has a speed 6 x 106 ± 1% m/s.
What is the uncertainty in its position (x)?
WAVE FUNCTIONS & QUANTUM MECHANICS:
Schrodinger developed Wave Functions, Ψ(psi), where Ψ2 is the probability of finding e- in a given space
Led to 4 quantum numbers that describe the e-'s position in a complex equation:
1. Only certain wave functions are allowed
2. Each Ψn corresponds to an allowed energy for e- in atom
3. Thus energy of e- is quantized
4. Ψ has no physical meaning, but Ψ2 give the probability density
5. Allowed energy states are called orbitals
6. 3 integer #'s req'd to solve Ψ2 for 3-D space: n, l, ml
Quantum Numbers and Atomic Orbitals
An atomic orbital is specified by three quantum numbers.
n = principal quantum number, a positive integer = 1, 2, 3,...
- determines total E of e- in its electron shell
- gives measure of prob distance from nucleus (orb size)
- 2 or more e-s can be in same electron shell
l = angular momentum or shape = < n - 1 , = 0,1,2,...
- subshells w/in main shell, characterized by certain
wave shapes
0 = s, 1 = p, 2= d, 3 = f, etc.
ml = magnetic q.n. = +l, +l - 1, +l - 2, … 0, ... -l
- specifies which orbital w/in a subshell e- is in
- differ only in orientation, not shape
Chapter 7: Quantum Theory and Atomic Structure
(later we’ll do ms = spin q.n., +½ or -½ for each e-)
Table 7.2 The Hierarchy of Quantum Numbers for Atomic Orbitals
Sample Problem 7.5
Sample Problem 7.6
3-D shapes:
Ψ21s – the 1s orbital is spherical.
Ψ22s – the 2s orbital has some density close to nucleus and then another sphere farther away – a sphere
within a sphere
2
Ψ 2p – the 2p orbitals have no probabilty of e- at the nucleus - called nodal plane
Can be oriented in 3 directions of 3-D graph - x, y, z.
2px, 2py, 2pz have the 3 ml “names” +1, 0 and -1
Ψ23d – the 3d orbitals have 5 ml values, and each has 2 nodal surfaces, so they are in four sections. 3dxy, 3dxz,
3dyz, 3dx2-y2, 3dz2
2
Ψ 4f – the 4f orbitals have 7 ml values, 3 nodal surfaces
Figure 7.15 Electron probability in the ground-state H atom
Figure 7.16 The 1s, 2s and 3s orbitals
Figure 7.17 The 2p orbitals
Figure 7.18 The 3d orbitals
Figure 7.19 One of the seven possible 4f orbitals
You have to draw:
Be able to draw 1s, 2s, 2p, and 3d orbitals.
Practice now!