Quantum Atom:

Atomic Structure, Electron Configuration, and Periodicity

Equations:

λν = c

E = hν energy of photon

∆E = hν difference of energy levels

λ = h/p
p = mu (momentum and particle wavelength) deBroglie Relation

(∆p)( ∆x) ≈ h  The Heisenberg Uncertainty Principle

1/ λ = RH( 1/ nl2 – 1/nu2)

l = lower u = upper

where h is Planck’s constant h= 6.63x10-34 J s

and c is speed of “light” c= 3.00 x 108 m/s

Electromagnetic Radiation

Positive and negative particles are attracted (electrostatic attraction) so what keeps
electrons (negative) separated from (positive) nucleus?

First idea is electron in orbit like the planet (common image but WRONG).
Small systems behave much differently than everyday world.

Before we can understand models for structure of atoms and “Quantum World” We need to
look at electromagnetic radiation and atomic spectra.

1
http://physics.uoregon.edu/~courses/BrauImages/Chap03/FG03_003.jpg)

amplitude (a) = height of the crest brightness proportional to a2

frequency (ν) = cycles of waves that pass a fixed point per unit of time (s-1)
Hertz (Hz) means the same as waves per second or (s -1)
ν is the Greek letter nu

wavelength (λ) = length of one cycle

units can be (m) or (cm = 10-2 m) or (nm = 10-9 m)
λ is the Greek letter lambda

Interference Property of Waves

2
http://theory.uwinnipeg.ca/mod_tech/node125.html

Velocity, Wavelength and Frequency

Speed that wave moves is how many waves per second (ν ) times length of wave (λ )

ν = 2 Hz 2 cycles/s

λ = 10 m 10 m apart

v = 1ms-1 v = λν = 20 m/s

v = λν

Electromagnetic radiation travels at the speed of light (c) = 3.00 x 108 m/s
so c = λν for electromagnetic radiation

So if know: λ can get ν

ν can get λ

Types of Electromagnetic Radiation include:

Length of λ (m) ν ( s-1) c (m/s)

Gamma < 1 x 10-10 3 x 1018 3.8 x 108 High energy

3
x-rays < 1 x 10-8 3 x 1016
Ultraviolet < 3.8 x 10-7 7.9 x 1014
Visible < 7.6 x 10-7 3.9 x 1014
Infrared < 1 x 10-3 3 x 1011
Microwave < 1 x 10-1 3 x 109
TV radio < 5.5 x 102 5.5 x 105 Low Energy

In the above note that x-rays are roughly less than 1x10-8 but longer than 1 x10-10 m and so
on for other examples ultraviolet less than 3.8 x 10-7 but more than 1 x 10-8 m, etc., etc.

Note that: Shorter wavelength  Higher Frequency  High Energy

Ex. If frequency of light is 4.00 x 1014 Hertz or (s-1), then what is the wavelength ( m, nm)?

c = λν

c/ ν = λ

= 3.00 x 108 ms-1 = 7.5 x 10-7 m or 7.5 x 10-7 m (109 nm/m) = 750 nm
4.0 x 1014 s-1

And what is the energy per photon?

E=hν where h is Planck’s constant h =

E = (6.63 x 10-34 Js)( 4.0 x 1014 s-1 )

E = 2.65 x 10-19 J for 1 photon

2.65 x 10-19 J (6.02 x 1023/ mol) = 1.60 x 105 J/mol = 160 kJ/ mol (mol of photons!)

Spectroscopy

Atomic spectra is used to study energy levels occupied by electrons in an atom

Prism or grating is used to separate light into different wavelengths

Continous emissions spectrum- white light (Tungsten in light bulb)

Discontinous emission spectrum- bright lights on dark background

4
 Discrete Energies

http://www.astro.washington.edu/labs/hubblelaw/knowgalaxies.html

Why is energy absorbed at discrete wavelengths?

1900-1905 Max Planck and Albert Einstein

Radiant Energy is discontinuous and comes in increments of energy or

quanta or particles given off photons

Radiant Energy is quantized

E = hν h = 6.63 x 10-34 Js = Planck’s constant

Light is not just like waves but also like particles

Bohr Model

More Energy Higher Frequency Shorter Wavelength

In atomic spectra if electrons can only be at certain discrete energies

(http://online.cctt.org/physicslab/content/Phy1/lessonnotes/atomic/atomicmodelsandspectra.asp)

5
 Explained Observation that

1/ λ = RH( 1/ nl2 – 1/nu2)

RH = Rydberg constant = 109,678 cm-1

Lyman n1=1 n2 = 2, 3, 4, 5, 6 ultraviolet

Balmer n1=2 n2 = 3, 4, 5, 6 visible

Paschen n1= 3 n2 = 4, 5, 6 infrared

Bohr Model Hydrogen Atom

(http://library.thinkquest.org/C006669/media/Chem/img/bohr.gif)

Electrons in fixed orbits around nucleus

Electrons in orbit do not gain or lose energy

When electron jumps from one orbit to another

Gain or lose set amount of energy
(drop to lower level then emits energy)
(jump to lower level then absorb energy)

Bohr used classical physics to balance electrostatic attraction with centrifugal force
away from center and derived equation

E = -A(1/n2) n= quantum number

6
 main energy level 1, 2, 3, 4 …

∆E = E2 – E1

∆E = -A/ n22 - -A/n12 A = 2πme4z2/ h2 = mass charge of electron

∆E = A( 1/n12 – 1/n22)

Recall: ∆E = hν λν =c

∆E = h(c/ λ) = A( 1/n12 – 1/n22)

1/ λ = A/hc( 1/n12 – 1/n22)

His theory agreed exactly with his known Rydberg constant

Explained Balmer, Paschen, Lyman Experiment

Important Ideas but does not work for other atoms (more than one
electron) need NEW physics

Wave Mechanics

Modern Electronic Theory

After description of radiant

Electromagnetic radiation waves Matter Particles

1924 DeBroglie suggested that all matter in motion must have wavelike properties

light wavelike characteristic  frequency (diffraction)

particle characteristic  photons (photoelectric effect)

λ = h/p p = momentum = mv = (mass) (velocity) (kg m/s)

Units: λ = meters (m) and h/p = Js/ (kg m/s)

Larger the particle then λ is very small relative to particle atoms

∴ macroscopic ignore, microscopic important!

Electron particles can be diffracted, they act like waves

7
Heisenberg Uncertainty Principle

Basically do not know exactly where electrons are

Impossible to exactly determine the momentum and position of object

X-rays observe the position, disrupt momentum

Not exact but probable position

(Δx)( mΔu) = h/4π= (Δp)(Δx)

Quantum Mechanics

Provides a unified description of the atomic and everyday world

Physics prior to 1930 could explain cannonballs but not electrons

Schrödinger equation relates HΨ = EΨ

Ψ = Position E = Total Energy H = Hamiltonian Operator

Total energy is the sum of kinetic and potential energy

Ψ wave function the region in space that the electron is most likely to be found in
this region related to the orbital

Ψ2 gives probable electron density

Transition absorb energy electron change orbitals and has higher energy

Use results of hydrogen atom for other atoms

Calculation predicts location in space in which electron is most likely
found and energy of electron

Orbitals  location of electrons

Shape is indicated by letter s, p, d, f

s orbital is spherical

Cannot say where an electron is but only where it is likely to be

Radial Probability
Sum of Ψ2 at distance r

8
 Surface of sphere 4πr2Ψ2 = radial distribution function
∴ Size of an atomic orbital increases as the principle quantum
number increases

n = primary (principle) quantum number ( 1, 2, 3 ...) = main energy level

-
(http://www.chemistry.uvic.ca/chem222/Notes/lect3v1.htm)

9
Radial Wave function of Electron

(http://www.physicsarchives.com/atomicphysics.htm)

10
Types of orbitals s, p, d, f
l = 0, 1, 2, 3

2 electrons per orbital

Quantum Numbers
n l

4p ___ ___ ___ 4 1

3d ___ ___ ___ ___ ___ 3 2

4s ___ 4 0

3p ___ ___ ___ 3 1

3s ___ 3 0

2p ___ ___ ___ 2 1

2s ___ 2 0
Energy
1s ___ 1 0

Ordering can change slightly

Same energy for hydrogen

Separate with more electrons

Because of order of penetration

ns ≥ np ≥ nd ≥ nf

11
Example Electron Configuration

1s 2s 2p 3s Electron Configuration

H __ 1s1

He __ 1s2

Li __ __ 1s22s1 [He] 2s1

Be __ __ 1s22s2

B __ __ __ __ __ 1s22s22p1

C __ __ __ __ __ 1s22s22p2

N __ __ __ __ __ 1s22s22p3

O __ __ __ __ __ 1s22s22p4

F __ __ __ __ __ 1s22s22p5

Ne __ __ __ __ __ 1s22s22p6

Na __ __ __ __ __ __ 1s22s22p63s1 [Ne] 3s1

Chemical properties of elements are determined by electron configuration

Xenon Xe [Kr] 5s24d105p6

Cesium Cs [Xe] 6s1

Barium Ba [Xe] 6s2

Lanthium La [Xe] 6s25d1

Cerium Ce [Xe] 6s25d14f1

Proseodymium Pr [Xe] 6s24f3

12
Exception occur in filling f order, Expect 6s25d14f2

More Exceptions
Half filled and filled subshells have unusual stability

Examples:

Chromium (Cr) 4s23d4  4s13d5

Copper (Cu) 4s23d9  4s13d10

Others: Pd, Ag, Mo

If can move 1 electron to get filled or half-filled d subshell will do so.

Know Normal Order and Exceptions!

Exceptions increase s go to higher weight elements

Periodic Table

(http://wps.prenhall.com/wps/media/objects/602/616516/Media_Assets/Chapter05/Text_Images/FG05_18.JP
G)

13
Quantum Numbers

Alternate way to specify type of orbital other than 1s, 2p etc

Orbital Designation

Specify the probable location and energy of electron found in orbitals

More complicated than just n= 1, 2, 3...

As go across periodic table add protons for new element also add electron

Specify the type of orbital for each electron

Principle Quantum Number shell n

Angular momentum Quantum Number subshell l

Magnetic Orbital Quantum Number orbital ml

Magnetic Spin Quantum Number spin mS

shell n 1, 2, 3, 4 ... main energy level

subshell l 0, 1, 2...(n-1) type of orbital, sublevel

orbital ml +- l, +-1l, 0 specific orbital

spin mS +1/2, -1/2 a specific electron spin

Pauli Exclusion Principle says no two electrons within the same atom can have
the same four quantum numbers

n l ml mS # of electrons
1s 1 0 0 +-1/2 2

2s 2 0 0 +-1/2 2

2p 2 1 +1, 0, -1 +-1/2 6

14
3s 3 0 0 +-1/2 2

3p 3 1 +1, 0, -1 +-1/2 6

3d 3 2 +2, +1, 0, -1, -2 +-1/2 10

Filling of orbitals by Aufbau Principlelowest energy upward

Hunds Rule  electrons unpaired as much as possible

For the same type of orbital, electrons go in separate ones first

Indicate electronic configuration with electronic notation

n = 1, 2, 3, 4...
l=0 s
=1 p px, py, pz
=2 d dx2-y2, dz2, dxy, dxz, dyz subscripts to indicate orbital
=3 f

Representation of 2p Orbital

Representation of the 3d Orbital

15
(http://www.chemistry.uvic.ca/chem222/Notes/lect3v1.htm)

s ml = 0
p ml = -1, 0, +1
d ml = -2, -1, 0, +1, +2
f ml = -3, -2, -1, 0, +1, +2, +3

n, l , ml specify one particular orbital

Filling in electrons lowest to highest energy

16
(http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson36.htm)

Electron Configuration Continued...

2p3
Where 2= main level number, p= sublevel letter, 3= electrons in sublevel

Electronic Configuration of Halogens

F 1s22s22p5
Cl 1s22s22p63s23p5
Br 1s22s22p63s23p64s23d104p5
I 1s22s22p63s23p64s23d104p65s25p5

Outer electrons similar orbitals, so properties the same, combine with alkali metal
NaF, NaCl, NaBr

Abbreviated Electronic Configuration

17
 F [He] 2s22p5
Cl [Ne] 3s23p5
Br [Ar] 3d104s24p5
I [Kr] 4d105s25p5

Paramagneticattracted external magnetic field (unpaired electrons)

Diamagnetic not attracted(slightly repelled) external magnet (all paired

electrons)

Nonmetals gain electrons (Electron Affinity more negative)

Metal lose electrons (low ionization energy)

Metals transfer electrons to oxygen to form ionic oxides which act as bases
Nonemetals share electrons with oxygen, covalent-oxides act as acids

Called Isoelectronic noble gas or Pseudo-noble gas

Electron with highest n value is lost first (except for Lathanides)

Atomic and Ionic Sizes

Determine spectroscopy, math models include size, radius

Atomic radii based on bond distance

Cl-Cl is 198 pm apart so the radius for Cl is 198pm/2 = 99 pm

C-Cl is 176 pm apart so radii 176-99 = 77 pm radius for C

The general trend for Atomic Radius is that it increases right to left across the
periodic table and increases from top to bottom.

Reason: down- filling shell so farther from nucleus

across- within shell remove e- and proton so remaining electrons are not
held as tightly

Ionic Radius in crystals like table salt have alternating negative-positive ions

Shielding

18
(http://www.webelements.com/webelements/elements/text/Li/econ.html)

The effective nuclear charge ~ +1

Representative elements change more than transition change in d and f

Size is fairly flat in filling d anf f orbitals since these are not outermost electrons

Lanthanide contraction

Left Periodic Table Right

Lose e- Gain e-
Cation Anion
Become smaller Become larger
Fe = 117 pm Cl = 99 pm
Fe 2+ =75 pm Cl- = 181 pm
Fe 3+ = 60 pm

Electron cloud responsible for size

X-ray diffraction to determine separation between nuclei in atomic crystals

Ionization Energy and Electron Affinity

First Ionization Energy energy to remove 1 outer electron

A(g)  A+ (g) + e-
Use beam of electrons to knock off electron to form ion

Exothermic- energy given off (-), electron moves down a level

Endothermic-energy taken in (+), electron moves up a level

Put energy into atom to ionize so + sign

1eV = 1.602 x 10-19 J = 96.5 kJ/mol

Observe Ionization Energies versus Atomic Number Graph

19
http://www.iun.edu/~cpanhd/C101webnotes/modern-atomic-theory/images/ionization-energy.jpg

The general trend is one of increasing ionization energy from right to left across the
periodic table and increase from bottom to top

Reason: Up- electron from lower level (closer to nucleus)is more difficult to remove
Across- have higher positive nuclear charge and so more attraction to nulecus

For alkali metal most of positive charge is shielded

Ex showing this is Francium Atomic Model:

20
http://pittsford.monroe.edu/pittsfordmiddle/rountree/rounweb_1_02/connimage_2.jpg

Second and Third Ionization Energy require more energy

But largest jump is after valence

Na 1 valence, outer shell electron

Mg 2
Al 3

Electron Affinity

Energy to add electron

e- + F (g)  F- (g) -322 kJ/mol (gives off energy, tendency to gain)

e- + Ne (g)  Ne- (g) +21 kJ/mol (require energy, does not tend to gain e-)

Halogens have strong tendency to GAIN electrons

Otherwise there is not a clear pattern

Summary of Periodic Trends

21
(http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/08.html)

22