Electronic Structure of Atoms6.4 The Wave Behavior of Matter

6.5 Quantum Mechanics and Atomic Orbitals

6.6 Representation of Orbitals

Bohr Model •Each energy level can contain more than 1 electron But the max # for each level is different•Electrons fill in energy levels starting from lowest energy level to the next higher energy level•REMEMBER # Protons = # Electrons in a neutral atom•Example = oxygen

6.4 The Wave Behavior of Matter

Louis de Broglie (1892-1987) •proposed if radiant energy (under appropriate conditions) could behave as a stream of particles and exhibit properties of wave could electrons orbiting nucleus behave as a wave

λ= h / mv h = Planck’s constant 6.626 x 10-34 J/s

m = mass v = velocity mv = momentum

PRACTICE: What is the wavelength of an electron moving with a speed of 5.97 x 106 m/s? mass of e- =9.11 x 10-31 kg. 1 J =1 kg m2/s2

Practicede Broglie’s hypo applicable to all matter any object of mass and velocity would have characteristics of a wave

•Q. Calculate the velocity of a neutron whose de Broglie wavelength is 500 pm. mass of neutron= 1.67 x 10-27 kg

λ= h / mv rearrange equationh = Planck’s constant 6.626 x 10-34 J/s m = mass v = velocity

6.626 x 10-34 kg m2/s2/s

(5x10-10m)(1.67 x 10-27 kg)

= 794 m/s or 7.92 x 102 m/s

Wave properties of e- demonstrated

experimentally…Electron diffraction

•as electrons are passed though a crystal they are diffracted

•stream of electrons exhibits similar kind of wave behavior as EM radiation•ex: technique used in electron microscope to obtain images at atomic scale (3,000,000 x magnification)

The Uncertainty PrincipleIf an e- exhibits wave properties, can we

calculate the position, direction of motion, and speed at any time???

Werner Heisenberg (1901- 1976) Uncertainty Principle Impossible to know both the exact momentum and exact location of an electron simultaneously

RESULT

De Broglie’s hypo and Heisenberg’s Uncertainty Principle set stage for new approach to atomic structure model

that describes energy of e- while describing probabilities of location

6.5 Quantum Mechanics and Atomic Orbitals

Erwin Schrodinger (1887-1961)•Austrian physicist •proposed wave equation incorporates wave and particle behavior of e- = quantum mechanics or wave mechanics Solving equation lead to Wave functions- def. mathematical description of an allowed energy state (an orbital) for an e- ex: Ψ Greek letter psiΨ2 provides info about e- location when in allowed energy state = probability density or electron density

Orbitals• Def. wave function; space where there is a

high probability that it is occupied by a pair of electrons; each orbital has a characteristic energy and shape

Quantum Numbers1. Principal Quantum

Number(n)• Indicates main energy levels n = 1, 2, 3, 4…

• as n increases = orbital becomes larger e spend more time farther from nucleus

• as n increases = e- has higher energy and bound less tightly to nucleus

• n determines the number of sublevels within the principle energy level

2. Angular Momentum Quantum Number (l)

• l = n – 1

• shape of orbital Each main energy level has sub-levels= s, p, d, f

3. Magnetic Quantum Number (ml)• describes

orientation of orbital in space

• # of orbitals• equal to –l to +l

ex: l = 3; then ml = -3,-2,-1,0,1,2,3

• Electron shell: all orbitals that have the same value of n

• Subshell: set of orbitals that all have the same n and l values

• Ground State: when electrons occupy lowest energy orbital

• Excited State: when electron occupies any other orbital; e- can be excited to higher-energy orbital by absorption of a photon of appropriate energy

Sample Exercise

• Predict the number of subshells in the fourth shell?

• 4• Give the label for each of these subshells• 4s, 4p, 4d, 4f• How many orbitals are in each of theses

subshells?

• 4s=1 (l=0 ml=0) 4p=3 (l=1 ml=-1,0,1)

• 4d=5 (l=2 ml=-2,-1,0,1,2) 4f =7

6.6 Representation of OrbitalsS orbital: spherical, 1 subshell

Radial Probability Density probability of finding an e- at specific distance from nucleusnode: intermediate point where probability goes to 0as n increases =size of orbital increases = increase in distance from nucleus

p Orbital• dumbbell shaped, 2 lobes

• ml = 3 possible values, -1,0,1

• p size increases as move from 2p to 3p etc

d and f Orbitalsd= four leaf clover shape orbitals

•five 3d orbitals, five 4d orbitals etc

•ml= -2,-1,0,1,2

f= complicated shape

•seven 4d orbitals, 5d

•ml = -3,-2,-1,0,1,2,3

Electron Spin

• e- behave as tiny sphere spinning on own axis

4. Spin Magnetic Quantum Number (ms) s = spin

+1/2 (clockwise) or -1/2 (counterclockwise)

Electron Configuration

• The arrangement of electrons in an atom around nucleus

• Ex: Hydrogen = 1s1

• Ex: Helium = 1s2

Orbitals in SublevelsSublevel # Orbitals # electrons

s 1 2

p 3 6

d 5 10

f 7 14

Standard Notation

of Fluorine

Main Energy

Level

Numbers

1, 2, 2Sublevels

Number of electrons in the sub level 2,2,5

1s2 2s2 2p5

Three rules are used to build the electron configuration:– Aufbau principle

– Pauli Exclusion Principle

– Hund’s Rule

Aufbau Principle• Electrons occupy orbitals of lower

energy first.

Pauli Exclusion Principle• no 2 e- in an atom can have the same 4 QN

• An orbital can hold only two electrons and they must have opposite spin.

Hund’s RuleIn a set of orbitals, the

electrons will fill the orbitals in a way that would give the maximum number of parallel spins (maximum number of unpaired electrons).

Analogy: Students could fill each seat of a school bus, one person at a time, before doubling up.

Orbital Diagram (Box Diagram)

• Diagram in which orbitals are represented by boxes grouped by sublevels with arrows indicating electrons

Aufbau Diagram for Hydrogen

Aufbau Diagram

for Helium

Aufbau Diagram

for Lithium

Aufbau Diagram

for Beryllium

Aufbau Diagram for Boron

Aufbau Diagram

for Carbon

Aufbau Diagram

for Nitrogen

Aufbau Diagram

Aufbau Diagram

for Fluorine

Shorthand Notation

• Use the last noble gas that is located in the periodic table right before the element.

• Write the symbol of the noble gas in brackets.

• Write the remaining configuration after the brackets.

• Ex: Fluorine: [He] 2s2 2p5

Blocks in the Periodic Table

HOMEWORK • Complete WS