De Broglie Berg Schrodinger Quantum Model

Quantum Mechanical Model of the Atom DeBroglie’s hypothesis, Heisenberg’s Uncertainty Principle, Schrödinger’s Wave Equations, Quantum Numbers

Warm Up! Two naturally occurring isotopes of gallium are: 69 Ga & 71Ga What is the percent abundance of each isotope?

Louis de Broglie (1892 – 1987) • Light was found to have properties of matter, but is the opposite true? Does matter have wave properties? • In 1923 Louis de Broglie sought an answer to this question. • For a particle with velocity v (not nu! It’s really a lower case v), it’s mass is equal to h/λ v. • Rearranging, we have λ =h/mv where mv is mass times velocity which is equal to momentum. This allows us to calculate the wavelength of a particle in motion.

de Broglie Waves

OK

OK

NOT OK

Louis de Broglie (1892 – 1987) Compare the wavelength for an electron (mass = 9.11 x 10-31 kg) traveling at a speed of 1.0 x 107 m/s with that for a ball (mass = 0.10 kg) traveling at 35 m/s.

Heisenberg Uncertainty Principle • It is impossible to know exactly the position and momentum (mass times velocity) of a particle. • The better we know one, the less certain we can know the other. • The act of measuring changes the properties.

More obvious with the very small • To measure where a electron is, we use light. • But the light moves the electron • And hitting the electron changes the frequency of the light.

Before Photon

Moving Electron

After Photon changes wavelength

Electron Changes velocity

Schrödinger's Wave Function

• In 1926, Erwin Schrödinger used the hypothesis that electrons have a dual wave-particle nature to create a wave function just gives you a formula for finding an electron in space • The function is given the symbol, ψ (psi). • More interesting to us is ψ 2 a probability function for where the electron is most likely to be. • These probabilities give us orbitals, which are probability fields of where an electron might be located.

Quantum Mechanical Orbitals According to Schrodinger, electrons are not constrained to specific pathways around a nucleus. There are mathematical equations to predict where an electron is likely to be The three dimensional representations of this probability are called orbitals

Orbital Shapes

The s orbital is spherical

The p orbitals are shaped like peanuts.

Four d orbitals are shaped like double dumbbells One d orbital is a dumbbell with a hoola hoop

F - Orbitals

Quantum Numbers symbol

name

formula

values

n

principle QN

integers > 0

1, 2, 3, 4…

l

angular momentum QN

0 – (n-1)

0, 1, 2…n-1

m (m ℓ)

magnetic QN

- ℓ – +ℓ

- ℓ,…-1, 0, 1, … ℓ

s (ms)

spin QN

±½

+½, -½

2

n

1

ℓ

0

0

m

0

0

-1

0

1

1s

2s

2px

2py

2pz

orbital

s

½

-½

1s has 2e

½

1

-½ ½

2s has 2e

-½ ½

-½ ½

2p has 6e

-½

Sublevels The number of the principle quantum number is the number of sublevels it has n=1 has one sublevel  1s n=2 has two sublevels  2s and 2p n=3 has three sublevels  3s, 3p, and 3d

Relative Energies

3d 4s

Increasing Energy

3p 3s 2p 2s 1s

Electron Configurations Aufbau Principle: Electrons go to the lowest energy orbital first. Pauli Exclusion Principle: Every orbital can hold two electrons if they have opposite spin. Hund’s Rule: Electrons would rather be alone if another equal energy orbital is available.

Orbital Diagram for Nitrogen 1s

2s

2p

N Nitrogen has 7 electrons. Following the aufbau principle we start with the lowest energy. Pauli says to fit two electrons, they must have opposite spins. Hund says put one e- in each orbital, they wont double up unless they have to.

Orbital Diagram Practice 1s 2s

2p

3s

Electron Configuration

Li

1s2 2s1

C

1s2 2s2 2p2

O

1s2 2s2 2p4

F

1s2 2s2 2p5

Ne

1s2 2s2 2p6

Na

1s2 2s2 2p6 3s1

Practice What are the orbital diagrams and electron configurations of the following atoms? 1s 2s 2p 3s 3p 4s 3d Cl Ca Cr Sn Cl 1s2 2s2 2p6 3s2 3p5 Ca 1s2 2s2 2p6 3s2 3p6 4s2 Cr 1s2 2s2 2p6 3s2 3p6 4s2 3d4 Sn 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p2

Practice Orbital diagrams and electron configurations for ions are just the same, but the appropriate number of electrons have been added or removed.

1s 2s S S2Co Co2+

2p

3s

3p

4s

3d

Orbital Blocks s 1

d

2

(n= row -1)

p

3 4 5 6

Mg [Ne] 3s2 row

electron block

Electron configuration – short hand • Write the electron configuration for each of these elements

Electron configuration Cl 1s2 2s2 2p6 3s2 3p5 Cl- 1s2 2s2 2p6 3s2 3p6 Cr 1s2 2s2 2p6 3s2 3p64s1 3d5 Ru2+

1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s0 4d6

Sn

1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s2 4d10 5p2

Leave this column blank

How do you remember the order? • Follow the order of elements on the PT

Electron configuration P

1s2 2s2 2p6 3s2 3p4

O2-

1s2 2s2 2p6 3s2 3p6

Ni

1s2 2s2 2p6 3s2 3p64s2 3d4

Ru

1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s2 4d6

Tl

1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s2 4d10 5p2

Vocabulary Core electron: an electron in an inner shell (orbital), not used in the chemistry of the atom Valence electron: an electron in the outermost shell (orbital), added since the last noble gas, important in chemistry. Core electrons  [Ar]

Valence electrons

V 1s2 2s2 2p6 3s2 3p6 4s2 3d3 V [Ar] 4s2 3d3

Electron configuration – shorter hand • Write the noble gas configuration

Electron configuration Cl 1s2 2s2 2p6 3s2 3p5 Cl- 1s2 2s2 2p6 3s2 3p6 Cr 1s2 2s2 2p6 3s2 3p64s1 3d5 Ru2+

1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s0 4d6

Sn

1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s2 4d10 5p2

Noble gas configuration [Ne] 3s2 3p5 [Ne] 3s2 3p6 [Ar] 4s1 3d5 [Kr] 5s0 4d6 [Kr] 5s2 4d10 5p2