The Wave Nature of Light

• All forms of NRG/Light have characteristic wavelengths (λ) and frequency (υ).– Inversely related

• λ υ = c (the speed of light)–Light visible to the naked eye exists as a

tiny portion of the electromagnetic spectrum

Electromagnetic Spectrum

Max Planck

• Transfer of energy was not continuous– Only came in certain

values (quantized)• ΔE = hν

– h = Planck’s constant = 6.626 x 10-34 Js

• Packets of energy (quantum

Albert Einstein

• Proposed that electromagnetic radiation was quantized and made up of a stream of particles– Photons

• The dual nature of light

• λ = h/mv (deBroglie equation)

Electrons as Waves

• Louis de Broglie (1924)

– Applied wave-particle theory to electrons– electrons exhibit wave properties

QUANTIZED WAVELENGTHS

Adapted from work by Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Standing Wave 200

150

100

50

0

- 50

-100

-150

-2000 50 100 150 200

Second Harmonic or First Overtone 200

150

100

50

0

- 50

-100

-150

-2000 50 100 150 200

Fundamental mode 200

150

100

50

0

- 50

-100

-150

-2000 50 100 150 200

Louis de Broglie~1924

Electrons as WavesQUANTIZED WAVELENGTHS

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Electrons as Waves

Evidence: DIFFRACTION PATTERNS

ELECTRONSVISIBLE LIGHT

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chemDavis, Frey, Sarquis, Sarquis, Modern Chemistry 2006, page 105

Spectrum

• Light is diffracted (bent) through different objects

• Hydrogen Spectra gave interesting results

Niels Bohr

• In the Bohr Model (1913) the neutrons and protons occupy a dense central region called the nucleus, and the electrons orbit the nucleus much like planets orbiting the Sun.

• They are not confined to a planar orbit like the planets are.

Bohr Model

After Rutherford’s discovery, Bohr proposed that electrons travel in definite orbits around the nucleus.

Planetary model

Bohr Cont.

• When the electrons are in their lowest possible NRG level, they are in their ground state.

• Electrons absorb NRG and go to a higher NRG level(Excited State)

• NRG (Light) is released when the electron jumps from a higher NRG level to a lower NRG level(Fluorescence)– Constantly happening

An unsatisfactory model for the hydrogen atom

According to classical physics, lightshould be emitted as the electron circles the nucleus. A loss of energywould cause the electron to be drawncloser to the nucleus and eventuallyspiral into it.

Hill, Petrucci, General Chemistry An Integrated Approach 2nd Edition, page 294

Quantum Mechanical Model

Modern atomic theory describes the electronic structure of the atom as the probability of finding electrons within certain regions of space (orbitals).

Niels Bohr &Albert Einstein

Modern View

• The atom is mostly empty space• Two regions

– Nucleus • protons and neutrons

– Electron cloud• region where you might find an electron

Quantum Mechanics

• Heisenberg Uncertainty Principle– Impossible to know both the velocity and

position of an electron at the same time

Microscope

Electron

g

Werner Heisenberg~1926

Quantum Mechanics

σ3/2 Zπ

11s 0

eΨ a

• Schrödinger Wave Equation (1926)

– finite # of solutions quantized energy levels

– defines probability of finding an electron

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Erwin Schrodinger~1926

Quantum Mechanics

• Orbital (“electron cloud”)– Region in space where there is 90% probability

of finding an electron

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Electron Probability vs. Distance

Ele

ctro

n P

roba

bilit

y (%

)

Distance from the Nucleus (pm)

100 150 200 2505000

10

20

30

40

Orbital

90% probability offinding the electron

Quantum Numbers

UPPER LEVEL

• Four Quantum Numbers:– Specify the “address” of each electron in an

atom

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Quantum Numbers

Principal Quantum Number ( n )

Angular Momentum Quantum # ( l )

Magnetic Quantum Number ( ml )

Spin Quantum Number ( ms )

Quantum Numbers

1. Principal Quantum Number ( n )

– Energy level

– Size of the orbital

– Integral values

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

1s

2s

3s

Quantum Numbers

s p d f

2. Angular Momentum Quantum # ( l )– Energy sublevel

– Shape of the orbital

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Angular Momentum Quantum # ( l )

• Has integral values from 0 to n-1– Related to the shape of the orbital

• l = 0 is called s• l = 1 is called p• l = 2 is called d• l = 3 is called f

Shapes of s, p, and d-Orbitals

Shape of f-orbitals

Quantum Numbers3. Magnetic Quantum Number ( ml )

– Orientation of orbital– Specifies the exact orbital within each sublevel– Has values between l and -l

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

Quantum Numbers

4. Spin Quantum Number ( ms )– Electron spin +½ or -½

– An orbital can hold 2 electrons that spin in opposite directions.

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem