Electromagnetic SpectrumElectromagnetic Spectrum

Light as a Wave - RecapLight as a Wave - Recap

Light exhibits several wavelike properties including

RefractionRefraction: Light bends upon passing from one substance to another)

DispersionDispersion: White light can be separated into colors.

DiffractionDiffraction: Light sources interact to give both constructive and destructive interference.

c = c = = wavelength

(m) = frequency (s-

1)cc = speed of light (3.00 108 m/s)

Blackbody Radiation & Max Blackbody Radiation & Max PlanckPlanck

The classical laws of physics do not explain the distribution of light emitted from hot objects.

Max Planck solved the problem mathematically (in 1900) by assuming that the light can

only be released in “chunks” of a discrete size (quantized like

currency or the notes on a piano). We can think of these “chunks” as particles of light

called photonsphotons.

E = hE = hE = hc/E = hc/

= wavelength (m)

= frequency (s-1)hh = Planck’s

constant (6.626 10-34 J-s)

Photoelectric EffectPhotoelectric EffectIn 1905 Albert

Einstein explained the photoelectric

effect using Planck’s idea of quantized

photons of light. He later won the Nobel Prize in physics for

this work.

Line Spectrum of HydrogenLine Spectrum of Hydrogen

In 1885 Johann Balmer, a Swiss schoolteacher noticed that the

frequencies of the four lines of the H spectrum obeyed the following

relationship:

= k [(1/2)= k [(1/2)22 – (1/n) – (1/n)22]]

Where k is a constant and n = 3, 4, 5 or 6.

n=3n=4n=5n=6

Rydberg EquationRydberg EquationWhen you look at the light given off by a H atom outside of the visible region of the spectrum, you can expand Balmer’s equation to a more general

one called the Rydberg Equation

= (cR= (cRHH)[(1/n)[(1/n11))22 – (1/n – (1/n22))22]]

1/1/ = R = RHH[(1/n[(1/n11))22 – (1/n – (1/n22))22]]

E = (hcRE = (hcRHH)[(1/n)[(1/n11))22 – (1/n – (1/n22))22]]

Where RH is the Rydberg constant (1.098 107 m-1), c is the speed of light (3.00 108 m/s), h is Planck’s constant (6.626 10-34 J-s) and n1 & n2 are positive

integers (with n2 > n1)

Bohr Model of the AtomBohr Model of the AtomIn 1914 Niels Bohr proposed that

the energy levels for the electrons in an atom are quantized

EEnn = -hcR = -hcRHH (1/n) (1/n)22

EEnn = (-2.18 = (-2.18 10 10-18-18 J)(1/n J)(1/n22))

Where n = 1, 2, 3, 4, …n=1

n=2n=3n=4

Louis DeBroglie & the Wave-Louis DeBroglie & the Wave-Particle Duality of MatterParticle Duality of Matter

While working on his PhD thesis (at the Sorbonne in

Paris) Louis DeBroglie proposed that matter could

also behave simultaneously as an particle and a

wave.

= h/mv= h/mv

= wavelength (m)

vv = velocity (m/s)hh = Planck’s

constant (6.626 10-34 J-s)This is only important for matter that has a very small

mass. In particular the electron. We will see later that in some ways electrons behave like waves.

Electron DiffractionElectron Diffraction

Transmission Electron Transmission Electron MicroscopeMicroscope

Electron Diffraction Electron Diffraction PatternPattern

Werner Heisenberg & the Werner Heisenberg & the Uncertainty PrincipleUncertainty Principle

While working as a postdoctoral

assistant with Niels Bohr, Werner Heisenberg

formulated the uncertainty principle.

x x p = h/4p = h/4xx = position uncertainty

pp = momentum uncertainty (p = mv)hh = Planck’s constant

We can never precisely know the location and

the momentum (or velocity or energy) of an object. This is only

important for very small objects.

The uncertainty principle The uncertainty principle means that we can never means that we can never simultaneously know the simultaneously know the

position (radius) and position (radius) and momentum (energy) of an momentum (energy) of an

electron, as defined in the Bohr electron, as defined in the Bohr model of the atom.model of the atom.

Schrodinger and Electron Schrodinger and Electron Wave FunctionsWave Functions

Erwin Schrodinger, an Austrian physicist,

proposed that we think of the electrons more

as waves than particles. This led to the field

called quantum mechanics.

In Schrodinger’s wave mechanics the electron is

described by a wave function, . The exact wavefunction for each electron depends upon

four variables, called quantum numbers they are

n = principle quantum numbern = principle quantum numberl = azimuthal quantum l = azimuthal quantum

numbernumbermmll = magnetic quantum = magnetic quantum

numbernumbermmss = spin quantum number = spin quantum number

s-orbital Electron Densitys-orbital Electron Density(where does the electron (where does the electron

spend it’s time)spend it’s time)

2 = Probability density

# of radial nodes = n – l – 1

Velocity is proportional to length of streak,

position is uncertain.

Position is fairly certain, but velocity is

uncertain.

Schrodinger’s quantum mechanical picture of the Schrodinger’s quantum mechanical picture of the atomatom

1. The energy levels of the electrons are well known

2. We have some idea of where the electron might be at a given moment

3. We have no information at all about the path or trajectory of the electrons

s & p orbitalss & p orbitals

d orbitalsd orbitals

# of nodal planes = l

Electrons produce a magnetic Electrons produce a magnetic field. field.

All electrons produce a All electrons produce a magnetic field of the same magnetic field of the same

magnitudemagnitudeIts polarity can either be + or Its polarity can either be + or -, like the two ends of a bar -, like the two ends of a bar

magnetmagnetThus the spin Thus the spin of an electron of an electron can only take can only take

quantized quantized values values

(m(mss=+½,-½), =+½,-½), giving rise to giving rise to

the 4th the 4th quantum quantum numbernumber

Single Electron Single Electron AtomAtom

Multi Electron Multi Electron AtomAtom