Visible light just a very small portion of the spectrum of electromagnetic radiation.

Electromagnetic radiation has an electric field component and a

magnetic field component.

c = λ∙νc = 2.998 x 108 m/s (speed of light in a vacuum)λ = wavelength (m)ν = frequency (s-1, or Hz)

Properties of Waves

MEMORIZE!

Waves have wavelength, frequency, and amplitude.

The double-slit experiment shows light acting as a wave.

h = 6.626 x 10-34 J∙s

The UV is a catastrophe!While trying to explain black-body radiation Max Planck hypothesized that energy can be gained or lost only in whole number multiples of hν. That is:

ΔE = nhνn = 1, 2, 3, ...

ν = the frequency of the electromagnetic radiation absorbed or emitted.

Einstein's analysis of the photelectric effect led him to conclude that light

could also act as a particle!

The law of conservation of energy strikes again.

Einstein: Ephoton = hν = hc/λ

KEelectron = ½ mv2 = Ephoton - W

W = work function (depends on the metal) = hν0

ν0 is called the threshold frequency

MEMORIZE!

Einstein also figured out that

E = mc2

m = E/c2

E = hc\λ

m = h/λc

The photon behaves as if it has (relativistic) mass!

Ex.// How fast does an electron travel that is ejected from a piece of tungsten when a photon with wavelength 212 nm hits the metal in a vacuum?

The rest mass of an electron is 9.109x10−31 kg

WW = 8.38 x 10−19 J

de Broglie: If waves (light) can acts like particles (photons), then maybe particles (electrons) can act like waves.

Wave-Particle Duality

2πr = nλr = nλ2πr = nλr = nλ

Einstein's famous equation led de Broglie to his conclusion.

m=hλ c

Einstein said, for a photon:

de Broglie said, for any particle:

m=hλ v

or

λ=hmv

Calculate the de Broglie wavelength, in angstroms, of a helium atom (m = 6.647 x 10─27 kg) that is traveling at 3,141 m/s.

(The atomic radius of the helium atom is about 0.32 Å)

The appearance of line spectrum was a mystery.

Johann Balmer discovered the Rydberg equation.

λ = wavelength of a line in the spectrumR∞= 1.097 x 107 m—1

n2 > n1 ; both are positive integers

1λ

=R∞ (1n12 −

1n22 )

Balmer's result was empirical, Bohr came up with a theory.

Bohr's theory led to an equation

Δ E=−2.178×10−18 J (Z2 ) (1n f2 −

1n i2 )

Z = the # of protons in the nucleus

MEMORIZE!

This equation works for hydrogen like atoms (atoms or ions with only one electron)

What is the wavelength, in nm, of a photon that is absorbed which causes an electron in a hydrogen atom to go from n = 2 to n = 5?

Δ E=−2.178×10−18 J (Z2 ) (1n f2 −

1n i2 )

Ephoton

= -ΔEelectron

Ephoton

= hc/λ