visible light just a very small portion of the spectrum of
TRANSCRIPT
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!
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)
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 )
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)