EM waves and Photons
Lecture 15
Review of L-14
• Waves are inverted when reflected from a hard (more dense
→ n2>n1) boundary – equivalent to a phase shift of 180°, or
λ/2, 3λ/2, 5λ/2, …
• Waves are not inverted when reflected from a soft (less dense
→ n2<n1) boundary – equivalent to no phase shift, or λ, 2λ,
3λ, …
• For circular aperture, diameter d, first destructive interference
at
λ
sin θ = 1.22
d
• Rayleigh criteria for minimum separation of objects to be
resolved
λ
λ
single-slit
y=L
d
circular aperture
y = 1.22 L
d
Is light a wave, or a particle?
• In ray optics, we can treat light as a particle
• But many features, like diffraction and interference, light acts like a wave
• In the late 1890’s and early 1900’s, experiments revealed a weakness with
the wave interpretation
– “black-body” radiation
– photoelectric effect
– discrete emission spectrum
• These were explained assuming that light was a particle
• Is light a particle or a wave?
– It’s both!
• Light comes quantized in the form of photons – a discrete amount of
radiation
• Physics of quantized particles is quantum mechanics
Blackbody radiation
• All objects with heat emit radiation
– “heat lamps”, light bulbs, etc.
• Classical theory gives the wrong answer for the spectrum from hot bodies
• Max Planck (1858-1947)
– Assumed that the atoms
giving off the radiation
had energy levels that
were quantized with
En=nhf with n integer,
and the quanta of
energy (light) had to
match the energy level
difference
– photon energy E=hf
Planck’s new formula
Object
temperature
“Classical” vs. Planck
• Classical physics – energy is continuous, i.e., can take any
value
• Planck’s hypothesis – energy is not continuous but only takes
on particular discrete values
– basic unit is h – Planck’s constant = 6.63 × 10−34 Js
– Often it is expressed as (“h bar”) = h/2π = 1.06 × 10−34 Js
= 6.62 × 10−16 eVs
where eV is the “electron volt”, a natural unit of energy for the atomic
scale
– Conversion factor for Joule to eV is
1 eV = 1.602 × 10−19 J (the conversion factor is the
absolute value of the charge of an electron)
Know this conversion!
Photoelectric effect
• Light striking certain metallic surfaces, e.g. sodium, causes
electrons to be emitted
Aspects of the photoelectric effect
1. Electrons emitted immediately
2. Increasing the light intensity increases the # of
photoelectrons, but not their max. kinetic energy
(KE)
3. Red light will not cause the ejection of
electrons, regardless of intensity
4. A weak violet light will eject only a few
electrons, but their max. KE are greater than
those for intense light of longer wavelengths
Photoelectric effect
• A. Einstein (1879-1955) explained these effects assuming
light acted like a particle, with energy E=hf (often see this as
E= ω, with ω = 2π f )
Data from light striking Na metal
ν = f on
plot
Photoelectric effect
• Photoelectron max. kinetic energy
KEe − = hf − Φ
where Φ is the “work function” (depends on the material) f
is the frequency of the light
• Φ varies with material
– Usually expressed in eV
Discrete emission spectrum
White light has a continuous
spectrum
Excited atoms
emit light at very
specific
wavelengths.
Wavelengths are
characteristic of
the element
Discrete emission spectrum
• Neils Bohr (1885-1962) pieced together several ideas
(Planck’s quantized energy levels, Einstein’s photons,
Rutherford’s nucleus, etc.) and obtained
13.6
En = − 2 eV, with n = 1,2,3,…
n
for the energy of the levels for the hydrogen atom
• The photon emission energy for hydrogen is
1
1
hf = Eni − En f = 13.6 2 − 2
n f ni
with n = 1,2,3,…, and ni > nf
eV,