Dual Nature of Light

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Dual Nature of Light
Is light a wave or a particle?
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Wave Properties
-Polarization -Diffraction -Interference
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Photoelectric Effect light/EM waves are
particles of energy called photons.
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Max Planck worked on how emitted light is related
to temperature. Energy of a vibrating molecule
is quantized--it could only take on certain
values. Molecular energy is proportional to the
frequency Energy come in little "chunks" of the
frequency multiplied by a constant now called
Planck's constant, h
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Matter absorbs emits energy in discrete units
called quanta or photons. Planks formula gives
the amount of energy based on the frequency of
waves.

• E hf.
• h is Planks constant 6.63 x 10-34 Js.
• E is energy in Joules
• f is frequency of radiation

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Ex 1. Each photon of green light has an energy of
2.5 eV. What is the frequency of green light?
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SolutionE hf f E/h convert eV to
Joules.(2.5 eV)(1.6 x 10-19J/eV) 6 x 1014 s-1
or Hz 6.626 x 10-34 J s
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Photoelectric EffectLight as Packets of Energy
When light shines on a metal surface, the surface
can emit e-. Current can start a circuit just by
shining a light on a metal. Materials that emit
e- in this way are called photoemissive. The
ejected e- are called photoelectrons.
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Light is a type of EM wave, and the waves carry
energy. If a wave of light hits an e- in an atoms
of the metal, it can transfer enough energy to
knock the electron out of its atom.
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The details of the photoelectric effect come out
differently depending on whether light consists
of particles or waves. If it's waves, the
energy contained a wave should depend on its
amplitude--on the intensity/brightness of the
light.
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Frequency, f, should make no difference. Red
light and UV light of the same intensity should
knock out the same number of electrons, and the
KE of both sets of electrons should be the same.
If the light is too faint, you shouldn't get any
electrons at all.
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Einstein realized that EM radiation is delivered
energy in chunks, or quanta, he called photons,
each photon had an energy according to Planck's (
E hf). Higher-frequency waves/photons have
more energy, so they make the e- come flying out
faster with greater KE.
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Increasing the intensity/amplitude, increases the
rate of e- emission or the current the number of
e- ejected, not the KE of ejected e-. Only
increased f increases KE of photoelectrons.If
the frequency is too low, none of the photons
will have enough energy to knock an electron out
of an atom.
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For each metal, there is a threshold fo
frequency. Light frequencies below the
threshold eject no electrons, no matter how
intense or bright the light.
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Light frequencies above the threshold eject
electrons, no matter how low the intensity or how
dim.
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Graph of max KE of e- vs. frequency for
photo-emissive material. As f increases, KE
increases, slope h. Wo work function, is
minimum E (Joules) needed to eject e-.
Work function
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The threshold frequency fo, is the minimum
frequency needed to eject e- so the minimum
energy, the work function in J is Wo hfo.
Any energy left over after the work function,
goes into KE of e-.
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The maximum KE of ejected e- is the photon energy
hf - the work functionKEelc hf Wo.
h is Planks constant Wo. is the work
function KEe- hf hfo. orThe total
energy of photoelectrons isEtot Wo KE.
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Einstein actually won the Nobel Prize for his
work on the photoelectric effect, not for his
more famous theory of relativity.
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Some experimental results, like this one, seem to
prove that light consists of particles others
insist, that it's waves. We can only conclude
that light is somehow both a wave and a
particle--or that it's something else we can't
quite visualize, which appears to us as one or
the other depending on how we look at it.
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All EM waves have energy Ephoton
hf or Ephoton hc/l. (for photon traveling at
speed of light).This is also the same energy
absorbed by photo-emissive materials.
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Ex 2 Photoelectric EffectLight having f 1
x 1015 hz shines on a sodium surface. The
photoelectrons have a maximum KE of 1.86
eV.Find the threshold frequency for sodium.
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KE total photon energy - work function Wo is
the minimum energy needed to eject e-. Wo hfo
where fo is the threshold frequency. KEmax hf
hfo Since we want to find fo, then
rearrangefo (hfphoton KEmax)/(h)
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change eV to Joules (1.78 eV) (1.6 x 10-19
J/eV) 2.85 x 10-19 J fo (hfphoton
KEmax)/(h) (6.63 x 10-34 Js)(1 x 1015 hz) -
(2.85 x 10-19 J) (6.63 x 10-34 Js) fo 5.7
x 1014 Hz. Below this frequency no electrons
will be ejected.
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Hwk read text pg 830 836 do pg 833 2-4 and
pg 836 1-2. Text856 2, 4, 5, 6, 7, 9, 10,
11, 14, 15, 16, 18.
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Equivalence of Mass Energy
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Einstein realized that matter contains energy.
There is an equivalence of mass energy.Energy
is stored in the nucleus of atoms.The energy
stored any mass obeys Einsteins equation E
energy in J.E mc2. m mass kg c vel
of light
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Ex 3 How much energy is produced when 2.5 kg of
matter are completely converted to energy?How
much energy is that in eV?
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E mc2.(2.5 kg )(3x108 m/s)2. 2.25 x 1017
Jin eV(2.25 x 1017 J)(1 eV / 1.6 x 10 19 J)
1.4 x 1036 eV.
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Atomic Mass Units amu or u

• Mass of atoms very small so they are measured in
  amu or u.
• Since mass is equivalent to energy,
• 1 amu 931 MeV or 931 x 106 eV.

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Ex 4 One universal atomic mass unit is
equivalent to an energy of 931 MeV. Calculate the
mass in kg of one universal mass unit.Hint Use
E mc2 where energy is known in eV.
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Dont forget to convert MeV to eV.(1 u) x (931
MeV/u) x (106eV/MeV) x (1.6 x 10 19 J / eV)
1.49 x 1010 J E mc2 so m
E/c2.(1.49 x 1010 J) / (3x108 m/s)2 1.66
x 10 27 kg
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Particle Properties of Waves extend to
conservation of energy and momentum.

• Photons may give up all or part of their energy
  in collisions, but the sum of the momentums and
  energy before must equal the sum after.

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Hwk Rev book pg 26 5, 17 26, 34 - 35
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Compton Effect
If light behaves like a particle, then a
collision btw photon e- should be similar to
billiard balls colliding. Photons must have
momentum (p), energy. In collision of photons
with particles (like e-), conservation of energy
conservation of momentum apply.
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If the photon gives only part of its energy
momentum to an e-, its momentum decreases after
the collision by the same amount as absorbed by
the electron. Therefore, the frequency or
energy of the photon decreases. The wavelength
increases. pbefore pafter.E photon before
KEelc after. E photon afterhfi KEelc
after hff photon after
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pphoton hf/c h/l. The wavelength of
the photon increases after collision.
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Matter has wave-like properties.1924 Louis
DeBroglie suggested that since waves had particle
properties, matter might have wave
properties.It turns out that matter does have
wave properties which are inversely related to
the momentum of the particle.
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For matter l h/p or l h/mv. Since
the mass of most objects is so large, the
wavelengths would be very small not
measurable.Electrons, however, do show
diffraction other wave characteristics.