Quantum Physics

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Quantum Physics
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Objectives After completing this module, you
should be able to

• Discuss the meaning of quantum physics and
  Plancks constant for the description of matter
  in terms of waves or particles.

• Demonstrate your understanding of the
  photoelectric effect, the stopping potential, and
  the deBroglie wavelength.

• Explain and solve problems similar to those
  presented in this unit.

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Planks Constant
In his studies of black-body radiation, Maxwell
Planck discovered that electromagnetic energy is
emitted or absorbed in discrete quantities.
Apparently, light consists of tiny bundles of
energy called photons, each having a well-defined
quantum of energy.
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Energy in Electron-volts
Photon energies are so small that the energy is
better expressed in terms of the electron-volt.
One electron-volt (eV) is the energy of an
electron when accelerated through a potential
difference of one volt.
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Example 1 What is the energy of a photon of
yellow-green light (l 555 nm)?
First we find f from wave equation c fl
E 3.58 x 10-19 J
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Useful Energy Conversion
Since light is often described by its wavelength
in nanometers (nm) and its energy E is given in
eV, a conversion formula is useful. (1 nm 1 x
10-9 m)
If l is in nm, the energy in eV is found from
Verify the answer in Example 1 . . .
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The Photo-Electric Effect
When light shines on the cathode C of a
photocell, electrons are ejected from A and
attracted by the positive potential due to
battery.
There is a certain threshold energy, called the
work function W, that must be overcome before any
electrons can be emitted.
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Photo-Electric Equation
The conservation of energy demands that the
energy of the incoming light hc/l be equal to the
work function W of the surface plus the kinetic
energy ½mv2 of the emitted electrons.
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Example 2 The threshold wavelength of light for
a given surface is 600 nm. What is the kinetic
energy of emitted electrons if light of
wavelength 450 nm shines on the metal?
K 2.76 eV 2.07 eV
K 0.690 eV
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Stopping Potential
A potentiometer is used to vary to the voltage V
between the electrodes.
Kmax eVo
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Slope of a Straight Line (Review)
The general equation for a straight line is
y mx b
The x-intercept xo occurs when line crosses x
axis or when y 0.
The slope of the line is the rise over the run
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Finding Plancks Constant, h
Using the apparatus on the previous slide, we
determine the stopping potential for a number of
incident light frequencies, then plot a graph.
Note that the x-intercept fo is the threshold
frequency.
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Example 3 In an experiment to determine Plancks
constant, a plot of stopping potential versus
frequency is made. The slope of the curve is 4.13
x 10-15 V/Hz. What is Plancks constant?
h e(slope) (1.6 x 10-19C)(4.13 x 10-15 V/Hz)
Experimental Plancks h 6.61 x 10-34 J/Hz
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Example 4 The threshold frequency for a given
surface is 1.09 x 1015 Hz. What is the stopping
potential for incident light whose photon energy
is 8.48 x 10-19 J?
Photoelectric Equation
W (6.63 x 10-34 Js)(1.09 x 1015 Hz) 7.20 x
10-19 J
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Total Relativistic Energy
Recall that the formula for the relativistic
total energy was given by
For a particle with zero momentum p 0
E moc2
A light photon has mo 0, but it does have
momentum p
E pc
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Waves and Particles
We know that light behaves as both a wave and a
particle. The rest mass of a photon is zero, and
its wavelength can be found from momentum.
All objects, not just EM waves, have wavelengths
which can be found from their momentum
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Finding Momentum from K.E.
In working with particles of momentum p mv, it
is often necessary to find the momentum from the
given kinetic energy K. Recall the formulas
K ½mv2 p mv
Multiply first Equation by m
mK ½m2v2 ½p2
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Example 5 What is the de Broglie wavelength of a
90-eV electron? (me 9.1 x 10-31 kg.)
Next, we find momentum from the kinetic energy
p 5.12 x 10-24 kg m/s
l 0.122 nm
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Summary
Apparently, light consists of tiny bundles of
energy called photons, each having a well-defined
quantum of energy.
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Summary (Cont.)
If l is in nm, the energy in eV is found from
Wavelength in nm Energy in eV
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Summary (Cont.)
Plancks Experiment
Incident light
Cathode
Anode
A
V

-
Potentiometer
Kmax eVo
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Summary (Cont.)
Quantum physics works for waves or particles
For a particle with zero momentum p 0
E moc2
A light photon has mo 0, but it does have
momentum p
E pc
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CONCLUSION Chapter 38BQuantum Physics