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Physics 30 – Electromagnetic Radiation – Part 2
Wave-Particle Duality
To accompany Pearson Physics
PowerPoint Presentation by R. Schultz
[email protected]
Wave-Particle Duality
2 “clouds” in physics at the beginning of the
20th century:
Weird relationship between temperature of
a material and the colour of light given off
Why the speed of light was unaffected by
Earth’s motion through space
14.1 The Birth of the Quantum
• a glowing hot object will emit
increasingly bluer light as it
temperature increases
• at “relatively” low
temperatures it will be red hot,
then yellow hot, and finally
white hot
actual behaviour
14.1 The Birth of the Quantum
• classical physics could only predict that intensity
would increase as frequency increased; it could
not make a prediction about any relationship
between temperature and frequency
classical physics
prediction
• Also the relationship between f and intensity
was weird – no red hot, yellow hot, white hot;
primarily ultra high frequency radiation, uv and
beyond!
14.1 The Birth of the Quantum
• Planck, 1900, able to explain actual
behaviour by saying that matter could
radiate (and absorb) only certain amounts
of energy (quanta):
E  nh f
1 quantum
where f is the lowest frequency possible
for that substance, h is Planck’s constant,
and n is a whole number, 1, 2, 3 …….
14.1 The Birth of the Quantum
• Quantization explained true behaviour
exactly, but even Planck didn’t accept it
• Too radical – like saying a pendulum
couldn’t swing starting at any level, only
certain allowed ones
• Quanta of light were later called photons
14.1 The Birth of the Quantum
• Examples:
SNAP, page 232
question 3
E  h f  6.63  10 34 J s  4.74  1014 Hz  3.14  10 19 J
question 5
E  hf  h
c

1.50 eV  1.60  10 19 J eV  6.63  10 34 J s 
3.00  10 8 m s
  8.29  10 7 m  829 nm
Do questions 4 and 6, page 232, SNAP

14.1 The Birth of the Quantum
• One key realization is that the higher the
frequency or shorter the wavelength of a
photon, the more energy it has
14.2 The Photoelectric Effect
• Demo with electroscope and (-) charge
• Introduction to the photoelectric effect
incoming “light”
e-
A
-
very low
+ voltage ……
14.2 The Photoelectric Effect
• Observations: when “light” of a certain
minimum frequency (threshold frequency, fo) or
higher was shone on cathode of tube, there was
an immediate photoelectric current
• Above fo, increasing intensity of light increases
photoelectric current
• Below fo, no current no matter how high
intensity of “light” or how long the light is shone
14.2 The Photoelectric Effect
• Measuring maximum kinetic energy of the
photoelectrons:
incoming “light”
eV
A
+
-
voltage
increased until
current drops
to 0
voltage direction reversed
14.2 The Photoelectric Effect
• If Vstop is the voltage required to stop the
photoelectric current, then
Ek max  qVstop
• Observations:
• Beyond fo, Ek max  f
Electrons have a range of
Ek, those from near the
surface of the metal have
the most
• “Light” intensity has no effect on Ek max
14.2 The Photoelectric Effect
• Einstein’s explanation (1905):
photons of light with energy E=hf, are spread
along wavefronts of light approaching surface
release of an electron is result of a single
collision of 1 photon with 1 electron
minimum photon energy for release of an
electron is W, the work function, and
W  h fo
14.2 The Photoelectric Effect
• Einstein’s complete equation: Ek max  hf  W
qVstop  hf  W
• This is a great equation for graphical analysis
If given a table of f and Ek max or f and Vstop
Ek max
Vstop
W
h

m= ;b=
q
q
x-int = fo
m = h; b = -W
x-int = fo
f
14.2 The Photoelectric Effect
• Millikan, in 1916, verified Einstein’s equation
• Examples, SNAP, page 241
• Question 3
E k max  hf  W  h
c

W
3.00  10 8 m s
 4.14  10 eV s 
 1.70 eV
7
5.30  10 m
 0.643 eV 1.60  10 19 J eV  1.03  10 19 J
15
or
14.2 The Photoelectric Effect
W  1.70 eV 1.60  10 19 J eV  2.72  10 19 J
Ek max  h
c

W
3.00  108 m s
19
 6.63  10 J s 

2.72

10
J
7
5.30  10 m
 1.03  10 19 J
34
• The first method is better when an answer in eV
is required
14.2 The Photoelectric Effect
• Question 6
λmax → minimum f = fo
W  h fo
fo 
max
3.10 eV
W
14


7.49

10
Hz
15
h 4.14  10 eV s
3.00  108 m s
c
7



4.01

10
m  401 nm
14
fo 7.49  10 Hz
14.2 The Photoelectric Effect
• Question 15
• Shortest wavelength radiation will produce
maximum kinetic energy of electrons
Ek max  hf  W  h
Ek max
c

W
8m
3.00

10
s
19 J
 6.63  10 34 J s 

2.30
eV

1.60

10
eV
4.0  10 7 m
 1.3  10 19 J
• Do SNAP, page 241, questions 4, 7, 8, 10, 11, 16,
19
14.3 The Photoelectric Effect
• Photoelectric Effect Applet experiment
14.3 The Compton Effect
• Compton observed a change in momentum (a
particle property) when X-rays scattered off
electrons
• According to Einstein
E  mc
2
E
m  2
c
• In classical physics
p  mv
substitute Einstein's mass equivalence into the expression
E
E
E
p  2  v , but for EMR v  c,  p  2  c 
c
c
c
14.3 The Compton Effect
• For EMR:
hf
E
h
p
or p 
or p 
c
c

• Change in λ for a scattered photon is given by
h
   f   i 
1  cos 
mc
where θ is the scattering angle and m is the
mass of the electron it scatters off of
14.3 The Compton Effect
• Examples: SNAP, page 252
• Question 3
p
h


h 6.63  1034 J s
10
 

8.5

10
m  0.85 nm
25 kg m
p 7.8  10
s
• Question 7 Read this question carefully – it’s an
electron, not a photon
p  mv  9.11 10 31kg  0.110  3.00  108 m s  3.01 10 23 kg m s
14.3 The Compton Effect
• Example: Practice Problem 1, page 724
 f  i 
h
1  cos 
mc
6.63  10 34 J s
 f  1.0  10 m 
1  cos 90 
31
8 m 
9.11 10 kg  3.00  10 s
11
 f  1.2  10 11m  0.012 nm
• There are no SNAP problems using this
formula, but it is on the Formula Sheet
14.3 The Compton Effect
• Do questions 1, 4, 6, 10, 11 from SNAP, page 252
• Question 11 is easier than it looks!
14.4 Matter Waves and the Power of Symmetric
Thinking
• De Broglie, 1924, if light can sometimes behave
as a particle (photoelectric effect, black-body
radiation, Compton effect) why couldn’t
classical particles, like electrons, sometimes
behave as waves??
• Compton:
• De Broglie:
p
h

for light
h
h
 
p mv
for particles
14.4 Matter Waves and the Power of Symmetric
Thinking
• Read and discuss Then, Now, and Future, page
727
• Examples: Practice Problem 1 (2nd set), page 728
6.63  10 34 J s
h
12



4.0

10
m
27
5m
mv 1.67  10 kg 1.0  10 s
14.4 Matter Waves and the Power of Symmetric
Thinking
• Evidence for the wave behaviour of electrons:
Davisson and Germer
G.P. Thomson
Electron scattering producing
interference patterns
• De Broglie’s concept of electron waves explains
why electron energy in an atom is quantized
• The particle in a box analogy on pages 731-3 is
interesting reading (you won’t be tested on this)
14.4 Matter Waves and the Power of Symmetric
Thinking
• The Heisenberg Uncertainty Principle
h
x p 
4
• Δ x = uncertainty in position
• Δ p = uncertainty in momentum
• You can never know with certainty where a
particle is and what it’s doing at the same time
h
• 4 is very tiny, so this doesn’t affect us
macroscopically
14.4 Matter Waves and the Power of Symmetric
Thinking
• Check and Reflect, page 736, questions 1, 2, 5,
6
• Discuss question 3
14.5 Coming to Terms
• Read pages 737 - 740
14.4 Matter Waves and the Power of Symmetric
Thinking