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CHAPTER 13
QUANTUM THEORY
Problems with Planetary Atomic Model
The electron, in orbiting the nucleus, undergoes an acceleration and should therefore continuously emit electromagnetic radiation
The predictions are completely wrong!!!
The successful model which came out of these attempts is now called the Bohr model and will be discussed in more detail later on
Photoelectric Effect
When light shines on a metal surface, the surface emits electrons.
For example, you can measure a current in a circuit just by shining a light on a metal plate
The current flow varies with the wavelength of light such that there was a sharp cutoff and no current flow for long wavelengths.
The photocurrent increases when the light intensity increases but the wavelength is held constant.
Einstein successful explained the photoelectric effect within the context of quantum physics.
Einstein proposed that light delivers its energy in chunks; light consists of little particles, or quanta, called photons, each with an energy of Planck's constant times its frequency.
E = h f
h: Planck’s constantF: Frequency of RadiationE: Energy
h = 6.6 x 10-34 J.s.
Each photon carries a specific energy related to its wavelength, such that photons of short wavelength (blue light) carry more energy than long wavelength (red light) photons
Photons when they impact a metal, if their frequency is large enough, can liberate an electron by overcoming the work function of the metal
Light made of two colors (two frequencies) shines on a metal surface whose photoelectric threshold frequency is 6.2 x 1014 Hz. The two frequencies are 5 x 1014 Hz (orange) 7 x 1014 Hz (violet).
(1) Find the energies of the orange and violet photons.
(2) Find the amount of energy a photon needs to knock electrons out of this surface.
(3) Do either the orange photons or the violet photons have this much energy?
1. The energy for the orange frequency is:E = hf = (6.6 x 10-34) x (5 x 1014) E = 3.3 x 10-19 J.
The energy for the violet light is:E = hf = (6.6 x 10-34) x (7 x 1014)E = 4.6 x 10-19 J.
2. The threshold energy isE = hf = (6.6 x 10-34) x (6.2 x 1014)
= 4.1 x 10-19 J.
3. The blue photons have sufficient energy to knock electrons out, but the orange photons do not.
The human eye can detect as few as 10,000 photons per second entering the pupil. About how much energy is this, per second?(Make an estimate)
10,000 = 104
The energy of 10,000 visible photons is:
(104) (hf) = 104 x (6.6 x 10-34 J-s) x (1015 Hz)
= 6.6 x 10-15 joules.
Solution
http://www.colorado.edu/physics/2000/applets/twoslitsa.html
Newtonian Physics
Regular old classical physics
When things get small
Quantum physics
When things get fast Special relativity
Quantum field theory
Small & fast
Classical Physics: Newtonian Physics
Modern Physics: Relativity, quantum physics, and any other field that employs these theories.
Quantum Physics: the “quantum” comes from quantization: we need to understand the origin of this.
The Photoelectric Effect
metal
light
Electron detector
electrons
metal
light
Electron detector
electrons
Actual Experimental Observations:
[1] There is no delay between the light hitting the surface and the electrons being ejected
[2] Electrons are ejected only if the incident light has a frequency above some threshold value (i.e., it depend on the color of the light!!)
frequency
# of electrons ejected
Red orange yellow green blue indigo violet ultraviolet
Threshold frequency
No emitted electrons
Many emitted electrons
Vibrating particle
Energy
Before Planck: the particle could have any energy
Vibrating particle
Energy
After Planck: the particle could have only specific, quantized energies
Vibrating particle
Energy
Same diagram as last slide except “blown up” to see the spacing better.
This means that if a particle is in some energy state, if it is to give up energy in the form of light, it has to give up a definite amount
E1
E2
Light with energy equal to E1-E2!!
Einstein argued that the emission of the light must occur in instantaneous bursts of radiation.
He then took this one step further: he said that all light had the following properties:
[1] All radiation occurs as tiny bundles (particles).
[2] The bundles always move a lightspeed (c).
[3] They have zero rest-mass.
[4] The energy of a photon is given by E = hf
h = Planck’s constant = 6.6 x 10-34 J x s
frequency
# of electrons ejected
Red orange yellow green blue indigo violet ultraviolet
Threshold frequency
No emitted electrons
Many emitted electrons
0
How do we explain why there is a threshold frequency?
The electron must get this much energy (E = hf) from the photon.
This energy is different for all metals and is called the work function of the metal.
Radiation: waves or particles?Radiation: waves or particles?
Radiation is made up of particles called photonsEvidence of the wave nature from interference
Essentially, wave/particle duality employs the notion that an entity simultaneously possesses localized (particle) and distributed (wave) properties.
Close inspection shows that an interference pattern is formed by individual photons hitting all over a screen!!!
Interference light were made up of waves. Pattern "speckled“ individual particle impacts
What is Light?
Is it a WAVE? Remember the interference pattern with the laser going through two apertures?
It definitely BEHAVES like a wave!
Is it a PARTICLE?Photoelectric effect: It BEHAVES like a particle.
So which one is it? Does it behave like a wave or a particle?!!
So which one is it? Does it behave like a wave or a particle?!!
Answer: It behaves like BOTH! We call this the wave-particle duality of radiation (light).
What is the universe made of? Matter and radiation (as far as we know anyway).
How do matter and radiation interact with each other??
Examples:
Reflection
Refraction
Absorption
Photoelectric effect
Burning/melting (lasers) …
Electrons
Interference: Wave-like behavior!!
De Broglie, a Ph.D. student at the University of Paris in 1923, felt that if radiation exhibits wave-particle duality, matter should have a dual nature too!!!!!
This was confirmed using a double-slit experiment with particles of matter, such as electrons.
http://www.colorado.edu/physics/2000/index.pl
Every material particle has wave properties with a wavelength equal to: = h/ms (De Broglie)
m: mass of particles: its speedh: Planck’s constant
In-class Problem
Calculate the de Broglie Wavelength of a basketball (m = 1 kg) moving at a speed of 1 m/s. How does this wavelength compare with the size of an atom (~ 1 x 10-9m)?
Solution:
= h/mv = (6.6 x 10-34 J·s)/(1 kg · 1 m/s) = 6.6 x 10-34 m (MUCH smaller than the atom!)
What is the de Broglie wavelength of an electron (m = 9 x 10-31 kg) moving at a speed of 1 x 107 m/s?
Solution:
= h/mv = (6.6 x 10-34 J·s)/{(9 x 10-31 kg · 1 x 107 m/s)
= (6.6/9)(10-34)/ (10-31 · 107 ) ( J · s · kg · m/s)
= 0.7 x 10-10 m (about the same size as an atom!)
sand electrons
sand electrons
sand electrons
Two overlapping piles of sand
Not just two overlapping “piles”
of electrons
sand electrons
Two overlapping piles of sand
Interference pattern
Since the wavelength of the electron is so small, the apertures have to be very narrow for us to see the interference. The experiment originally devised to observe this interference was to force electrons through a metallic foil. The separation of atoms in the foil was the aperture size.
Electrons
Metal foil
Note: J. J. Thompson discovered the electron in 1900 and called it a “charged particle.”
In 1927, G. P. Thomson did the “electron interference” experiment to show that electrons behaved like waves.
G. P. was J. J.’s son!
The wave theory of matter: Every particle has wave properties with a wavelength equal to h/mv, where m is the particle’s mass, v its speed, and h is Planck’s constant.
The Strange World of Quantum Physics
The Strange World of Quantum Physics
Photons (particles!)
The Strange World of Quantum Physics
One Photon
Where does it hit the screen??
Let’s watch one at a time…
Screen
Screen
Given ONE photon, we cannot predict exactly where it will hit.
We can only predict the PROBABILITY that it will hit a certain place on the screen: i.e., we can predict the pattern that many photons will make!!
We can only predict the PROBABILITY that it will hit a certain place on the screen: i.e., we can predict the pattern that many photons will make!!
This is where Einstein had a problem with quantum mechanics, and also the origin of his famous quote: “ … God does not play dice with the universe.”
The pattern we observed can be predicted through the application of quantum theory. Erwin Schroedinger came up with an equation that predicts the “probability wave” (psi). We call it a psi-wave.
This mathematical term psi, is used predict all kinds of physical phenomena at the atomic level—from interference patterns to light emitted from atoms.
A physicist will have had 2 to 3 full years of quantum mechanics classes just to be functional with the theory!!
One of quantum theory’s main applications: describing the atom
Gas tube
aperture
prismscreen
Why LINES?
One type of spectroscope:
Energy
E1
E2
E3
E4
E5
What energy transitions are possible?
E4—E3, E4—E2, E4—E1
If these energy differences are:
2 x 10-19J, 5 x 10-19J, 9 x 10-19J,
Respectively, what are the frequencies of the emission lines that we should see?
E = hf so f = E/h where(f = frequency, h = 6.6 x 10-34 J·s)
For E4—E3,f = (2 x 10-19J) / (6.6 x 10-34 J·s) = 0.3 x 1015 Hz f = 3.0 x 1014 Hz
Similarly,
f = 7.5 x 1014 Hz (for E4—E2)
f = 13.5 x 1014 Hz (for E4—E1)
Energy
E1
E2
E3
E4
E5
Not only can these atom only EMIT photons of a certain frequency, but they can only ABSORB light of a certain frequency.
Photon
Gas tube
aperture
prismscreen
To get atoms to EMIT light, we use the discharge tube. We had to give it energy to “pump up” the electrons in the atoms so that they could fall back into lower rungs on the ladder and emit photons.
One of quantum theory’s main applications: describing the atom
aperture
prismscreen
White light
What should we see??!!
Volume of atoms (gas)
Parts of the spectrum are absorbed, i.e., those at frequencies of allowed transitions.
1
2
34
A certain type of atom has only four energy levels, as shown in the diagram. The "spectral lines" produces by this element are all visible, except for one ultra-violet line. The quantum
jump that produces the UV line is (a) state 2 to 1. (b) state 4 to 1. (c) state 4 to 3. (d) state 1 to 4
(e) impossible to determine without further information.
1
2
34
Continuing the preceding question, the total number of spectral lines produced by this
element is (a) 3. (b) 4. (c) 6.
(d) 10. (e) impossible to determine without further
information.
Comparing a radio photon with an infrared photon, (a) they both have the same wavelength, and the infrared
photon moves faster. (b) the radio photon has the longer wavelength, and the
infrared photon moves faster. (c) the radio photon has the shorter wavelength, but they
both move the same speed. (d) the radio photon has the longer wavelength, but they
both move the same speed. (e) the radio photon has the longer wavelength and it also
moves faster.
