Download Class 22

Announcements
•  No Office hours today for DR
•  Exam next Thur. Mar 13 will cover all
material through HW 7
•  Prof. Smalyukh will lecture Fri and Mon.
Today
•  Finish quantum nature of light
•  Atoms and atomic spectra
Photon about to go through the slits
Photon as little segment of
wave moving towards slits
Intensity of wave in various places, indicates probability
of finding the photon there if you looked at that moment.
Photon after it went through the slits
Still only one photon!
(But this photon has
a slightly complicated
wave function.)
Photon is a wave…
It can interfere with itself.
Intensity of wave in various
places indicates the probability of
finding the photon at that spot, if I
had detector there (e.g. a bunch
of atoms or a sheet of metal)
Photon after it went through the slits
When photon interacts with
one electron or atom, all
energy ends up in
(“collapses into”) one
spot… Here it behaves like
a particle with energy = hc/
λ
Probability of hitting at a
specific place is proportional
to the square of the field
amplitude at that location.
Which slit did this photon go through?
a. left
b. right
c. both
d. neither
e. either left or right we just cannot know which one
Which slit did this photon go through?
If one slit:
Get single slit pattern
(i.e. no interference)
Like this:
or this:
The sum of the two:
But not like this:
But: that photon is part
of the two slit interference pattern.
The probability pattern of where it lands is described by the 2 slit
interference pattern (the photon has to ‘know’ about both slits!)
à It must have gone through both slits, i. e. as a wave!
(When it interacts with the screen it behaves particle-like!)
quantum-wave-interference_en.jar
Random nature of the photons
is a consequence of:
a)  quantum theory of light
b)  can be proven by thought experiments
starting from Maxwell’s equations
c)  not a consequence of anything: this is
just what the experiments show.
Random nature of the photons
is a consequence of:
a)  quantum theory of light
b)  can be proven by thought experiments
starting from Maxwell’s equations
c)  not a consequence of anything: this is
just what the experiments show.
It is a postulate of quantum theory of light, i.e. a
statement without theoretical explanation. This is simply
what experiments show. (analogous to the speed of light
being the same in all ref. frames)
Atoms and atomic spectra
Atoms and Atomic spectra
•  What are atoms made off? JELL–O?
•  What happens when we hit atoms with various
stuff?
•  How do atoms interact with light? à Develop
model of how light interacts with and is
produced by individual atoms (Will help us learn
how atoms ‘work’)
Early ideas about atoms
invisible!
•  Atom - Greek “indivisible unit”
•  The Blueberry-Muffin-Atom-Model (aka.
‘The Thomson model’): Uniform distribution
of positive charges with negative electrons
embedded in it.
à But wait! We can get electrons from them
(scraping, chemical, or photoeffect) but no
positive charges. Hmmm?!...
-
Step 1: Shoot the JELL–O atom!
Have a heavy blob that seems like grape JELL–O, and you
have gun with rubber bullets. How to find out what the middle
of the blob is like?
Have a heavy blob that seems like grape JELL-O, and you
have gun with rubber bullets. How to find out what the middle
of the blob is like? Shoot bunch of bullets into it and see this.
What is the inside like?
Have a heavy blob that seems like grape JELL-O, and you
have gun with rubber bullets. How to find out what the middle
of the blob is like? Shoot bunch of bullets into it and see this.
What is the inside like?
a. hollow
b. solid JELL-O
c. hard heavy core surrounded by JELL-O
d. bunch of hard little objects distributed through blob
Have a heavy blob that seems like grape JELL-O, and you
have gun with rubber bullets. How to find out what the middle
of the blob is like? Shoot bunch of bullets into it and see this.
What is the inside like?
Hard heavy core surrounded by JELLO
Only one thing is reflecting bullets, sending them straight
back so must be hard and heavy.
Essentially Rutherford experiment and conclusion (TZD 3.12).
Rutherford shot alpha particles = 2 protons, 2 neutrons
n
pn Positive charge
Bullets =
p
The Rutherford experiment
Detector
rutherford-scattering_en.jar
The Rutherford atom:
Tiny nucleus with protons and neutrons (~99.98% of mass)
Surrounded by large diffuse cloud of low mass electrons
10-10 m
n n
pnp p
pn
p
10-14 m
The ‘Rutherford atom’ is a much better model
than the ‘Thomson model’, but it is still far
from helpful.
A good model should:
•  explain how stuff works
•  predict the behavior of it
•  be quantitative
•  etc.
à Need a better model!
increasing
energy
What do the vertical arrows represent?
allowed energies in an atom
Reading Quiz
“ground state”
a. arrows on right represent absorption of light,
arrows on left represent emission.
b. arrows on both left and right represent emission
c. arrows on both left and right represent absorption
d. arrows on left represent absorption of light,
arrows on right represent emission.
increasing
energy
allowed energies
ground state
d. arrows on left represent absorption of light,
arrows on right represent emission.
Let’s see how atoms behave
when shot-at! (with
(with electrons)
electrons)
http://www.jstor.org/discover/
10.2307/40677461?
uid=3739568&uid=2129&uid=2
&uid=70&uid=4&uid=3739256&
sid=21101136089553
What happens if we bash atoms with
electrons?
In atomic discharge lamps, lots of electrons are given kinetic
energy (accelerated by a high voltage). When they bash into
atoms some of this kinetic energy is transferred to the atom
à Atom get's excited!! (“Neon” lights, Mercury street lamps)
- 120V +
Cathode (hot metal, so
electrons can come out)
Anode (positive potential)
Note: ‘Anode’ and ‘Cathode’ have different meanings in physics or
chemistry. Remember ‘Cathode Ray Tube’ (CRT): Electrons
leave the cathode (in physics).
Use a grating to look at the spectrum of
the discharge lamps
Hold grating only by edges...oil from hands ruins grating!
Hold close to eye... See rainbow from lights. Turn grating
so rainbow is horizontal. (Rainbow appears quite a bit to
the side of the actual lamp.
Hydrogen
Na
Hydrogen
neon
neon
neon
Hydrogen
White light = whole spectrum.
Each type of atom produces
unique set of colors, called its
“spectrum”. None of the atoms
produces white light!
Na Na
Na
NaNa
Hydrogen
Hydrogen
Hydrogen
Hg
Hg
Hg
Hg
Hg
What colors from white light?
What colors from neon?
What colors from hydrogen?
What from mercury?
What from sodium?
400
500
600
Wavelength (nanometers)
700
800
Each type of atom produces unique set of colors.
Discussion: Given that we now know that light comes
quantized in photons with energy E=hc/λ= hf. What do these
observations imply about electrons in atoms?
Student suggestions:
a.
b.
c.
d.
e.
Each type of atom produces unique set of colors.
Discussion: What does this imply about electrons in atoms?
Implies that electrons only change between very specific energies.
Each time a photon is emitted an electron must be changing in
energy by that amount (releasing energy).
Only way for individual atoms to give off energy is as light.
Atoms are lazy - always want to go back to lowest energy state.
2. Excited atom ..electron
3. Electron
1.  Fast electron in atom goes to higher
jumps back to
hits atom
energy
low energy
Less KE
e
Higher
energy
e
Ground
state
~10ns
Excited
state
e