Download Playing with Light

Playing with Light
Revised: 6/4/15
Playing with Light
Report Instructions:
Work in a group as described after the introduction section. All notes should be entered in your
ELN. No formal objective or procedures are required. One final report is due from your group
during week 9 (your TA will set the exact due date).
Introduction:
Light, electromagnetic radiation, plays an important role in many chemistry experiments. In
spectroscopy, light is shined on or through a chemical sample and then detectors measure how
the light is changed. Spectroscopy is one of the most powerful tools a chemist has to analyze
samples. It can be used to find the concentration of an analyte, to determine the structure of an
unknown molecule, or even to watch chemical reactions and molecular motions as they
happen. Therefore, an understanding of the properties of light is very useful for chemists. This
lab introduces several important ways light interacts with matter.
Physicists call the world we live in classical. Conveniently, our classical world has many
deterministic properties. For example, if I throw a ball, an equation can tell me exactly where it
will land. Classical physics applies to things about our size (millimeters or meters) and moving
at speeds we are familiar with (meters / second).
Figure 1. According to classical mechanics, the ball lands exactly at the end of the
dashed line. According to quantum mechanics, it lands somewhere in the gray fuzzy
area, with the probability indicated by the intensity of the shading.
When things are moving very quickly, for example, a tenth or more of the speed of light (3.0 x
108 m/s), the rules change. The rules of relativity, which Einstein is famous for inventing, take
over. Furthermore, when things are very small (for example, 10-9 m), another set of rules called
quantum mechanics is applied (which, by the way, Einstein never really believed). The rules of
quantum mechanics, and how chemists use them, are what you’re going to learn about in this
lab. (Incidentally, when things are both very, very small and very, very fast, both relativity and
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quantum mechanics must be used - this has not been completely worked out yet and, therefore,
leads to some pretty crazy stuff.)
Quantum mechanics is much less convenient than classical physics. If I throw an electron,
unlike the ball in the previous paragraph, no complete equation exists to tell me exactly where it
will land. The best equation we have is by a guy called Schrödinger - it gives the probability of
the electron landing in a given spot. This is why quantum mechanics is probabilistic - we are
always uncertain about the electron's location. In fact, there is a rule for this - the Uncertainty
Principle. It says that the more we know about where an object is, the less we know about how
fast it is going, and vice versa. So, when I throw an electron, if I know exactly how fast it is
going in the air, then I have no idea where it is and I can’t know where it will land.
An important idea to come out of quantum mechanics is that light can be thought of in two
seemingly unrelated ways: 1) Light is a wave traveling through the air that can interfere with
other light the same way sound waves interfere; 2) Light is a stream of particles, each with a
mass and discrete location, called photons. This is called wave-particle duality. Both are
equally accurate pictures of what is going on (the truth is a combination of both) and the picture
used depends on what is easier for the question being studied. Incidentally, electrons also
display a wave-particle duality, as do molecules, cells, and even people – all matter has a
wavelength. However, we are unaware of the wavelengths for objects in our daily lives because
they are very short.
Radio waves
λs
1m
Microwaves
Infrared
Visible
Light
Ultraviolet X-Rays
Gamma
Rays
1000 µm
10 µm
500 nm
50 nm
0.5 Å
Excitations Molecular
rotations
Molecular
vibrations
Valence electron
excitations
1 nm
Core electron
excitations
Nuclear
excitations
Figure 2. The electromagnetic spectrum, with representative wavelengths and excitations.
Light comes in a broad range of energies. The most important areas for chemists correspond to
energies that excite (create) particular motions in molecules. Microwaves are the right energy to
change the speed of rotation of molecules. Infrared light, which we associate with heat, is the
right energy to excite the vibrations of molecules, making the bonds stretch and bend more
quickly. Finally, in the visible and near ultraviolet regions, light has the right energy to promote
electrons from one electronic energy level to another.
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This lab focuses on light in the visible portion of the spectrum, where photons have enough
energy to excite valence electrons into outer orbitals. For hydrogen (or any atom ionized down
to one electron) a simple formula tells which photons will be absorbed or emitted - Rydberg’s
formula:
E = RH (1/ni2 – 1/nf2)
RH is called Rydberg’s constant, and is 2.18 x 10-18 J. This energy can be converted to
wavelength using E = hν and c = λν. The principal quantum numbers for the initial and final
states are represented by ni and nf.
The Rydberg formula has a few implications: 1) When there is only one electron, the energy of
the ground state atom can be determined by just one quantum number, ni. 2) If a photon has an
energy equal to the energy difference between two levels, that photon can be absorbed by the
atom. 3) When the atom is in an excited state – for example, electricity creates samples of
excited atoms in the gas discharge tubes in the fourth part of this experiment – then the energy
difference between two levels the energy of the photon that will be emitted when the electron
relaxes to its ground state.
Absorption:
nf
nf
Ephoton = ΔE = hν
ΔE
ni
ni
Ground State
Excited State*
Emission:
nf
nf
ΔE
Ephoton = ΔE = hν
ni
Excited State*
ni
Ground State
Rydberg’s formula completely describes the simple emission spectrum of a one electron atom
with only the principle quantum numbers. When an atom has more than one electron, the
electrons interact and other quantum numbers are needed to describe the atom's total energy.
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Because no simple formula describes the emission spectrum of a multi-electron atom it is a
complicated mess of lines, with no simple mathematical relationship.
For molecules, the situation is even more complex. Many electrons are interacting with each
other, and several nuclei, which can move relative to each other, are present. This nuclear
motion creates a spectrum with broad bands - there are no discrete lines.
Before starting the experiment, the TA will randomly ask students to do a quick demonstration or
talk-through the following:
1) What needs to be done with the sparklers before throwing them away?
For this lab, you will work in groups of 4 or 5, with assigned duties. Before you begin, assign
each group member to a role for each activity. Switch roles for each activity. The lab report will
be completed as a group and you will receive a peer grade as well as an instructor grade.
Activity 1
Activity 2
Activity 3
Activity 4
Manager
Technician
Recorder
Photographer
Duties:
Manager: The manager is responsible for supervising all elements of the activity and making
sure all procedures are carried out and data is recorded.
Technician: Perform the experimental manipulations.
Recorder: Data collection: qualitative observations and measurements. Individuals with the
Recorder duty are responsible for the recording data in and attaching files to the ELN.
Therefore, each person in a group of 4 will have recorded the observations for one activity.
Photographer: Take pictures of all important experimental set-ups.
Your final report will be a 4-5 page magazine article for nonscientists. It must be well illustrated
with pictures & figures of an appropriate size. Points will be given for content and presentation.
Safety:
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Lasers: This lab contains class II and class IIIa lasers. The beam of Class II lasers are only
dangerous with deliberate attempt to damage the eye – if accidentally exposed you will blink
before any damage is done. Class IIIa lasers can be dangerous if focused, but unfocused they are
no more dangerous than class II. Neither level poses any danger to your skin. Before you begin
each laser activity, record the laser class (it should be marked on the laser itself) in your ELN.
Flames: You will be burning candles and sparklers in this lab. Please use common sense to
avoid harming yourself. Sparklers should be dipped in a 1L beaker of water before throwing
away.
Activity 1: Total Internal Reflection in Water
When light passes between two substances, it bends. Think of looking at fish in a fish tank –
they’re not actually where they appear to be, because the light bends when it passes from the fish
tank to the air on its way to your eye. The amount the light bends depends on the index of
refraction (n) of each medium. The index of refraction is a way of quantifying how fast light
travels through that substance: high index materials have slow velocities of light. The index of
refraction of vacuum is defined to be 1, and everything else is defined relative to that. Table 1
lists the index of refraction for several common materials.
Material
Vacuum
Air (at STP)
Water
Glass
Diamond
Cubic Zirconia
Snell’s Law:
!"# !!
!"# !!
!
!
= !! = !!
!
!
n
1 (by definition)
1.000277 (you
can call it 1)
1.3330
1.4-1.75
2.4
2.2
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where θ = the angle that the light enters the material, v = the velocity of light in that material.
Snell’s law gives the relationship between the refractive index of the two materials and the
relative angles. For instance, because nair < nwater, light traveling from air into water will bend
towards the normal. To start with, you’re going to play with how light bends between air and
water. Follow the directions below, entering all of your observations in your ELN.
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1. Take a pen or pencil that you don’t mind getting wet, and stick it into the fish tank at the
angles shown by the arrows below. (To see the pencil bend, you will have to look at an angle
from in front and above the fish tank.).
2. Did the pencil bend in the direction you thought it would? Record (sketch) the pen’s or
pencil’s appearance in the water. Provide an explanation of what is happening.
3. Now we’re going to play with a laser pointer, shining it in the tank from the front towards the
back wall. Before you do it, make some predictions on the images below as to where the
beam will go.
4. Now use the laser pointer and draw in what actually happens. Be sure to watch for beams
going in multiple directions. The water needs to be a bit cloudy for this step. There
should be starch powder in the water but you may need to stir it if it has all settled. The
tank should be on a piece of paper with arrows drawn on it showing you where to put the
laser pointer for each of these pictures. These positions aren’t very intuitive because the
light bends when it enters the water also.
Laser Class: Explain what you think is going on.
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5. Hopefully, you found an angle after which the light no longer transmits through the back of
the fish tank. This angle is called the critical angle, and is very important. Calculate the
critical angle for the air/water interface in your experiment (ignore the glass wall of the fish
tank).
6. When the light is past the critical angle, does it interact at all with the air outside the tank?
Explain why or why not.
Activity 2: Tunneling of Light
Answer questions 1 - 3 after completing Activity 1.
1. Using what you learned in Activity 1, draw what a laser would do when going through a
prism at the angles shown below.
θ > θcrit θ = θcrit θ < θcrit 2. What do you think would happen if the second prism is put next to the first, as in the picture
on the left? What if it was moved away just a little bit, like in the picture on the right?
θ > θcrit θ > θcrit 3. In the picture on the right in the question above, does the distance between the two prisms
matter? Do you think changing the material the prism is made out of would change the affect
distance has? How about changing the laser: Would the wavelength affect the distance?
Would the energy of the laser?
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4. Now your TA will show you the tunneling of light experiment. Draw all of the parts of the
experiment and label the parts.
Laser Class: 5. Your TA is now going to show you the tunneling demonstration. Write down what you see.
6. In activity one, you found that light reflects completely when you’re past the critical angle.
That’s the classical answer. As is often the case, the quantum answer is fuzzier. The laser in
this experiment is hitting the back wall of the prism at an angle greater than the critical angle,
but the light is going through anyway. Because we know the _______________ of the
material very well, the ______ of the light is known very accurately. By the _____________
______________, this means that the _________ of a photon is _______________________.
This means that some photons skip the barrier between the first prism and the air completely,
and form a funny thing called an evanescent wave that can go between the two prisms. This
process is called tunneling.
7. The intensity of tunneled light depends on the distance between the two prisms. Record data
of tunneling intensity as a function of distance. Is the relationship linear?
Distance
Signal
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Activity 3: Emission Spectroscopy of Sparklers and Candles
1. This activity should be performed entirely in a fume hood. Be careful with open flames.
You should have the following: a set of colored candles, several colored sparklers, and
several handheld spectroscopes.
2. The spectroscope works by using something called a diffraction grating, which spreads out
light so that each color is going a slightly different direction, so that you can see it’s
component parts. One end is a narrow slit so the light observed is from a single source and
all going the same direction – this is called collimated light. The other end (the one you
hold up to your eye) has a circular opening containing the diffraction grating. Look through
the spectroscope at the room lights. You should see something like this:
Red side Blue side Blue side Red side Spectrum Slit Spectrum 3. You should see the emission spectrum
of the lab lights. It contains broad bands of color
across the spectrum that we see combined as white light. Now turn on the white LED and
record the difference.
4. Now observe the emission spectra of several burning sources. One at a time, light each of
the colored candles and observe them with a spectroscope. In your ELN, draw the spectra as
you see them. (It’s okay to make a colored drawing and attach a digital picture).
Red
Red side Blue side Orange
Green
Blue
Purple
White
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5. For each candle, write if you think the substance making the color is a single electron atom, a
multi-electron atom, or a molecule. It could also be a combination.
Candle
Classification
Red
Orange
Green
Blue
Purple
White
6. Now, one at a time, light each sparkler and draw the spectrum in your ELN:
Red
Red side Blue side Blue
Green
7. Now classify each sparkler as single electron, multi-electron, or molecule.
Classification
Candle
Red
Green
Blue
8. Based on your answers to questions 4-7, do you think any of the sparklers contain the same
substances as one of the candles? If so which?
9. Were there any bands that you saw in all of the spectra? If so, give an explanation for what
they might be.
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Activity 4: Analysis of Emission Standards
1. Find the station with the emission spectrum power supply:
Tubes can be
removed to check
the label here
Active tube
Screw holes for attaching
spectrometer mount
It should be pre-loaded with several spectrum tubes for various gases. The black section in
the middle of the power supply can be rotated to select which tube will be powered. It
supplies an electric current to a tube filled with the labeled gas, causing the gas to emit
photons. Turn on the power supply. After less than a minute, the tube in the active position
(the flat side opposite the on/off switch) should light up.
2. See Activity 3 step 2 for instructions on how to use the spectroscope if you haven’t done that
activity yet. Look at each gas in the power supply through the spectroscope. One of those
three tubes contains hydrogen, one neon, and one nitrogen. What do you think the identity of
each tube is, and why? Hints: What kind of excitation happens in the visible spectrum?
Should hydrogen’s spectrum be very simple or very complicated? Nitrogen (N2) is the only
molecule in the group – how do you think that would affect its spectrum?
3. Now, check your guess. The tubes can be removed by rotating them to the hole on the
opposite side of the power supply and then gently pushing them up through the hole. Each
tube is labeled on the back. Write down the identities of each tube in the following table.
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Tube 1
Tube 2
Tube 3
4. You should also find at your station a plastic piece labeled “Spectrometer mount”. It screws
onto the power supply. There should be two black thumb screws to attach it with – be
careful not to lose these! Attach it and plug in the Ocean Optics Spectrometer.
Insert the
spectrometer
fiber here
Screws for
adjusting left/right
position
Screw holes for attaching
spectrometer mount
5. Attached to the computer is a spectrometer with a fiber optic attachment. This inserts into
the hole at the top of the spectrometer mount, and is secured using the screw on top.
6. Open up Logger Pro (if a previous group left the program open, close it and reopen it to reset
the program). Change unit to “Intensity”: Experiment→Change
Units→Spectrometer→Intensity.
7. Press “Collect”, and the spectrum should start updating automatically. Now you’re going to
have to fiddle around to get a good spectrum. Try slightly adjusting the position of the
spectrometer fiber. Also, you may need to change the integration time (Experiment→Set up
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sensors→Spectrometer→Sample Time) if the signal is too low. A higher integration time
means a higher signal. Somewhere between 10 ms and 100 ms should be good.
8. Record a spectrum for each gas onto a USB memory device. Attach all of the files to your
ELN.
9. For the hydrogen spectrum, record the peak positions. Using Rydberg’s formula, for each
peak calculate the states involved in the transition.
Peak Wavelength
(nm)
n1
n2
Final Report Instructions
One report is due from your group during week 9. The report should be written like a magazine
article to the general public. Be sure to integrate pictures, graphs, and diagrams into the text to
illustrate your many of the points of your discussion of your observations and conclusions.
Indicate within the report which person(s) contributed to each section. The recorder for a
particular activity is not allowed to be the significant author of that activity in the report. A
bibliography is required. Each group member should attach the completed file to their ELN and
one group member should be designated to upload the file to turnitin.com.
Have fun and be creative!