As a beam of light passes through a medium, it commonly gets
weaker, because some light gets absorbed by the atoms or molecules it passes.
The goal of this lab is to compare the measured behavior of absorption with
distance and the predicted behavior. (The theory section appears first, but it
you prefer, you can take data first and tackle theory later.)
I.
Theory: light absorption as a population process
If one thinks of light as composed of photons, one can treat
light absorption as a population process and model it by a differential
equation.
Consider the following statements:
§
Light intensity is proportional to number of photons per second passing through
a unit area;
§
Each atom or molecule absorbs a certain (small) proportion of the photons that
pass by it;
§ If
you think of a material as composed of many thin layers, you can see that each
layer subtracts an amount of intensity proportional to the intensity that
reaches it from the preceding layer, and proportional to the number of
absorbing atoms or molecules in the layer.
Using
these statements,
II.
Visible Light Absorption, Part I (distance)
The first experimental task is to measure the fall-off of
light intensity as a function of distance, using the Ocean Optics spectrometer.
Since you are familiar with the instrument, we can go straight to the questions
to answer: (1) how does light intensity fall off with distance into an
absorbing medium? (2) does it fall off the same way at each wavelength? and (3)
does the fall-off at a given wavelength follow the exponential decay predicted
by the differential equation?
The light-absorbing medium is weighing paper, and you can
easily vary the distance light travels through it by adding thicknesses to the
light path. You can use the cuvet holder to hold the papers in place, taking
trouble to ensure that the paper is flat and perpendicular to the light path.
Make sure the spectrometer is in ‘Intensity’ mode (blue I on toolbar). It may be necessary to calibrate the instrument
first, as we did last week, using a modified version of the dark and light
reference current procedure (see last week’s handout), where the light
reference current is taken when the lamp is on but the sample holder is empty,
to reference the maximum measured intensity.
Record intensity at several different wavelengths as a
function of number of thicknesses of weighing paper, then convert to intensity
as a function of distance, by measuring the thickness of the paper. Then answer
the questions above.
III.
Absorption of Nuclear Radiation
As nuclear radiation passes through matter, it experiences
absorption, too. Again, intensity is proportional to number of particles, and
absorption is a certain small proportion of the particles/photons which pass
by; so the differential equation is the same one, except that the parameters
have different numerical values.
You can measure intensity of nuclear radiation from the
source we provide, by using the radiation counter in the Logger Pro system. You
can try using different absorbing materials placed between the source and the
counter, such as aluminum foil, weigh paper, Kimwipes, etc, making sure you
keep the distance between source and counter constant, varying only the amount
of material (as measured by its thickness).
In this case, we have no way of differentiating wavelengths, so we deal
with the whole spectrum at once. There are just two questions: (1) how does
radiation intensity fall off with distance into an absorbing medium? and (2)
does it follow the predicted exponential decay?
IV. (optional)
The Beer-Lambert Law (a.k.a. Beer’s Law)
The theory of part I also predicts that the intensity of
light falls off exponentially as the concentration (number per unit volume) of
absorbing atoms or molecules increases. This result forms the basis for measuring
the concentration. One passes light through a fixed distance of absorbing
material, for example a standard sized container of liquid, and compares the
received intensity of a standard, known concentration with the received
intensity for an unknown sample.
Use your solution functions for the differential equation to
show that the logarithm of the ratio of the two intensities is linearly related
to the ratio of the two concentrations. This is a version of what is known as
the Beer-Lambert Law, or Beer’s Law.
Prepare a few samples of differing concentrations of the
organic dyes we used last week and measure the received intensities. Make a graph of the logarithm of intensity
as a function of concentration.