Aside from making neat patterns, the diffraction grating
has a very functional use: It can be used to determine the spectra
of different materials. Each material has its own certain spectra.
This can be used to analyze and further define that specific material.
The spectrum is so individual to an object because it is made by an objects
atoms colliding. Atoms - even in a gas - have fixed orbits unique
to that element, when they are excited the change orbits, these new high
energy orbits are very unstable so the atoms are forced to fall back into
their original orbit. When they fall back a wonderful amount of energy
is released. All energy has a corresponding wavelength, the
wavelengths are represented by a line on the table below:
To obtain data we used a very unusual diffraction grating:
one that is holographic (of known pitch). We also used a eyeball
spectra graph grab the different wavelengths. Using this grating
we observed the hydrogen spectrum, this divided the light into a blue,
green, and red spectrum. Here is a picture of the spectrum taken
by a classmate from a previous year:
To further analyze the data we used a video camera focused
on the spectrum with the grating in-between:
This can record the wavelength for each of the spectrum shown.
The ruler as well as an accurate measurement for D is
necessary to determine qi, having this angle
is important because it coupled with the pitch of the known holographic
grating will yield the qd (the angle in which
the light is diffracted). This phenomena of diffraction angles is
represented in the following image:
The following table has the necessary
values to find the angles for q
and their
corresponding experimental wavelengths.
|
D
|
153.7 cm
|
|
qi
|
0.48
|
|
Xcen
|
80.1 cm
|
|
a(qd)
|
+0.0210
|
|
b(qd)
|
-0.1024
|
|
g(qd)
|
-0.1466
|
|
d(qd)
|
-0.1626
|
|
a(l)
|
647 nm
|
|
b(l)
|
482 nm
|
|
g(l)
|
425 nm
|
|
d(l)
|
402 nm
|
The following table shows the book
values for Balmer series of lines.
|
a(l)
|
656.3 nm
|
|
b(l)
|
486.1 nm
|
|
g(l)
|
434.1 nm
|
|
d(l)
|
410.1 nm
|
The following table shows the percent of
error between the experimental values and
the book values.
|
a(l)
|
1.4%
|
|
b(l)
|
0.9%
|
|
g(l)
|
2.6%
|
|
d(l)
|
2.0%
|
The experiment was rather successful as the percent of
error fell well within an acceptable range of values.
