Video Transcript
The lines shown in the following
graph represent the spectra of light emitted by some objects. Which color line corresponds to the
spectrum with the greatest spectral width? (A) The red line, (B) the green
line, (C) the spectra all have the same spectral width.
Looking at our diagram, we see
several intensity-versus-wavelength curves. Each one of these curves represents
the spectrum, all the wavelengths of light, and their corresponding intensities
emitted by a set of objects. So we could think of it as one
object emitting light as this green curve shows, one object emitting light as the
orange curve shows, and another emitting light as the purple curve and a final one
as the red curve show. These are the spectra of light
emitted by four objects. We want to identify which color
line corresponds with the greatest spectral width.
At first, we might think the
spectral width of a given line is measured down here on the wavelength axis. It’s standard, however, to measure
the spectral width of a given spectrum using what’s called the full width half
maximum or full width half max of that spectrum. The idea with this is that if we
have some spectrum, like this one here, we find the maximum height of that spectrum,
divide that number in half, and then measure the full width of the spectrum at that
half-maximum height. The spectral width then of this
example spectrum will be measured by this difference in wavelength. So now let’s apply the same
approach to our original diagram and the four spectra there.
The maximum of the green spectrum
is here, and half of that value is here on the intensity axis. The full width of the green
spectrum at this half height is shown by this horizontal line. Now, it so happens that this half
height of the green curve is also the maximum height of the orange one. Half of that height is here on our
intensity axis. And the width of the orange
spectrum at this height is given by this line length. Note that this height is the
maximum height of the purple curve. Half of that maximum gives us this
value. And the width of the purple curve
at this half of its maximum height is given by this line length.
This same process repeats for the
red spectrum. Half the maximum height of that
spectrum is here. And so our red spectrum has this
spectral width. Lining up these four spectral
widths, we see that they all cover the same span of the wavelength axis. In other words, the spectral width
of the light from each of these four objects is the same. Even though the peaks of these
spectra all have different heights, their widths, that is, their spectral widths,
are all the same. We choose option (C) for our
answer.
