spectrophotometry

Spectrophotometry is an analytical tool used to measure absorbance or percent transmittance of photons of light through a chemical sample.

A basic spectrophotometer setup is shown in the following diagram.

As light of a specific wavelength is passed through a sample solution, it may be absorbed by the molecules in that solution. When it does, the light intensity drops, and this decrease in light intensity is measured.

The incoming light intensity, or //incident light// (I 0 ) passes through a sample in a small container called a cuvette, which has a certain width called a //path length//. This path length (labeled b) is measured in centimeters.

The outgoing light intensity (I t ) is then measured using a detector such as a CCD.

The ratio of outgoing light intensity to incoming light intensity is called //transmittance// (T).

**T = I t / I 0 ** It can also be expressed as //percent transmittance// (%T):

**%T = I t / I 0 x 100**

Another way of measuring this phenomenon is with //absorbance// (A).

Absorbance is a mathematical play on transmittance:

**A = log(1/T) **

It is a dimensionless (no units) expression of the amount of light passing through a sample. The less light that makes it through, the higher the absorbance.

Wavelength and Frequency
A photon travels in wave form. This wave will have 'crests' and 'troughs' just like a wave in water. The distance from one peak to the next, or a complete cycle, is called a //wavelength//.



For visible light, these wavelengths are typically between 400 nanometers and 700 nanometers long. A radio wave is much longer, in the meter range, and an X-ray is much shorter (tenths of a nanometer).

The number of wave cycles a photon makes per second is called its //frequency//.

The wavelength and frequency of a photon are related mathematically:

The value for the speed of light is approximately 3.0 x 10 8 meters per second.


 * Energy of a Photon**

The energy in Joules of a photon can be calculated using Planck's constant, h = 6.63 x 10 -34 joule seconds.

The equation is: **E = h v** For example, a UV photon having a wavelength of 100 nm will have an energy of 2 x 10 -18 J. Worksheet:


 * Beer's Law**

The relationship between the absorbance of a substance, its molar concentration, and the path length of the container is summed up in an equation called the //Beer-Lambert Law//, or simply Beer's Law.

**A = a b c**

Here, absorbance (A) is proportional to the path length (b), molar concentration (c), and something called //molar absorptivity// (a).

Molar absorptivity is defined as the ability of a substance to absorb a certain wavelength of light, and has the unit 1/(M cm).

Using Beer's Law, the absorbance of a substance can be used to determine its molar concentration, which is a very useful analytical tool for the detection of an analyte.

Typically, the analyte and its wavelength of maximum absorbance are known. The wavelength of maximum absorbance can be found rather easily by scanning the visible spectrum (or UV, IR) and finding the highest peak. Here is an example of a wavelength scan:



The wavelength of maximum absorbance for this substance would be around 310 nm.

Next, the spectrophotometer is adjusted so that it filters out all light but that at the substance's wavelength of maximum absorbance (310 nm, for example). A series of solutions containing the substance at known concentrations (called standards) are then measured and their absorbances are plotted against their concentrations to produce a "standard curve".

Here is an example of a standard curve:



Note that this is a linear fit (not sure why they call it a standard "curve"). So the data points have been interpolated (and can be extrapolated) using the linear function y = m x + b.

The absorbance is y, the concentration is x, and the molar absorptivity is the slope, m.

Hopefully the y-intercept, b, is at or very near zero. In fact, there should always be a standard called a //blank//, where the spectrophotometer was "zeroed" using a sample containing no analyte (hence no absorbance and 100% transmittance.

Here are some practice problems: