# Transmittance: what is it, molecular energy diagram and exercise

The transmittance optics is the ratio of the intensity of the emerging light and the intensity of light incident on a translucent solution sample was illuminated with monochromatic light.

The physical process of passing light through a sample is called light transmission and transmittance is a measure of light transmission. Transmittance is an important value in determining the concentration of a sample that is usually dissolved in a solvent such as water or alcohol, among others.

An electrophotometer measures a current proportional to the intensity of light affecting its surface. To calculate transmittance, the intensity signal corresponding only to the solvent is usually measured first and this result is recorded as Io .

The dissolved sample is then placed in the solvent with the same lighting conditions and the signal measured by the electrophotometer is indicated as I ; transmittance is calculated according to the following formula:

T = I / I or

It should be noted that transmittance is a dimensionless quantity, because it is a measure of the light intensity of a sample in relation to the transmittance intensity of the solvent.

## What is transmittance?

### Absorption of light in a medium

When light passes through a sample, some of the light’s energy is absorbed by the molecules. Transmittance is the macroscopic measure of a phenomenon that occurs at the molecular or atomic level.

Light is an electromagnetic wave, the energy it carries is in the electric and magnetic field of the wave. These oscillating fields interact with the molecules of a substance.

The energy that carries the wave depends on its frequency. Monochromatic light has only one frequency, while white light has a frequency range or spectrum.

All frequencies of an electromagnetic wave travel in a vacuum at the same speed of 300,000 km/s. If we denote by c the speed of light in a vacuum, the relationship between the frequency f and the wavelength λ is:

c = λ⋅f

Since c is a constant at each frequency it corresponds to its respective wavelength.

To measure the transmittance of a substance, the visible electromagnetic spectrum regions (380 nm to 780 nm), the ultraviolet region (180 to 380 nm) and the infrared region (780 nm to 5600 nm) are used.

The speed of propagation of light in a material medium is frequency dependent and is less than c . This explains the scattering in a prism with which the frequencies that make up white light can be separated.

### Molecular Theory of Molecular Absorption

Atoms and molecules have quantified energy levels. At room temperature, molecules are at their lowest energy levels.

The photon is the quantum particle associated with the electromagnetic wave. The photon energy is also quantized, that is, a photon of frequency f has energy given by:

E = h⋅f

where h is the Planck constant whose value is 6.62 × 10 ^ -34 J⋅s.

Monochromatic light is a beam of photons of a given frequency and energy.

Molecules absorb photons when their energy coincides with the difference needed to drive the molecule to a higher energy level.

Energy transitions through the absorption of photons in molecules can be of several types:

1- Electronic transitions, when electrons from molecular orbitals pass to higher energy orbitals. These transitions usually occur in the visible and ultraviolet range and are the most important.

2- Vibrational transitions, the energies of molecular bonds are also quantized and when a photon is absorbed from the infrared region, the molecule moves to a state of higher vibrational energy.

3- Rotational transitions, when the absorption of a photon takes the molecule to a higher energy rotational state.

## Molecular energy diagram

These transitions are best understood with a molecular energy diagram shown in Figure 2:

Figure 2. Molecular energy diagram. Source: F. Zapata.

In the diagram, the horizontal lines represent different levels of molecular energy. The E 0 line is a fundamental or lower energy level. Levels E1 and E2 are higher energy excited levels. Levels E0, E1, E2 correspond to the electronic states of the molecule.

Sublevels 1, 2, 3, 4 within each electronic level correspond to the different vibrational states corresponding to each electronic level. Each of these levels has finer subdivisions that are not shown and correspond to the states of rotation associated with each vibrational level.

The diagram shows vertical arrows representing photon energy in the infrared, visible, and ultraviolet range. As can be seen, infrared photons do not have enough energy to promote electronic transitions, while visible and ultraviolet radiation do.

When the incident photons of a monochromatic beam coincide in energy (or frequency) with the energy difference between the molecular energy states, photon absorption occurs.

### Factors on which transmittance depends

According to what was said in the previous section, transmittance will depend on several factors, among which we can mention:

1- The frequency with which the sample is illuminated.

2- The type of molecule you want to analyze.

3- The concentration of the solution.

4- The length of the path taken by the light beam.

Experimental data indicate that transmittance T decreases exponentially with concentration C and with the length L of the optical path:

T = 10 -a⋅C⋅L

In the expression above, a is a constant that depends on the frequency and type of substance.

## Exercise solved

### Exercise 1

A standard sample of a given substance has a concentration of 150 micromoles per liter (μM). When its transmittance is measured with 525 nm light, a transmittance of 0.4 is obtained.

Another sample of the same substance, but of unknown concentration, has a transmittance of 0.5 when measured at the same frequency and with the same optical thickness.

Calculate the concentration of the second sample.

#### Response

The transmittance T decays exponentially with the concentration C:

T = 10 -b⋅L

If the logarithm of the previous equality is adopted, it will remain:

log T = -b⋅C

Splitting member to member the previous equality applied to each sample and clearing the unknown concentration is:

C2 = C1⋅ (log T2 / log T1)

C2 = 150μM⋅ (log 0.5 / log 0.4) = 150μM⋅ (-0.3010 / -0.3979) = 113.5μM