The Stark-Einstein Law of Photochemical Equivalence PDF 12: A Key Concept in Photochemistry

Photochemistry is the branch of chemistry that deals with the interactions of light and matter. Photochemistry is important for many natural and artificial processes, such as photosynthesis, vision, solar energy conversion, photography, and more. Photochemistry is also a fascinating field of study, as it reveals the quantum nature of light and its effects on molecules.

One of the fundamental concepts in photochemistry is the Stark-Einstein law of photochemical equivalence, which relates the absorption of light by molecules to the occurrence of photochemical reactions. The Stark-Einstein law was proposed by Johannes Stark and Albert Einstein in the early 20th century, based on their experiments and theories on the photoelectric effect and the quantum theory of radiation.

The Stark-Einstein law states that in a photochemical process, one photon (or quantum) of light is absorbed by one molecule, causing the main photochemical reaction. For example, in photosynthesis, one photon of light is absorbed by one chlorophyll molecule, which initiates the conversion of carbon dioxide and water into glucose and oxygen.

The Stark-Einstein law does not imply that one molecule must react for each photon absorbed. In some cases, one molecule may absorb a photon and transfer its energy to another molecule, which then reacts. In other cases, one molecule may absorb a photon and undergo multiple reactions. The Stark-Einstein law only applies to the primary (or first) step of a photochemical process.

The Stark-Einstein law can be used to calculate the quantum yield of a photochemical reaction, which is the ratio of the number of molecules that react to the number of photons that are absorbed. The quantum yield can vary from zero to infinity, depending on the efficiency and complexity of the photochemical process. The quantum yield can also be expressed as a function of the wavelength or frequency of the light source.

The Stark-Einstein law is a useful and simple way to describe the relationship between light absorption and photochemical reaction. However, it is not a universal law that applies to all photochemical processes. Some photochemical processes may involve more than one photon per molecule, such as multiphoton absorption or upconversion. Some photochemical processes may involve non-radiative transitions or energy transfer mechanisms that are not accounted for by the Stark-Einstein law. Therefore, the Stark-Einstein law should be applied with caution and verification.

Prepare a solution of the substance of interest and a solution of the reference substance with the same concentration and volume.
Expose both solutions to the same light source for the same duration and under the same conditions.
Analyze both solutions to determine the amount of product formed in each reaction.
Calculate the quantum yield of the substance of interest by using the following formula:
$\phi = \frac{\phi_{ref} \times P}{P_{ref}}$
where $\phi$ is the quantum yield of the substance of interest, $\phi_{ref}$ is the quantum yield of the reference substance, P is the amount of product formed by the substance of interest, and P_ref is the amount of product formed by the reference substance.

Some examples of reference substances that are commonly used as actinometers are potassium ferrioxalate, uranyl oxalate, hydrogen peroxide, and anthracene. The choice of the reference substance depends on the wavelength and intensity of the light source, the type and mechanism of the photochemical reaction, and the availability and stability of the reference substance.

How to Apply the Stark-Einstein Law to a Specific Example

One of the classic examples of a photochemical reaction that can be explained by the Stark-Einstein law is the photolysis of hydrogen bromide (HBr). Photolysis is the decomposition of a substance by light. In this case, hydrogen bromide molecules absorb ultraviolet light and break down into hydrogen atoms (H) and bromine atoms (Br). The overall reaction can be written as:

$HBr \xrightarrow{h\nu} H + Br$

The Stark-Einstein law states that one photon of light is absorbed by one molecule of hydrogen bromide, causing the photolysis reaction. Therefore, the quantum yield of this reaction is one, meaning that one molecule of hydrogen bromide reacts for each photon absorbed. This can be verified experimentally by measuring the amount of product formed and the amount of light absorbed.

For example, suppose that a solution of hydrogen bromide is exposed to ultraviolet light with a wavelength of 200 nm and an intensity of 1.0 W/m. The absorption coefficient of hydrogen bromide at this wavelength is 1.0 x 10 m. The volume of the solution is 1.0 L and the concentration of hydrogen bromide is 0.01 mol/L. The duration of the exposure is 10 minutes.

To apply the Stark-Einstein law, we need to calculate the following quantities:

The energy of one photon of light:
$E = h\nu = \frac{hc}{\lambda} \approx 6.626\times 10^{-34} \times 3.0\times 10^8 \div 200\times 10^{-9} \approx 9.939\times 10^{-19} J$
The number of photons absorbed by the solution:
$N = \frac{IAt}{E} \approx \frac{1.0\times 1.0\times 600}{9.939\times 10^{-19}}\times e^{-\epsilon lC} \approx \frac{6.03\times 10^{20}}{e^{-1.0\times 10^4\times 1.0\times 0.01}}\approx 2.23\times 10^{16}$
The number of moles of hydrogen bromide reacted:
$n = \frac{N}{N_A} \approx \frac{2.23\times 10^{16}}{6.02\times 10^{23}}\approx 3.70\times 10^{-8} mol$
The quantum yield of the reaction:
$\phi = \frac{n}{N} \approx \frac{3.70\times 10^{-8}}{2.23\times 10^{16}}\approx 1$

As expected, the quantum yield of the photolysis of hydrogen bromide is one, which confirms the Stark-Einstein law.

How to Compare the Stark-Einstein Law with Other Laws or Theories in Photochemistry

The Stark-Einstein law is one of the earliest and simplest laws or theories in photochemistry, but it is not the only one. There are other laws or theories that describe different aspects or phenomena of photochemistry, such as the Grotthuss-Draper law, the Jablonski diagram, the Franck-Condon principle, the Kasha rule, the Förster resonance energy transfer, and more. These laws or theories are not necessarily contradictory or incompatible with the Stark-Einstein law, but rather complementary or supplementary to it.

The Grotthuss-Draper law states that only the light that is absorbed by a substance can cause a photochemical reaction. This law implies that the absorption spectrum of a substance determines its photochemical reactivity. The Grotthuss-Draper law is consistent with the Stark-Einstein law, as both laws emphasize the importance of light absorption for photochemistry.

The Jablonski diagram is a graphical representation of the electronic states and transitions of a molecule that absorbs or emits light. The Jablonski diagram shows the different energy levels and pathways that a molecule can undergo after absorbing a photon, such as fluorescence, phosphorescence, internal conversion, intersystem crossing, quenching, etc. The Jablonski diagram is more detailed and comprehensive than the Stark-Einstein law, as it accounts for various factors and mechanisms that affect the fate and outcome of a photochemical process.

The Franck-Condon principle states that electronic transitions between different energy levels of a molecule are much faster than nuclear motions or vibrations. This principle implies that a molecule absorbs or emits light when its nuclei are in the same position or configuration. The Franck-Condon principle is related to the Stark-Einstein law, as both principles assume that one photon corresponds to one electronic transition of one molecule.

The Kasha rule states that a molecule in an excited electronic state will relax to the lowest vibrational level of that state before emitting light. This rule implies that the emission spectrum of a substance is independent of the wavelength of the light source. The Kasha rule is an extension of the Stark-Einstein law, as it explains why some photochemical processes involve more than one photon per molecule.

The Förster resonance energy transfer (FRET) is a phenomenon in which a molecule in an excited electronic state transfers its energy to another molecule without emitting light. This phenomenon depends on the distance and orientation between the two molecules, as well as their spectral overlap. The FRET is an exception to the Stark-Einstein law, as it involves non-radiative transitions and energy transfer mechanisms that are not accounted for by the law.

Conclusion

In this article, we have discussed the Stark-Einstein law of photochemical equivalence, which is a fundamental concept in photochemistry. We have explained the meaning and implications of the law, which states that in a photochemical process, one photon of light is absorbed by one molecule, causing the main photochemical reaction. We have also shown how to apply the law to a specific example, which is the photolysis of hydrogen bromide. We have calculated the quantum yield of this reaction, which is one, confirming the law. We have also compared the law with other laws or theories in photochemistry, such as the Grotthuss-Draper law, the Jablonski diagram, the Franck-Condon principle, the Kasha rule, and the Förster resonance energy transfer. We have demonstrated that these laws or theories are not necessarily contradictory or incompatible with the Stark-Einstein law, but rather complementary or supplementary to it.

The Stark-Einstein law is a useful and simple way to describe the relationship between light absorption and photochemical reaction. However, it is not a universal law that applies to all photochemical processes. Some photochemical processes may involve more than one photon per molecule, such as multiphoton absorption or upconversion. Some photochemical processes may involve non-radiative transitions or energy transfer mechanisms that are not accounted for by the law. Therefore, the law should be applied with caution and verification.

Photochemistry is a dynamic and evolving field that requires constant learning and experimentation. Therefore, we encourage you to continue exploring and expanding your photochemistry skills and knowledge. You can use various sources and resources for further learning, such as books, websites, blogs, podcasts, videos, courses, workshops, seminars, conferences, journals, magazines, newsletters, organizations, associations, networks, communities, mentors, peers, and experts in the field of photochemistry. By doing so, you will be able to keep up with the latest trends and developments in photochemistry, and enhance your professional growth and career opportunities.

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