Photochemistry – Chemistry Study Notes

Fundamental Laws of Photochemistry

When studying light-induced chemical changes, competitive exam aspirants must understand the foundational principles governing how matter interacts with electromagnetic radiation. The first governing principle is the Grotthus-Draper Law (also known as the Principle of Photochemical Activation), formulated independently by Theodor Grotthus in 1817 and John William Draper in 1842. This law states that only the light rays that are absorbed by a system can produce a chemical change; light that is transmitted or reflected by the system is completely ineffective in initiating a reaction.

While the Grotthus-Draper law is qualitative, the quantitative foundation was established by the Stark-Einstein Law (also called the Law of Photochemical Equivalence), proposed independently by Johannes Stark and Albert Einstein between 1905 and 1912. This law states that one atom or molecule is activated by the absorption of one photon of radiation. Mathematically, the energy absorbed by one mole of reactant molecules (known as one Einstein) is expressed by the relation:

$E = N_A h\nu = \frac{N_A hc}{\lambda}$
Where $N_A$ is Avogadro’s number, $h$ is Planck’s constant, $\nu$ is frequency, $c$ is the speed of light, and $\lambda$ is the wavelength.

Although the Stark-Einstein law holds strictly true for the primary photochemical step (the initial absorption event), secondary thermal reactions often follow, causing the overall experimental outcome to deviate from a simple 1:1 molecule-to-photon stoichiometry. This brings us to the crucial concept of quantum efficiency.

Quantum Yield and Deviations

In competitive examinations like JEE and NEET, numerical problems frequently revolve around the concept of Quantum Yield (or Quantum Efficiency), denoted by the Greek letter symbol $\Phi$. By definition, quantum yield measures the efficiency of a photochemical process and is given by:

• $\Phi = \frac{\text{Number of molecules reacting or formed}}{\text{Number of photons absorbed}}$
• Alternatively: $\Phi = \frac{\text{Moles of substance reacted}}{\text{Moles of photons absorbed (Einsteins)}}$

Quantum yields vary widely across different photochemical systems, ranging from extremely small values to millions. Understanding why these variations occur is vital for scoring high in exams:

• Low Quantum Yield ($\Phi < 1$): Occurs when the absorbed photons are deactivated before reaction (via fluorescence, collisional deactivation, or heat dissipation), or when the primary photoproducts recombine back to form reactants. Example: The combination of hydrogen and bromine ($H_2 + Br_2 \rightarrow 2HBr$) has a low quantum yield because the primary bromine atoms frequently recombine.
• High Quantum Yield ($\Phi \gg 1$): Occurs when a single photon initiates a self-sustaining chain reaction. For instance, the photochemical reaction between hydrogen and chlorine ($H_2 + Cl_2 \rightarrow 2HCl$) can exhibit quantum yields ranging from $10^4$ to $10^6$ because one chlorine radical starts a rapid radical chain mechanism.

Jablonski Diagram and Radiative Transitions

When an atom or molecule absorbs a photon, its electron is promoted to a higher electronic energy state. The electronic states of organic molecules are typically categorized into singlet states (where electron spins are paired, total spin $S = 0$) and triplet states (where electron spins are parallel, total spin $S = 1$). The pathways by which these excited molecules return to the ground state are elegantly mapped using the Jablonski Diagram.

Radiative transitions involve the emission of light as the molecule drops from an excited state to a lower energy state. The two primary phenomena here are fluorescence and phosphorescence:

• Fluorescence: This is an instantaneous radiative transition occurring when an electron drops from an excited singlet state ($S_1$) back to the ground singlet state ($S_0$). Because no change in spin multiplicity occurs ($\Delta S = 0$), the process is quantum-mechanically allowed and extremely fast, with a lifetime typically ranging from $10^{-9}$ to $10^{-8}$ seconds. The emission ceases the moment the external light source is removed.
• Phosphorescence: This is a delayed radiative transition that occurs when an electron undergoes intersystem crossing (ISC) from an excited singlet state to a metastable triplet state ($T_1$). Transition from the triplet state back to the singlet ground state involves a change in spin multiplicity ($\Delta S \neq 0$), which is quantum-mechanically “forbidden.” Consequently, phosphorescence has a much longer lifetime (ranging from milliseconds to several hours). The glow persists even after the excitation source is cut off.

Non-radiative transitions, such as internal conversion (IC) and intersystem crossing (ISC), dissipate energy internally as heat without emitting radiation, competing directly with fluorescence and phosphorescence.

Photosensitized Reactions and Chemiluminescence

Many molecules do not absorb light in the specific wavelength region required to undergo a desired chemical transformation, or they decompose destructively upon direct irradiation. To overcome this, chemists use photosensitized reactions. In these processes, a foreign substance called a photosensitizer is added to the reaction mixture. The photosensitizer absorbs the incident light, reaches an excited state, and subsequently transfers its excitation energy collisionally to the reactant molecules, which then undergo the intended reaction without absorbing light directly.

A classic textbook example tested in competitive exams is the photosensitized dissociation of hydrogen or the photosensitization of alkenes by mercury vapor ($Hg^*$) or benzophenone. Mercury atoms absorb resonance radiation at $253.7\text{ nm}$ to reach an excited state, which then transfers energy to other reactants.

Conversely, chemiluminescence is the phenomenon where chemical energy is directly converted into light energy without the initial absorption of photons from an external light source. A chemical reaction produces an intermediate in an electronically excited state, which subsequently emits a photon as it relaxes to the ground state. Prime biological and chemical examples include the glow of fireflies (involving luciferin and luciferase), the oxidation of luminol used in forensic science to detect trace bloodstains, and the functioning of commercial light sticks.

Important Facts / Formulas

Key Points to Remember

• The primary photochemical step always obeys the Stark-Einstein law of photochemical equivalence, regardless of whether the overall quantum yield is fractional or extremely high.
• Fluorescence is a spin-allowed, rapid radiative process ($S_1 \rightarrow S_0$) with a lifetime of nanoseconds.
• Phosphorescence involves a spin-forbidden transition from a metastable triplet state ($T_1 \rightarrow S_0$), resulting in a delayed, long-lived emission.
• Intersystem crossing (ISC) is a radiationless transition between states of different spin multiplicities (e.g., Singlet to Triplet).
• Photosensitizers act as energy intermediaries; they absorb light and transfer energy to reactants that cannot absorb light directly.
• Chemiluminescence converts chemical bond energy directly into light emission, bypassing external irradiation entirely.
• High quantum yields ($> 1$) are hallmarks of free-radical chain mechanisms such as the formation of $HCl$ from $H_2$ and $Cl_2$.
• Low quantum yields ($\le 1$) indicate rapid deactivation pathways like fluorescence, thermal dissipation, or immediate radical recombination.

Previous Year Question Hints

• Hint 1 (Quantum Yield Calculation): When given the power of a monochromatic light source, wavelength, and the moles of product formed in a given time, calculate the total photons (Einsteins) per second using $E = \frac{hc}{\lambda}$, multiply by time, and substitute into the quantum yield formula.
• Hint 2 (Jablonski Transitions): Questions frequently ask to distinguish between internal conversion and intersystem crossing. Remember: internal conversion occurs between states of the same multiplicity, whereas intersystem crossing occurs between states of different multiplicities (singlet to triplet).

Quick Revision Summary

• Photochemical reactions are driven exclusively by absorbed radiation, as mandated by the Grotthus-Draper law.
• The Stark-Einstein law establishes that one photon activates one molecule in the primary activation step.
• Quantum yield ($\Phi$) quantifies reaction efficiency; chain reactions exhibit $\Phi \gg 1$, while deactivation channels drop $\Phi < 1$.
• Fluorescence is fast, spin-allowed ($S_1 \rightarrow S_0$), and stops immediately when light is removed.
• Phosphorescence is slow, spin-forbidden ($T_1 \rightarrow S_0$), and persists as a delayed glow.
• Photosensitizers absorb light and transfer energy to unreactive species via intermolecular collisions.
• Chemiluminescence produces light directly from exothermic chemical reactions without external illumination.
• Non-radiative transitions like internal conversion and vibrational relaxation dissipate electronic excitation energy as heat.