The quantum yield of the photolysis of benzene at a certain wavelength is the ratio of the number of molecules that undergo a photochemical reaction to the number of photons absorbed by the system. In other words, it represents the efficiency of the photolysis process.To determine the quantum yield, we need to understand the photophysical processes involved in the photolysis of benzene. When benzene absorbs a photon of light at a specific wavelength, it gets excited from its ground state S0 to an excited state Sn . This process is called absorption. Once in the excited state, benzene can undergo several processes:1. Internal conversion IC : The molecule relaxes from the excited state to a lower energy state S1 by converting the excess energy into heat. This process is non-radiative and does not involve the emission of a photon.2. Fluorescence: The molecule relaxes from the excited state S1 to the ground state S0 by emitting a photon. The emitted photon has a lower energy longer wavelength than the absorbed photon.3. Intersystem crossing ISC : The molecule undergoes a spin flip and transitions from the singlet excited state S1 to a triplet excited state T1 . This process is also non-radiative.4. Phosphorescence: The molecule relaxes from the triplet excited state T1 to the ground state S0 by emitting a photon. The emitted photon has a lower energy longer wavelength than the absorbed photon and is typically slower than fluorescence.5. Photochemical reaction Photolysis : The molecule undergoes a chemical reaction in the excited state, leading to the formation of products.To calculate the quantum yield of the photolysis of benzene, we need to know the number of molecules that undergo photolysis Np and the number of photons absorbed by the system Na . The quantum yield is then given by the formula: = Np / NaIn practice, it can be challenging to directly measure the number of photons absorbed and the number of molecules undergoing photolysis. Instead, we can use the following equation to calculate the quantum yield: = [A] / [A] / [B] / [B] where [A] and [B] are the changes in the concentrations of the reactant benzene and the product, respectively, [A] and [B] are the molar absorption coefficients of the reactant and product at the specific wavelength, respectively.To determine the quantum yield of the photolysis of benzene at a certain wavelength, you would need to perform a controlled experiment where you measure the changes in the concentrations of benzene and the product s formed during the photolysis process. Additionally, you would need to know the molar absorption coefficients of benzene and the product s at the specific wavelength. With this information, you can then use the above equation to calculate the quantum yield.