Use bond energies to estimate the maximum wavelength of light that will cause the reaction $$ \mathrm{O}_{3} \stackrel{\mathrm{h} \mathrm{m}}{\longrightarrow} \mathrm{O}_{2}+\mathrm{O} $$

Understanding Planck's equation is crucial to grasp how energy is quantized in the realm of quantum mechanics. This fundamental theory connects the energy of a photon, the most elementary particle of light, to its frequency and wavelength.

Planck's equation is mathematically expressed as:
\[E = h u = \frac{hc}{\lambda}\]
where:

• \(E\) stands for the energy of a photon,
• \(h\) represents Planck's constant, a crucial universal constant in quantum physics,
• \(u\) is the frequency of the photon,
• \(\lambda\) is the wavelength of the light,
• and \(c\) is the speed of light in a vacuum.

By using this equation, you can calculate the energy of a photon if you know its wavelength or frequency, and vice versa. This concept is pivotal in the study of not just theoretical physics but practical applications, including reaction wavelength estimation in chemistry.

Chemical bond energy refers to the amount of energy required to break a bond between two atoms in a molecule or the energy released when a bond is formed. It's a critical factor that influences how chemical reactions occur and is measured in kilojoules per mole (kJ/mol).

In chemical reactions, breaking bonds requires energy (endothermic process) and forming bonds releases energy (exothermic process). The overall energy change in a reaction is the difference between the energy needed to break the reactant bonds and the energy released upon forming product bonds.

For example, in the exercise provided, the energy change for the reaction involving ozone (\(O_3\)) is calculated by subtracting the energy of the bonds formed in the oxygen molecule (\(O_2\)) and atomic oxygen (\(O\)) from the energy required to break bonds in the ozone molecule. Understanding this helps one predict if a reaction will release heat to the surroundings or absorb it.

Reaction wavelength estimation is a practical application of Planck's equation in chemistry. It allows us to estimate the maximum wavelength of light needed to induce a chemical reaction. By calculating the difference in bond energies, which gives us the energy change (\(\Delta H\)) of the reaction, we can use Planck’s equation to find the exact wavelength capable of providing that amount of energy.

In the textbook exercise, we solve for the maximum wavelength (\(\lambda\)) by rearranging Planck’s equation to get:\[\Delta H = \frac{hc}{\lambda}\]
By substituting the calculated change in bond energy (\(\Delta H\)) and known constants for Planck's constant (\(h\)) and the speed of light (\(c\)), we find the wavelength that corresponds to the energy absorbed to cause the reaction. This is fundamental in fields like photochemistry, where light is used to initiate chemical reactions.