One type of sunburn occurs on exposure to UV light of...

One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 $\mathrm{nm} .$ (a) What is the energy of a photon of this wavelength? (b) What is the energy of a mole of these photons? (c) How many photons are in a 1.00 $\mathrm{mJ}$ burst of this radiation? (d) These UV photons can break chemical bonds in your skin to cause sunburn-a form of radiation damage. If the 325 -nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in kJ/mol.

One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 $\mathrm{nm} .$ (a) What is the energy of a photon of this wavelength? (b) What is the energy of a mole of these photons? (c) How many photons are in a 1.00 $\mathrm{mJ}$ burst of this radiation? (d) These UV
photons can break chemical bonds in your skin to cause sunburn-a form of radiation damage. If the 325 -nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in kJ/mol.

Key Concepts

Planck's Relation (E = hc/?)

This fundamental concept in quantum mechanics states that the energy of a photon is directly proportional to the frequency of the light and inversely proportional to its wavelength. It uses constants such as Planck's constant and the speed of light to quantify the discrete packets of energy carried by electromagnetic radiation.

Avogadro’s Number and the Mole Concept

This principle connects the microscopic world of atoms and photons to the macroscopic scale by defining a mole as a specific number of entities (Avogadro’s number). It is essential for converting the energy associated with a single photon to the energy contained in a mole of photons, bridging quantum mechanics with bulk material properties.

Energy Conversion and Unit Analysis

Proper energy calculations require converting between different units (such as nanometers to meters and Joules to kilojoules) to ensure consistency across calculations. This concept underpins accurate measurement and computation in physical sciences, connecting theoretical models to real-world phenomena.

Photochemical Bond Breaking and Chemical Bond Energy

This concept explains how photons of sufficient energy can break chemical bonds by transferring energy to molecular bonds. It is crucial for understanding processes like radiation damage and other photochemical reactions, where the energy of light is directly related to the chemical changes in materials.

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