Excessive exposure to sunlight increases the risk of skin...

Excessive exposure to sunlight increases the risk of skin cancer because some of the photons have enough energy to break chemical bonds in biological molecules. These bonds require approximately $250-800 \mathrm{~kJ} / \mathrm{mol}$ of energy to break. The energy of a single photon is given by $E=h c / \lambda,$ where $E$ is the energy of the photon in $J, h$ is Planck's constant $\left(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right),$ and $c$ is the speed of light $\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right) .$ Determine which kinds of light contain enough energy to break chemical bonds in biological molecules by calculating the total energy in $1 \mathrm{~mol}$ of photons for light of each wavelength. (a) infrared light $(1500 \mathrm{nm})$ (b) visible light $(500 \mathrm{nm})$ (c) ultraviolet light $(150 \mathrm{nm})$

Excessive exposure to sunlight increases the risk of skin cancer because some of the photons have enough energy to break chemical bonds in biological molecules. These bonds require approximately $250-800 \mathrm{~kJ} / \mathrm{mol}$ of energy to break. The energy of a single photon is given by $E=h c / \lambda,$ where $E$ is the energy of the photon in $J, h$ is Planck's constant $\left(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right),$ and $c$ is the speed of light $\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right) .$ Determine which kinds of light contain enough energy to break chemical bonds in biological molecules by calculating the total energy in $1 \mathrm{~mol}$ of photons for light of each wavelength.
(a) infrared light $(1500 \mathrm{nm})$
(b) visible light $(500 \mathrm{nm})$
(c) ultraviolet light $(150 \mathrm{nm})$

Key Concepts

Electromagnetic Spectrum and Wavelength Dependence

The electromagnetic spectrum encompasses a variety of light types, each characterized by its wavelength. Different regions—such as infrared, visible, and ultraviolet—have distinct wavelengths and therefore different photon energies. Shorter wavelengths (like ultraviolet light) result in higher photon energies, which can exceed the energy required to break chemical bonds, while longer wavelengths (like infrared) produce lower photon energies.

Photon Energy Calculation

This concept involves using the equation E = hc/? to determine the energy of a single photon based on its wavelength. Here, h represents Planck’s constant and c represents the speed of light. This fundamental relationship in quantum mechanics links the wave nature of light to its particle-like energy characteristics, and it is crucial for understanding how electromagnetic radiation interacts with matter.

Avogadro's Number and the Mole Concept

When dealing with chemical processes, energies are often considered per mole rather than per individual photon. Avogadro's number (approximately 6.022 x 10^23) tells us how many particles (in this case, photons) are present in one mole. Multiplying the energy of a single photon by Avogadro's number converts the energy from a per-photon basis to a per-mole basis, which is essential for comparing photon energies with typical chemical bond energies.

Chemical Bond Energy

Chemical bonds, including those in biological molecules, require a certain threshold of energy to break, typically within the range of 250-800 kJ/mol. Understanding the energy required to disrupt these bonds is key in fields like photobiology and chemistry. Comparing the energy provided by one mole of photons at various wavelengths to these bond energies allows us to assess whether a particular type of light can cause bond dissociation, potentially leading to chemical changes or damage in biological systems.

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