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To understand the energy of a single photon, we make use of Planck's equation. This fundamental equation allows us to calculate the energy of a photon based on its wavelength and is given by:\[ E = \frac{h \cdot c}{\lambda} \]Where:- \( E \) is the energy of the photon.- \( h \) is Planck's constant, valued at \( 6.626 \times 10^{-34} \text{Js} \), a fundamental constant in physics.- \( c \) is the speed of light, approximately \( 2.998 \times 10^8 \text{m/s} \).- \( \lambda \) is the wavelength of the radiation in meters.This equation tells us that as the wavelength \( \lambda \) decreases, the energy \( E \) of a photon increases. For ultraviolet light with a short wavelength of 25 nm, which is equivalent to \( 25 \times 10^{-9} \text{m} \), the energy is relatively high. This high energy is what makes UV photons capable of inducing mutations in DNA.

Avogadro's number is a fundamental concept in chemistry that allows us to relate the small world of atoms and molecules to the macroscopic quantities we deal with in daily life. Avogadro's number is approximately \( 6.022 \times 10^{23} \) and represents the number of atoms, ions, or molecules in one mole of a substance.

Application in Photon Energy Calculation

When you want to calculate the energy of not just one photon, but a whole mole of photons, Avogadro's number becomes essential. By multiplying the energy of a single photon by Avogadro's number, you obtain the total energy of a mole of photons, which is especially useful in practical applications where handling individual photons isn't feasible.In the context of UV-light, knowing the energy per mole of photons helps in understanding how much energy is involved in processes like DNA mutations.

Understanding the wavelength of light is crucial for calculations involving photon energy. The wavelength \( \lambda \) is the distance over which the light wave's shape repeats, typically expressed in meters, nanometers, or angstroms.

Converting Wavelength Units

In scientific calculations, it's essential to convert units consistently. For UV light, you might be given the wavelength in nanometers (nm), like 25 nm. Since Planck's equation requires meters, convert this by recognizing that 1 nm equals \( 10^{-9} \text{m} \). Thus, 25 nm becomes \( 25 \times 10^{-9} \text{m} \).Knowing how to switch between different units of measurement ensures accuracy in energy calculations and helps unlock a deeper understanding of how light's properties affect its interactions with matter.