One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (b) What is the energy of a mole of these photons?

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First, understand that the energy of a photon can be calculated using the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength of the light.

Convert the given wavelength from nanometers to meters. Since 1 nm = \( 10^{-9} \) m, the wavelength \( \lambda = 325 \text{ nm} \) is equivalent to \( 325 \times 10^{-9} \text{ m} \).

Substitute the values of \( h \), \( c \), and \( \lambda \) into the energy equation: \( E = \frac{(6.626 \times 10^{-34} \text{ J s})(3.00 \times 10^8 \text{ m/s})}{325 \times 10^{-9} \text{ m}} \).

Calculate the energy of a single photon using the equation from the previous step. This will give you the energy in joules for one photon.

To find the energy of a mole of photons, multiply the energy of a single photon by Avogadro's number \( (6.022 \times 10^{23} \text{ mol}^{-1}) \). This will give you the energy in joules per mole of photons.

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주요 개념

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Photon Energy

Photon energy is the energy carried by a single photon, which can be calculated using the equation E = hc/λ, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. For UV light at 325 nm, this formula allows us to determine the energy of individual photons.

Mole Concept

The mole is a fundamental unit in chemistry that quantifies the amount of substance. One mole contains Avogadro's number of entities, approximately 6.022 x 10^23. When calculating the energy of a mole of photons, we multiply the energy of a single photon by Avogadro's number to find the total energy associated with that quantity of photons.

Wavelength and Energy Relationship

The relationship between wavelength and energy is inversely proportional; as the wavelength decreases, the energy of the photon increases. This principle is crucial in understanding electromagnetic radiation, including UV light. Shorter wavelengths, like 325 nm, correspond to higher energy photons, which can have significant biological effects, such as causing sunburn.