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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Textbook Question

An AM radio station broadcasts at 1000 kHz and its FM partner broadcasts at 100 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.

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Textbook Question

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

Textbook Question

One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (c) How many photons are in a 1.00 mJ burst of this radiation?

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Textbook Question

One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (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.

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Textbook Question

The energy from radiation can be used to rupture chemical bonds. A minimum energy of 192 kJ/mol is required to break the bromine–bromine bond in Br2. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

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