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?

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Understand the relationship between wavelength and energy. The energy of a photon can be calculated using the formula: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy, \( h \) 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.

Convert the wavelength from nanometers to meters. Since 1 nm = \( 10^{-9} \) m, the wavelength \( \lambda = 325 \text{ nm} \) can be converted to meters as \( 325 \times 10^{-9} \text{ m} \).

Substitute the values into the energy formula: \( E = \frac{(6.626 \times 10^{-34} \text{ J s})(3.00 \times 10^{8} \text{ m/s})}{325 \times 10^{-9} \text{ m}} \).

Perform the calculation by multiplying Planck's constant \( h \) and the speed of light \( c \), then divide by the wavelength \( \lambda \) in meters.

The result will give you the energy of a single photon in joules. This energy represents the amount of energy carried by a photon with a wavelength of 325 nm.

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Key Concepts

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

Photon Energy

The energy of a photon is directly related to its wavelength and 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. This relationship shows that shorter wavelengths correspond to higher energy photons.

Wavelength and Frequency Relationship

Wavelength and frequency are inversely related properties of electromagnetic radiation. The relationship is described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν (nu) is the frequency. As the wavelength decreases, the frequency increases, which in turn affects the energy of the photon.

Ultraviolet (UV) Radiation

Ultraviolet radiation is a type of electromagnetic radiation with wavelengths shorter than visible light, typically ranging from about 10 nm to 400 nm. UV radiation is divided into three categories: UVA, UVB, and UVC, with varying effects on biological systems, including the potential to cause sunburn and skin damage due to its higher energy compared to visible light.

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Textbook Question

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?

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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