Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 29d

Chapter 6, Problem 29d

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.

Verified step by step guidance

Convert the wavelength of UV light from nanometers to meters by multiplying by \(10^{-9}\).

Use the speed of light (\(c = 3.00 \times 10^8 \, \text{m/s}\)) and Planck's constant (\(h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s}\)) to calculate the energy of a photon with the given wavelength using the formula \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of the photon and \(\lambda\) is the wavelength.

Convert the energy of the photon from joules to kilojoules by multiplying by \(10^{-3}\).

Calculate the energy per mole of photons by using Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}\)). Multiply the energy of one photon by Avogadro's number to get the energy per mole.

The result from the previous step gives the average energy of the chemical bonds in the skin in kJ/mol, which is the energy required to break them.

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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, c is the speed of light, and λ is the wavelength. For UV light at 325 nm, this relationship allows us to determine the energy of the photons responsible for breaking chemical bonds in skin.

Chemical Bond Energy

Chemical bond energy refers to the amount of energy required to break a bond between two atoms in a molecule. This energy is typically expressed in kJ/mol and varies depending on the type of bond. Understanding this concept is crucial for estimating the average energy of bonds that UV photons can break, as it directly relates to the energy provided by the photons.

Conversion of Energy Units

When calculating energy in chemistry, it is often necessary to convert between different units, such as joules and kilojoules. Since the energy of photons is typically calculated in joules, converting this value to kJ/mol involves using Avogadro's number to account for the number of particles in a mole. This conversion is essential for expressing the energy of chemical bonds in a standard format.

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Textbook Question

A stellar object is emitting radiation at 3.0 mm. (a) What type of electromagnetic spectrum is this radiation (b) If a detector is capturing 3.0 3 108 photons per second at this wavelength, what is the total energy of the photons detected in 1 day?

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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. (b) What is the energy of a mole of these photons?

Textbook Question

Molybdenum metal must absorb radiation with an energy higher than 7.22 * 10-19 J ('energy threshold') before it can eject an electron from its surface via the photoelectric effect. (a) What is the frequency threshold for emission of electrons?

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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

A diode laser emits at a wavelength of 987 nm. (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How many photons per second are being emitted by the laser?

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