Ch.6 - Electronic Structure of Atoms

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problem 29c

Chapter 6, Problem 29c

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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Convert the energy of the burst from millijoules to joules. Remember that 1 mJ = 0.001 J.

Calculate the energy of a single photon using the formula: \( E = \frac{hc}{\lambda} \), where \( h \) 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 in meters (325 nm = 325 \(\times\) 10^{-9} \(\text{ m}\)).

Determine the number of photons by dividing the total energy of the burst by the energy of a single photon: \( \text{Number of photons} = \frac{\text{Total energy}}{\text{Energy per photon}} \).

Ensure all units are consistent, particularly energy in joules and wavelength in meters, to maintain dimensional accuracy.

Perform the division to find the number of photons, ensuring to keep track of significant figures based on the given data.

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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 determined by 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. For UV light at 325 nm, this relationship allows us to find the energy of a single photon.

Conversion of Units

In chemistry, it is essential to convert units appropriately to ensure consistency in calculations. In this case, the energy burst of 1.00 mJ must be converted to joules (1 mJ = 0.001 J) to match the units used in the photon energy equation. This step is crucial for accurately determining the number of photons in the given energy burst.

Calculating Number of Photons

To find the number of photons in a given energy burst, divide the total energy by the energy of a single photon. This is expressed mathematically as N = E_total / E_photon, where N is the number of photons, E_total is the total energy in joules, and E_photon is the energy of one photon calculated from its wavelength. This calculation provides insight into the quantized nature of light.

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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. (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

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

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

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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