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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBrown 14th EditionCh.6 - Electronic Structure of AtomsProblema 31
Capitolo 6, Problema 31

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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Step 1: Identify the portion of the electromagnetic spectrum where the radiation is found. The wavelength of the radiation is given as 987 nm. This falls within the near-infrared (NIR) region of the electromagnetic spectrum, which ranges from about 800 nm to 2500 nm.
Step 2: Calculate the energy of a single photon. Use the formula E = hc/λ, where 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. Remember to convert the wavelength from nm to m by multiplying by 10^-9.
Step 3: Calculate the total number of photons absorbed by the detector. Divide the total energy absorbed by the energy of a single photon. This will give you the total number of photons absorbed.
Step 4: Calculate the number of photons emitted per second. Divide the total number of photons absorbed by the total time in seconds. This will give you the number of photons emitted per second by the laser.

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Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, arranged by wavelength or frequency. It includes gamma rays, X-rays, ultraviolet light, visible light, infrared radiation, microwaves, and radio waves. A wavelength of 987 nm falls within the infrared region, which is just beyond the visible spectrum, indicating that this radiation is not visible to the human eye but can be detected by specialized instruments.
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Electromagnetic Spectrum

Photon Energy

Photons are particles of light that carry energy, 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 the diode laser emitting at 987 nm, this equation allows us to determine the energy of a single photon. Understanding photon energy is crucial for calculating the number of photons emitted based on the total energy detected.
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Photon Energy Formulas

Photon Emission Rate

The photon emission rate refers to the number of photons emitted per unit time, typically expressed in photons per second. To find this rate, one can divide the total energy detected by the energy of a single photon and then divide by the time period over which the energy was measured. This concept is essential for quantifying the output of the laser in terms of its photon production, which is relevant in various applications, including telecommunications and medical devices.
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Gamma Emission
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