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

Brown 14th Edition

Ch.6 - Electronic Structure of Atoms

Problema 26b

Capitolo 6, Problema 26b

(b) What is the energy of one of these photons?

Guida verificata passo dopo passo

insert step 1> Identify the formula to calculate the energy of a photon, which is given by the equation: E = h \(\cdot\) f, where E is the energy of the photon, h is Planck's constant (6.626 \(\times\) 10^{-34} \(\text{ J}\) \(\cdot\) \(\text{s}\)), and f is the frequency of the photon.

insert step 2> If the frequency (f) is not provided, use the relationship between frequency and wavelength: c = \(\lambda\) \(\cdot\) f, where c is the speed of light (3.00 \(\times\) 10^8 \(\text{ m/s}\)) and \(\lambda\) is the wavelength. Rearrange this equation to solve for frequency: f = \(\frac{c}{\lambda}\).

insert step 3> Substitute the value of the wavelength (\(\lambda\)) into the equation from step 2 to find the frequency (f) of the photon.

insert step 4> Substitute the calculated frequency (f) from step 3 into the energy equation from step 1: E = h \(\cdot\) f.

insert step 5> Calculate the energy (E) using the values of Planck's constant (h) and the frequency (f) obtained in the previous steps.

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Photon Energy

Photon energy is the energy carried by a single photon, which is a quantum of electromagnetic radiation. It is directly proportional to the frequency of the radiation and inversely proportional to its wavelength. The energy can be calculated using the formula E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the photon.

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Photon Energy Formulas

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is a key component in the equation E = hν, where it provides the proportionality factor that allows for the conversion between the frequency of electromagnetic radiation and its energy. Understanding this constant is essential for calculating photon energy.

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Photons and Planck's Constant

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Each type of radiation has a specific wavelength and frequency, which determines its energy. Understanding where a photon falls within this spectrum is crucial for determining its energy, as different regions correspond to different energy levels.

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Electromagnetic Spectrum

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(b) Calculate the energy of a photon of radiation whose wavelength is 413 nm.

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