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Ch.7 - Quantum-Mechanical Model of the Atom
Tro - Chemistry: A Molecular Approach 4th Edition
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTro 4th EditionCh.7 - Quantum-Mechanical Model of the AtomProblema 46
Capitolo 7, Problema 46

How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. γ-ray photons with a wavelength of 2.15×10–5 nm

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Identify the formula to calculate the energy of a photon, which is given by E = \(\frac{hc}{\lambda}\), where E is the energy of the photon, h is Planck's constant (6.626 x 10^{-34} J\(\cdot\) s), c is the speed of light in a vacuum (3.00 x 10^8 m/s), and \(\lambda\) is the wavelength of the photon.
Convert the given wavelengths from nanometers to meters for each type of photon. Recall that 1 nm = 1 x 10^{-9} m.
Substitute the values of h, c, and the converted wavelength (\(\lambda\)) into the formula E = \(\frac{hc}{\lambda}\) to calculate the energy of one photon for each type of radiation (X-ray and gamma-ray).
Since the question asks for the energy contained in 1 mol of photons, use Avogadro's number (6.022 x 10^{23} mol^{-1}) to find the total energy. Multiply the energy of one photon by Avogadro's number to get the energy per mole of photons.
Repeat the calculation for each type of photon (X-ray and gamma-ray) using their respective wavelengths to find the energy contained in 1 mol of each type of photon.

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Energy of Photons

The energy of a photon is directly related to its wavelength, described by 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. Shorter wavelengths correspond to higher energy photons, making this concept essential for calculating the energy contained in X-ray and gamma-ray photons.
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Photon Energy Formulas

Moles and Avogadro's Number

A mole is a unit that quantifies a substance, defined as containing Avogadro's number of entities, approximately 6.022 x 10²³. When calculating the total energy in 1 mole of photons, it is crucial to multiply the energy of a single photon by Avogadro's number to find the total energy for the mole.
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Moles and Particles Conversion

Wavelength and Frequency Relationship

The relationship between wavelength and frequency is given by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. Understanding this relationship is important because it allows for the conversion between wavelength and frequency, which can be useful when discussing the energy of photons in different contexts.
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Frequency-Wavelength Relationship
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