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Ch.7 - Quantum-Mechanical Model of the Atom
Chapter 7, Problem 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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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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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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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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