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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주요 개념

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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.

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.

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.

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