Multiple Choice
How much energy (in joules) is contained in 1.00 mole of 552 nm photons?
9. Quantum Mechanics
The Energy of Light
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Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because these kinds of radiation carry enough energy to break bonds within the molecules. A typical carbon–carbon bond requires 348 kJ/mol to break. What is the longest wavelength of radiation that can break a carbon–carbon bond?
A
344 nm
B
346 nm
C
345 nm
D
343 nm
Verified step by step guidance1
Understand that the energy required to break a carbon-carbon bond is given as 348 kJ/mol. This energy corresponds to the energy of the radiation needed to break the bond.
Use the formula that relates energy and wavelength: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy per photon, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength in meters.
Convert the energy from kJ/mol to J/photon. Since 1 mole of photons contains Avogadro's number \( (6.022 \times 10^{23}) \) of photons, divide the energy in kJ/mol by Avogadro's number and convert kJ to J: \( 348 \text{ kJ/mol} = 348,000 \text{ J/mol} \).
Calculate the energy per photon: \( E_{\text{photon}} = \frac{348,000 \text{ J/mol}}{6.022 \times 10^{23} \text{ photons/mol}} \).
Rearrange the energy-wavelength formula to solve for wavelength: \( \lambda = \frac{hc}{E_{\text{photon}}} \). Substitute the values for \( h \), \( c \), and \( E_{\text{photon}} \) to find the longest wavelength that can break the carbon-carbon bond.
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