객관식
How much energy (in joules) is contained in 1.00 mole of 552 nm photons?
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9. Quantum Mechanics
The Energy of Light
객관식
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
검증된 단계별 안내1
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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