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Multiple Choice
Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. A carbon-carbon bond requires 348 kJ/mol to break. What is the longest wavelength of radiation that can still break a carbon-carbon bond?
A
346 nm
B
345 nm
C
343 nm
D
344 nm
Verified step by step guidance
1
Understand that the energy required to break a carbon-carbon bond is given as 348 kJ/mol. This energy can be related to the wavelength of radiation using the equation: E = (hc)/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength.
Convert the energy from kJ/mol to J/photon. Since 1 mol contains Avogadro's number of molecules (6.022 x 10^23), the energy per photon is calculated by dividing the energy per mole by Avogadro's number: E_photon = (348,000 J/mol) / (6.022 x 10^23 molecules/mol).
Substitute the value of E_photon into the equation E = (hc)/λ to solve for the wavelength λ. Rearrange the equation to find λ: λ = (hc)/E_photon.
Substitute the known values for h, c, and E_photon into the equation to calculate the wavelength λ. Ensure that all units are consistent, particularly that energy is in joules and wavelength will be in meters.
Convert the wavelength from meters to nanometers by multiplying by 10^9, since 1 meter = 10^9 nanometers. This will give you the longest wavelength of radiation that can break a carbon-carbon bond.