Final answer:
To calculate the maximum wavelength of light for which a carbon-carbon double bond could be broken, divide the energy of the bond by Avogadro's number to get the energy per photon. Use the formula E = hc/λ, rearrange it to solve for λ, and plug in the values to calculate the wavelength. The maximum wavelength of light for which a carbon-carbon double bond could be broken is 194.6 nm.
Step-by-step explanation:
To calculate the maximum wavelength of light for which a carbon-carbon double bond could be broken by absorbing a single photon, we need to calculate the energy of the photon needed to break the bond. The given energy to break a carbon-carbon double bond is 614 kJ/mol. To convert this energy to Joules per photon, we divide it by Avogadro's number (6.022 x 10^23) to get 1.019 x 10^-21 J/photon. Using the formula 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 (2.998 x 10^8 m/s), and λ is the wavelength, we can rearrange the formula to solve for λ. Plugging in the values, we get λ = hc/E = (6.626 x 10^-34 J*s * 2.998 x 10^8 m/s) / (1.019 x 10^-21 J) = 1.946 x 10^-7 m or 194.6 nm. Rounding to 3 significant digits, the maximum wavelength of light for which a carbon-carbon double bond could be broken is 194.6 nm.