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 with enough energy to break carbon–carbon bonds?

Video transcript

Hello everyone. Today, we have the following problem, 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 kilojoules per mole to break what is the longest wavelength of radiation with enough energy to break carbon carbon bonds. So the first step with this is we need to find the energy of the photon in joules from the given energy. So we first start with our 348 kilojoules per mole. And we use the conversion factor of avogadro's number such that and we multiply this as well. We can say that one mole is equal to 6.022 times 10 to the 23rd photons. We then lastly will multiply this by the conversion factor to get from kilojoules to joules, one kilojoule is equal to 1000 joules. If we cross our units kilojoules cross out and solar malls such that we are left with 5.7 79 times 10 to the negative 19 joules per photon, then we have to manipulate the photon energy formula to get the wavelength and plug in the values. So that formula we have the energy of a photon is equal to planks constant multiplied by the speed of light all divided by the wavelengths. So if we manipulate this equation to solve for wavelengths, we get wavelengths is equal to that blinks constant times the speed of light divided by the change and the energy of a photon. And this will translate into the following. So planks constant is 6.626 times 10 to the negative 34 joules times a second. And we multiply that by the speed of light which is three times 10 to the 8 m per second. And then we divide that by that energy of that photon that we calculated for earlier in step one, which is 5.779 times 10 to the negative 19 joules per photon. We then are able to cancel out some of our units such that we can arrive at an answer of 3.44 times 10 to the negative 7 m or answer twice A. And with that, we have solved the problem overall, I hope it helped. And until next time.