One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (d) These UV photons can break chemical bonds in your skin to cause sunburn—a form of radiation damage. If the 325-nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in kJ>mol.

Video transcript

Hey everyone in this example, we are told that UV light is used to initiate radical reactions in organic chemistry for a hydrochloric acid molecule. The quanta of UV light is used to break the bond between the chlorine atom and the hydrogen atom. We have to assume that one photon of UV light with a wavelength of 280. nanometers can break one hydrochloric acid bond and calculate the bond energy and kilo jewels Permal. So we should recall that our formula for energy of a photon is equal to a value of or equal to the formula where we take plank's constant. We're going to multiply that by the speed of light and we're going to divide by our wavelength. So calculating for our energy of a photon, we would get that energy is equal to Planck's constant, which we should recall is 6.626 times 10 to the negative 34th power in units of jewels, times seconds. We're multiplying by the speed of light, which we recall is 3.0 times 10 to the eighth power meters per second. And then in our denominator, we're going to plug in our wavelength given in the prompt as 280.4 nanometers. We want to go ahead and be able to cancel out meters in our numerator. So we're going to convert this wavelength from nanometers two m. By recalling that in one nanometer we have 10 to the negative ninth power meters. So now we're able to get rid of nanometers as well as meters. And we can also cancel out seconds with inverse seconds here, leaving us with jewels as our final unit for our energy. So what we're going to get is that our energy is equal to a value of 7.0 nine times 10 to the negative 19th power. And we're left with units of jewels. But this is interpreted as jewels per photon of our UV light. So we're going to use this energy of our photons to find our bond energy of the Or of breaking the hydrogen chlorine single bond by starting out with our value calculated above. So we have 7.09 times 10 to the negative 19th power jewels per photon. And we're going to recall that this is applicable to avocados number which we can use as a conversion factor so that we have units of moles as our final answer. Rather kilograms per mole as stated in the prompt. So to get moles in the picture, we're gonna use avocados number, which we would recall Is 6.02, 2 times 10 to the 23rd power in this case we're going to interpret it as bonds per more. So for one more and now we're going to go ahead and as you notice we can actually interpret our photons as bonds. So jules per bond so that our bond unit can cancel out. And for our last conversion factor we need to get kayla jewels in our setup. So we're going to recall that we have 10 to the third power jewels equal to one kg jule. And so now we're able to get rid of our units of jewels. We're also able to get rid of bond and we're left with kayla jules Permal as our final units, which is what we want according to the prompt. So what we're going to get for our bond energy is a value equal to 427 kayla jewels per more. And this is the bond energy to break the hydrogen chlorine single bond. So this would be our final answer to complete this example. I hope that everything I went over was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.