What is the energy (in kJ) of one mole of photons of ultraviolet light with a wavelength of 85 nm? (LO 5.3) (a) 1.4 * 10-6 kJ (b) 1.4 * 103 kJ (c) 2.4 * 1014 kJ (d) 2.4 * 10-15 kJ

Video transcript

Hi everyone. This problem reads how much energy and kill a jules does one mole of photon of visible light possess. If it has a 450 nanometer wavelength. So the question that we want to answer here is energy and we want to answer the question of energy in relation to wavelength. So the equation that we're going to want to write out to solve this problem is energy is equal to Plank's constant times the speed of light over wavelength. Okay. And Plank's constant is represented by the number 6.626 times 10 to the negative 34 C is the speed of light. And this number is represented by three times 10 to the eighth and lambda is represented or it represents wavelength and we want this in m. Alright, so the wavelength that we're given is 450 nm. So let's go ahead and convert this to meters. In one nanometer, There is 10 to the -9 m. So our units of nanometers cancel. And we're left with units of meters. So when we do this calculation, our wavelength in meters is 4.5 times 10 to the negative seven m. Alright, so let's go ahead and plug these values into our equation so that we can calculate the energy. So we're going to get energy is equal to Plank's constant. So 6.6, 2, 6 times 10 To the -34. And we're going to multiply this by the speed of light three times 10 to the eight. And this is all over wavelength in nanometers. So this is over 54.5 times 10 to the negative seven m. So the energy we're going to get when we do this calculation Is 4.42 times 10 to the negative 19 jewels per photon. So this is the energy and jules per photon. But we want the energy and kill a jules. Okay? And this is and kill jules per one mole. Alright, So we need to go from jules per photon to kill a jules. So let's go ahead and do this conversion. All right. So in one mole We're going to write down avocados number. There is 6.022 times 10 to the 23 photons. Okay, that's how many photons are in one mole. So you see here that our unit of photon is going to cancel and we're left with unit of mole. So now we know jules per mole, but it asks us for the energy and kill a jules per mole. Okay, So we need to go from jewels to kill a jewels. So the conversion that we're going to use for this is in one kill a jewel Or let's do it in the same colour. We'll do this in red and one kill a jewel. There is 1000 jewels. All right. So we see here that Jules cancel and we're left and kill a jewel. So this is going to be the energy and kill a jules per mole. Alright, so let's go ahead and do this calculation. All right. So when we do this calculation, what we're going to get is the energy and killer jules is 266 killer jewels, and this is going to be our final answer. All right. This is how much energy and kill a jules, one mole of one mole of photon invisible light possesses. If it has a 450 nanometer wavelength, that is it for this problem. I hope this was helpful.