A 5.00-mL ampule of a 0.100-M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 12.3 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Video transcript

welcome back everyone In this example we have a 10 millimeter solution of 100.5 molar benzene which absorbs light and releases 10.5 jewels of light with a wavelength of 300 nanometers. We need to calculate the percentage of benzene molecules that release the light here. So we want to go ahead and recognize that because we're given volume as well as more clarity. We're going to recall that polarity can be interpreted as moles per leader. And we want to begin our solution by finding our number of our total number of benzene molecules. So C6 age six molecules So beginning with that unit for volume were given 10 ml. And we want to recall that our prefix milli tells us that we have 10 to the negative third power leaders for our base unit of our base unit from our one middle leader. And so we're able to cancel our units. Middle leaders were left with leaders and next we can focus on incorporating that polarity term from the prompt which tells us that we have for one liter of solution, 0.500 molds of benzene. So this allows us to cancel out leaders. Now moving from molds of benzene. We want to get into our final unit being molecules of benzene. And so we would want to recall that we can use avocados number. So that tells us that for one mole of our benzene We have the quantity 6.022 times 10 to the 23rd power molecules of benzene. And so this allows us to cancel out moles of benzene leaving us with molecules of benzene as our final unit. And in our calculators we're going to get a value equal to 3. times 10 to the 20th power molecules. So moving on in our solution, now that we have our total number of benzene molecules, we want to figure out our energy per benzene molecule and this is specifically our energy of the photons of light emitted from these benzene molecules. And so we should recall that we're going to utilize the energy for a photon formula, which we will call is equal to Planck's constant, multiplied by the speed of light and divided by our wavelength represented by lambda. And we're actually given our wave length here equal to 300 nanometers. So we're going to incorporate this information below and we would say that our energy of our photon is equal to in our numerator. We recall that plank's constant is 6.626 times 10 to the negative 34th power units of jewels, time seconds per molecule. And then this is then going to be multiplied by our speed of light, which we should recall is 3.0 times 10 to the eighth power units of meters per second in our denominator. We're going to go ahead and plug in that given wavelength in the prompt as 300 nanometers, which we should recall, we need to convert to meters because we have meters in our numerator. And so we need that to cancel out. So we would recall that our prefix nano tells us that we have 10 to the negative ninth power meters from one nanometer. This allows us to cancel out nanometers, leaving us with meters in the denominator. Which we can then cancel out with meters in the numerator. And we can also get rid of seconds in the numerator. And this leads us with jewels per molecule as our final unit for energy, which is what we want. So in our calculators we're going to get a value for the energy per benzene molecule Equal to 6. times 10 to the negative 19th powered jewels per molecule. And so now that we have the energy emitted from each benzene molecule, we want to calculate the percentage here. So the percentage of benzene molecules that emit like. And so we would take our total number of molecules which we calculated above as 3.011 times 10 to the 20th power molecules. And we're going to multiply this by the total energy emitted from these molecules. So that above we calculated as 6.62, 6 times 10 to the negative 19th power jewels per molecule. This allows us to cancel out our units of molecules leaving us with jewels. And this gives us our total energy of 199. jules. So just to avoid confusion will color code this accordingly because above it was blue. So we have 3.11 times 10 to the 20th power molecules of benzene which we canceled out here. So now we have our total energy and we can use that to find our percent of benzene that emits light. So our percent of bending molecules that emit light would be found by taking the energy of light emitted from the prompt given as 10. jewels of light. And we would divide this by our total energy which above we found as 199.51 jewels of energy. So we're then going to take this entire quotient and because we need this to be a percentage, we want to multiply by 100%. So this gives us our value for the percentage of benzene molecules that emit light equal to a value of 5.26%. So this would actually complete this example as our final answer for the percent of benzene molecules that emit light. So I hope that everything that I explained was clear. If you have any questions, please lead them down below and I will see everyone in the next practice video