Calculate the energies of the following waves in kilojoules per mole, and tell which member of each pair has the higher value. (a) An FM radio wave at 99.5 MHz and an AM radio wave at 1150 kHz

Video transcript

Hi everyone. This problem reads calculate the respective energies and kill a joules per mole of two lamps at 1875 gigahertz and 857 terror hurts. And identify which lamp has higher energy. So the two things that we want to calculate here are the respective energies and kill a jules per mole for each of the lamps. And then we want to identify which lamp has the higher energy. Okay, So we're going to write down the equation that relates energy with frequency. Okay. And that equation is energy is equal to Plank's constant times frequency. Okay. And the problem is asking us to calculate the respective energies and kill a jules per mole for each lamp. So what we're going to need to do is H represents Plank's constant and Planck's constant is six point Times 10 to the -34. And the represents frequency. So in this problem we're told what the frequencies are but we're going to want to convert these frequencies to hurts. Okay, so let's go ahead and do that. Alright, so for our first frequency we're told that so we'll write this one is V one and this one is V two. Okay, so V one we're told is gigahertz. Okay, so we want to go from gigahertz to hurts. Alright, so the conversion that we're going to use for this is in one gigahertz. There is 10 to the nine hertz. Okay, so our gigahertz cancels and we're left. And units of hurts. Alright, so this is going to equal 1. times 10 to the 12 hurts. Okay. And For V two we have 857 Terror hurts. So we want to go from Terror hurts to hurts. Okay, so we're going to write that our conversion is in. Let's see. We have 850 terror hurts and one terror hurts. There is 10 to the 12 hertz. Okay, So our value is going to be 8.57 times 10 to the hurts. All right. So let's go ahead and calculate the energy and kill a jewels for our first lamp. Okay, so we'll go ahead and write E one which is our energy for first one is going to equal plank's constant, which is 6.626 Times to the negative 34 jewel seconds times 1.875 Times 10 to the 12 Hz. All right. So what we're going to get for our energy Is 1. 2375 times To the negative 21 jules per photon. Okay, and the question asks us for the energies and kill a jules per mole. So we want to go from jules per photon to kill a jewels per mole. So what we're going to do here is we're first gonna go from, you were gonna use the conversion for photons to moles. Okay, so in one more Avocados number tells us we have 6.02, 2 times 10 to the photons. Okay? And we want to go from jewels to kill a jewels And one kill a jewel. There is 1000 jewels. So let's just make sure our units cancel properly here. Our jewels cancel and photons cancel. And we wanted our energy and kill a jewels per mole. And as you can see here, we have units of joules per mole. So let's go ahead and do this calculation. And when we get when we do this calculation, we're going to get the energy for our first lamp. Our energy for a lamp at 1875 gigahertz is equal to 0. kg joules per mole. Okay, so that is our first energy. So this is the energy for the lamp at gigahertz. Alright, so let's go ahead and highlight this as our answer for the energy for the first lamp, let's go ahead and do the same thing. But for the energy of our second lamp. All right, so for our second lamp will say you too, and we can do this in a different color. So, our energy for a second lamp is going to equal plank's constant, which is 6.626 times 10 to the negative 34 jewels, times seconds times the frequency. So our frequency for our second lamp is 8.57 times 10 to the hertz. Okay, so when we do this calculation, the energy that we're going to get and jewels per Fulton is 5. 5. times 10 to the negative jewels per photon. Okay, and we want to go from jules per photon to kill a jules per mole. So let's go ahead and do that calculation. And one mole There is using avocados number 6.022 times 10 to the 23 photons. And we want to go from jewels to kill a jewels and one killer jewel there is 1000 jewels. So making sure our units cancel, jewels cancel and photons cancel. And we're left with units of kilo joules per mole. So let's go ahead and do this calculation. And when we do this calculation we're going to get the energy is equal to 342 kg joules per mole for the lamp that is at 857. Terror hurts. Alright, so we'll go ahead and highlight this As the energy for that. And the last question asked us to identify which lamp has a higher energy. Okay, so our lamp at 857 terror hurts which is the one we just calculated has the higher energy. Okay, so let's go ahead and highlight that. So we just answered the questions for this problem. The respective energies and kill a joules per mole for the two lamps and which lamp has the higher energy? That is it for this problem? I hope this was helpful.