What is the energy of each of the following photons in kilojoules...

Question

What is the energy of each of the following photons in kilojoules per mole?
(a) v = 5.97 * 1019 s-1
(b) v = 1.26 * 106 s-1 
(c) <lamba> = 2.57 * 102 m

Accepted Answer

Hello everyone. So you're the falling problem, calculate the energy and calories per mole of each of the following photons given either the frequency or the wavelength. So first we need to recall our photon energy formula which is the energy being equal to Planck's constant times V. Or the frequency in seconds raise to the power of negative one. So with our first photon we are being given our The or the frequency. So we have our 1.6 times 10 to the 14th seconds, raise the power of -1. We're going to recall our formula here, I think we're going to plug in our values. So the energy is going to be able to plank's constant which can be found in a reference text which is 6.626 times 10 raised to the power of negative 34 jewels times seconds. And then of course we're gonna multiply by our frequency which is 1.6 times 10 to the 14th seconds raised to the power of negative one. And of course we have to have our answer in terms of killing jewels. So we'll need to use a conversion factor. That one kg joule is equal to 10 to the third jewels. And then lastly we also need moles. So we're gonna use the conversion factor, that one mole is equal to six point oh two times 10 to the 23rd. And this can be adam's particles or molecules that really just depends on what you're working with. And so because it didn't specify, we'll just leave it at that and this is gonna give us an energy of 63.8 kg joules per mole. And so this is going to be our first answer. Next. We have been given 2.34 times 10 to the 14th seconds raised to the power of -1. As before. We're going to use our formula here where we have planks constant, we're gonna plug in our frequency which was 2.34 times 10 to the fourth seconds raised to the power of negative one. We're gonna do the following. Use the conversion factor that one kg joules equal to 10 to the third jewels. And then our last conversion because we need this in molds as well, avocados number When our units cancel, we're left with an energy level of 93.4 kg joules per mole. And lastly we have 1.09 times 10 to the negative six m. Now, this is actually not going to be the frequency. This is going to be our wavelength. So we're going to use this formula once again that the energy is equal to Planck's constant times the frequency. However, we're going to substitute what our frequency could be broken down into further more. So our frequency or V can be found by saying that, or the frequency is equal to r C, which is the speed of light over our wavelength. So we're going to rewrite this to say that the energy level is equal to Planck's constant times our speed of light divided by our wavelength. And so we're going to plug this in. We have our planks constant. Then we're going to have our speed of light, which is three times 10 to the eighth meters per second. And this can be found in the reference text as well, divided by the wavelength, which is 1.9 times 10 to the negative six m As before. We're gonna use the conversion factor, that one kg is equal to 10 to the third jewels. And then our Alejandro's number for the moles over one mole. And then when we solve this, we're going to get 110 kg joules per mole. And so with that we have solved this problem overall, I hope this helped. And until next time.

What is the energy of each of the following photons in kilojoules per mole? (a) v = 5.97 * 1019 s-1 (b) v = 1.26 * 106 s-1 (c) = 2.57 * 102 m

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