The human eye contains a molecule called 11-cis-retinal that changes shape when struck with light of sufficient energy. The change in shape triggers a series of events that results in an electrical signal being sent to the brain that results in vision. The minimum energy required to change the conformation of 11-cis-retinal within the eye is about 164 kJ/mol. Calculate the longest wavelength visible to the human eye.

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All right. Hello everyone. So this question says that the human eye contains a molecule called 11 cis retina that changes shape when struck with light of sufficient energy. The change in shape triggers a series of events that results in an electrical signal being sent to the brain that results in vision, the minimum energy required to change the confirmation of 11 cysts right now within the eye is about 164 kg jules per month, calculate the longest wavelength visible to the human eye. And here we have four different answer choices labeled A through D proposing different wavelengths in units of meters. So let's go ahead and get started right? Because we're discussing a correlation between light and energy. We're going to have to use the photon energy formula to find the wavelength for this question. No, with that in mind, recall that the photon energy formula is as follows deltic E is equal to HC divided by lambda. Now delta E refers to the energy of the photon in units of joules per photon H is planks constant or 6.626 multiplied by 10 to the power of negative 34 dual seconds. Whereas C is the speed of light or approximately 3.00 multiplied by 10 to the power of 8 m per second. And lambda would be the wavelength in units of meters. But before we can go ahead and solve for the wavelength, we have to know what the value of delta E happens to be. And so before we can go ahead and use the photon energy formula, we have to first find what delta E is in units of jules per photon. And in this case, we can use the energy value provided which is 164 kilojoules per mole. So let me go ahead and move this formula off to the side. So I can use the right side of the screen for the other calculation or actually let me go ahead and scroll down so I can do that first calculation. All right. So in this case, we're going to go ahead and start off by taking our energy. That's 164 kilo jules per more and converting this number so that it's expressed in units of tools per photon. So not only are we going from kilo jewels to jewels, we're going from moles to individual photons. Now recall that we can use avogadro's number to convert moles into individual units. In other words, atoms, molecules, ions or photons in this case. So that's what we're going to do. First, I'm going to start with my 164 kilo jules per more. And I'm going to use Avogadro's number to go from moles to photons. Now, Avogadro's number states that one mole is equal to 6.022 multiplied by 10 to the 23rd bots. Now, to be more specific, I could say particles because the same relationship applies for atoms, molecules, ions, et cetera. But in this case, we're talking about photons. So that's the terminology that I'm going to use. But with that being said, we can use Avogadro's number as a conversion factor in our calculations. So in my conversion factor, I'm going to go ahead and treat it as a fraction and recall that the idea when using conversion factors is to cancel out your starting units. So here because I'm trying to go from moles to photons, I need to cancel out my units of moles. So in this case, in my starting value, right, my 164 kg joules per mole for my energy moles are in the denominator. This means that in my conversion factor, moles should be in the numerator to make sure they cancel out. And so Avogadro's number would be in the denominator and this ensures that moles cancel out. Now at this point, my answer would be in units of kilojoules per photon. So I need one more conversion factor to convert from kilojoules into jewels. Now recall that 1 kg jewel is equal to 1000 jules. So I'm going to use this relationship to cancel out units of kilojoules and leave my answer in units of jewels per photon. So Jules would go in the numerator of my conversion factor which allows kilo jewels to cancel out. So after I go ahead and evaluate this number, our energy is equal to 2.72 335 multiplied by 10 to the power of negative 19 jewels per photon. Now, at this point in the process, I'm keeping my value for the energy ungrounded to make my next calculation as accurate as possible. Because recall that this value in units of joules per photon is delta E in the photon energy formula. So our next step is to use the photon energy formula to calculate the value of lambda or the wavelength. So let me scroll down one more time. Now, in this case, we're going to have to rearrange the photon energy formula. So that Lambda is by itself on one side of the equation because that is the value that we're solving for. So here when I rearrange this equation, I get that lambda is equal to HC divided by delta E. So now let's go ahead and plug in our information. So LAMBDA is equal to HC divided by delta E. So H was planks constant multiplied by the speed of light and then divided by the value that we just calculated or delta E in units of joules per photon. So solving for this expression and rounding to three significant figures are value for lambda becomes 7.30 multiplied by 10 to the power of negative 7 m. Because at this point, all units except for meters have canceled out. And so our final answer is 7.30 multiplied by 10 to the power of negative 7 m. And this number corresponds to option C in our multiple choice. So option C is our answer and there you have it. So with all of that being said, if you watch this video until the end, thank you very much. I appreciate it. And I hope you found this helpful.

Verified Solution

Key Concepts

Energy and Wavelength Relationship

Visible Spectrum

Conformational Change in Molecules