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.

검증된 단계별 안내

First, we need to understand that the energy of a photon is given by the equation E = h*c/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength.

Next, we need to convert the energy given in the problem from kJ/mol to J/photon. We know that 1 mol of photons contains Avogadro's number (6.022 x 10^23) of photons. So, we multiply the given energy by 1000 to convert from kJ to J, and then divide by Avogadro's number to convert from mol to individual photons.

Then, we substitute the energy value obtained in the previous step into the equation E = h*c/λ. We rearrange the equation to solve for λ, which gives us λ = h*c/E.

Now, we substitute the values of h, c, and E into the equation to calculate the wavelength. Remember to keep the units consistent.

Finally, the wavelength obtained will be in meters. To convert it to nanometers (which is a more common unit for wavelength), multiply the result by 1 x 10^9.

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주요 개념

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Energy and Wavelength Relationship

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This relationship indicates that higher energy photons correspond to shorter wavelengths, while lower energy photons correspond to longer wavelengths.

Visible Spectrum

The visible spectrum is the portion of the electromagnetic spectrum that can be detected by the human eye, typically ranging from about 380 nm (violet) to 750 nm (red). Understanding this range is crucial for determining the longest wavelength that can still trigger the conformational change in 11-cis-retinal, which is essential for vision.

Conformational Change in Molecules

Conformational change refers to the alteration in the shape of a molecule due to external stimuli, such as light. In the case of 11-cis-retinal, the absorption of a photon with sufficient energy causes it to change from a cis to a trans configuration, initiating a biochemical cascade that ultimately leads to vision.