The minimum energy required to change the conformation of 11-cis-retinal within the eye is about 164kJ/mol.
Calculate the longest wavelenght visible to the human eye
To calculate the longest wavelength visible to the human eye, we can use the relationship between energy and wavelength. The longest visible wavelength corresponds to the lowest energy color within the visible spectrum.
The formula relating energy and wavelength is:
E = hc/λ
where E is the energy of the photon, h is the Planck's constant (6.626 x 10^-34 J∙s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength of the light.
To find the wavelength corresponding to a given energy, we rearrange the formula:
λ = hc/E
Given that the minimum energy required to change the conformation of 11-cis-retinal is 164 kJ/mol, we need to convert it to joules per photon.
1 kJ/mol = 1000 J/mol
1 mol = 6.022 × 10^23 particles (Avogadro's number)
First, convert kJ/mol to J/mol and divide by Avogadro's number to get energy per photon:
Energy per photon = (164,000 J/mol) / (6.022 × 10^23 photons/mol)
Next, we substitute the values into the formula to find the longest wavelength:
λ = (6.626 x 10^-34 J∙s * 3.0 x 10^8 m/s) / Energy per photon
Now we can calculate the longest wavelength visible to the human eye.
E = hc/lambda
Change 164 kJ to J, then change to per photon (divide by 6.02 x 10^23). Solve for lambda.