The human eye contains a molecule called 11-cis-retinal that changes shape when struck with light of sufficient energy. the chan
ge in shape triggers a series of events that results in an electrical signal being sent to the brain. the minimum energy required to change the conformation of 11-cis-retinal within the eye is about 165 kj/mol. calculate the longest wavelength of light visible to the human eye. (avogadro's number is 6.022 x 1023 units/mole)
<span>725 nm
The energy needed for a single molecule to change will be the energy for a mole to change divided by avogadro's number, so
165000 / 6.022 x 10^23 = 2.74x10^-19 J
The energy of a photon is expressed as
E = hc/l
where
E = energy
h = Planck constant (6.626070040Ă—10^â’34 Js)
c = speed of light (299792458 m/s)
l = wavelength
Now solve for l
E = hc/l
El = hc
l = hc/E
Now substitute known values.
l = hc/E
l = 6.626070040Ă—10^â’34 Js * 299792458 m/s / 2.74x10^-19 J
I = 7.25x10^-07 m
l = 725 nm</span>
