NOTE: The given question is incomplete.
The complete question is given below.
The human eye contains a molecule called 11-cis-retinal that changes conformation when struck with light of sufficient energy. The change in conformation 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 164 kJ/mole. Calculate the longest wavelength visible to the human eye.
Solution:
Energy (E) = 164 kJ/mole
E = 164 kJ/mole = 164 kJ /6.023 x 10²³
= 2.72 x 10⁻²² kJ = 2.72 x 10⁻¹⁹J
Planck's constant = 6.6 x 10⁻³⁴ J s,
Speed of light = 3.00 x 10⁸ m/s
Let the required wavelength be λ.
Formula Used: E = hc / λ
or, λ = hc / E
or, λ = (6.6 x 10⁻³⁴ J s)× (3.00 x 10⁸ m/s) / (2.72 x 10⁻¹⁹J)
or, λ = 7.28 x 10⁻⁷ m
or, λ = (7.28 x 10⁻⁷ m) ×( 1.0 x 10⁹ nm / 1.0 m)
or, λ = (7.28 x 10² nm)
or, λ = 728 nm
Hence, the required wavelength will be 728 nm.
