Calculate the longest wavelength visible to the human eye. express the wavelength in nanometers to three significant figures.

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.

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