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In: Physics

A dye molecule has electrons that are free to travel up and down a chain of...

A dye molecule has electrons that are free to travel up and down a chain of atoms, giving electron energy states that are given by the particle-in-a-box model, with En=(0.34eV)n2. What are the three longest wavelengths of visible light that the molecule will absorb?

Expert Solution

The visible spectrum of light range from 380nm to 740 nm.

Energy states for particle in a box is given by :

Let n₁= 1

hc = 1240 nm eV

n₂² = 2.016/ 0.34 = 6.194

n₂= 2.488

So to find the longest wavelength,

let n₂ = 3 and n₁ =2

0.34 ( 9-4) = 1240 /

1.7= 1240/

= 729.411 nm= this is the longest wavelength absorbed in visible light.

Similarly we can calculate wavelength for (b) n2 = 4 and n1 =3 = 521 nm

(c) n2 =5 and n1 = 4 = 405.288 nm

genius_generous answered 4 months ago

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