Question

What is the wavelength and color of light emitted in an ECL experiment in which the redox potential associated with the HOMO is 1.5 V and that associated with the LUMO is -0.9 V? The experiment is conducted in a non-aqueous solution.

Short answer

The wavelength of light is 517 nm, and the color of the light is green in an ECL experiment.

Step-by-step solution

The concept

Photon energy is related to wavelength by

$\begin{array}{l}\text{E=h}\upsilon \text{or}\\ \text{E=}\frac{\text{hc}}{\text{λ}}\end{array}$

Here,

$\text{λ}$is the wavelength.

h is the Planks constant.

c is the speed of light.

The energy band gap.

Given data;

Redox potential of HOMO = 1.5 V

Redox potential of LUMO = -0.9 V

The below expression gives theenergy band gap;

$\text{E=E}\left(\text{HOMO}\right)\text{-E}\left(\text{LUMO}\right)$

Put the values in the above equation,

$\begin{array}{c}\text{E=1.5V-}\left(\text{-0.9V}\right)\\ \text{=2.4V}\\ \text{=2.4eV}\\ \text{=2.4V}\left(\frac{{\text{1.60×10}}^{\text{-19}}\text{J}}{\text{1eV}}\right)\end{array}$

Therefore,

${\text{E=3.8×10}}^{\text{-19}}\text{J}$

The wavelength of light

By rearranging the above formula, we get;

$\begin{array}{c}\text{λ=}\frac{\text{hc}}{\text{E}}\\ \text{=}\frac{{\text{6.626×10}}^{\text{-34}}\text{×}\left({\text{3×10}}^{\text{8}}{\text{ms}}^{\text{-1}}\right)}{{\text{3.8×10}}^{\text{-19}}\text{J}}\end{array}$

$\begin{array}{l}{\text{λ=517×10}}^{\text{-9}}\text{m}\\ \text{λ=517nm}\left({\text{1nm=10}}^{\text{-9}}\text{m}\right)\end{array}$

Thus, the wavelength of the light is517 nm.The color of the light isgreenbecause the wavelength falls in the color range of green.