Question

Rose bengal is a chromophore used in biological staining that has an absorption maximum at 559.1 nm and several other shorter wavelength absorption bands in the ultraviolet and visible regions of the spectrum when dissolved in ethanol. What is the energy difference (in kJ/mol) between the absorption maximum at 559.1 nm and a band at 321.7 nm?

Answer 1

Answer:

The energy difference is 158.318 kJ/mol

Explanation:

The energy can be calculated by the following formula.

$Energy\, (E)=\frac{hc}{\lambda}$

$h\,=plank's \,consant\,=6.626\times10^{-34}m^{2}kg/s$

$c=\,velocity\,of\,light\,= 3\times 10^{8}\,m/s$

Let's calculate the energy at maximum:

Maximum energy = $559.1 nm = 559.1\times 10^{-9}\,cm$

$E_{1} = \frac{6.626\times 10^{-34}\times 3\times 10^{8}}{559.1\times 10^{-9}} =3.55\times J/atom$

Let's calculate the energy at minimum:

Minimum energy = $321.7 nm = 321.7\times 10^{-9}\,cm$

$E_{1} = \frac{6.626\times 10^{-34}\times 3\times 10^{8}}{321.7\times 10^{-9}} =6.179\times J/atom$

$The\,energy\,\,difference\,\Delta E = E_{2}-E_{1}$

$=6.179\times J/atom-3.55\times J/atom = 2.629 \times J/atom$

The number molecules present in one mole is $6.022 \times 10^{23}$

$\Delta \times N_{A} = 2.629 \times 10^{-19} \times 6.022 \times 10^{23}$

$=158.318 \times 10^{3}\,J/mol$

$=158.318 \,KJ/mol$

Therefore, the energy difference is 158.318 kJ/mol.