Q14-13P - Organic Chemistry (Mcmurry)

Question

Calculate the energy range of electromagnetic radiation in the UV region of the spectrum from 200 to 400 nm (see Section 12-5). How does this value compare with the values calculated previously for IR and NMR spectroscopy?

Step-by-Step Solution

Answer

The energy range of electromagnetic radiation in the UV region of the spectrum from 200 to 400 nm is ${\text{6.0×10}}^{\text{2}}\text{\hspace{0.17em}kJ/mol}$ and ${\text{3.0×10}}^{\text{2}}\text{\hspace{0.17em}kJ/mol}$.

The energy required for UV transition is greater than for IR or ${}^1\mathrm{H}$NMR transition

Step 1:Electromagnetic Radiation

Electromagnetic radiation is the “form of energy” with both electric and magnetic fields. It is generated by the sun, in which the electric field and magnetic field oscillate perpendicular.

 

Electromagnetic waves are of many types depending upon the type of oscillation.

Step 2: Comparison of energy in UV region with IR and NMR

Conversion of 200 nm and 400 nm wavelength to a meter is done as follows:

$\begin{array}{c}{\text{λ = 200×10}}^{\text{-9}}\text{m}\\ {\text{= 2×10}}^{\text{-7}}\text{m}\\ {\text{λ = 400×10}}^{\text{-9}}\text{m}\\ \text{hence }\lambda {\text{= 4×10}}^{\text{-7}}\text{m}\end{array}$

The energy of electromagnetic radiation of ${\text{2×10}}^{\text{-7}}\text{m}$ wavelength is given as follows:

$\begin{array}{c}\text{E = }\frac{{\text{1.20×10}}^{\text{-4}}\text{\hspace{0.17em}kJ/mol}}{\text{λ}\left(\text{in m}\right)}\\ \text{= }\frac{{\text{1.20×10}}^{\text{-4}}\text{\hspace{0.17em}kJ/mol}}{{\text{2.0×10}}^{\text{-7}}}\\ {\text{= 6.0×10}}^{\text{2}}\text{\hspace{0.17em}kJ/mol}\end{array}$

The energy of electromagnetic radiation of ${\text{4×10}}^{\text{-7}}\text{m}$ wavelength is given as follows:

$\begin{array}{c}\text{E = }\frac{{\text{1.20×10}}^{\text{-4}}\text{\hspace{0.17em}kJ/mol}}{\text{λ}\left(\text{in m}\right)}\\ \text{ = }\frac{{\text{1.20×10}}^{\text{-4}}\text{\hspace{0.17em}kJ/mol}}{{\text{4.0×10}}^{\text{-7}}}\\ {\text{= 3.0×10}}^{\text{2}}\text{\hspace{0.17em}kJ/mol}\end{array}$

Therefore the energy of electromagnetic radiation in the spectral region from 200 nm to 400 nm is 300-600 kJ/mol.

The energy of electromagnetic radiation in kJ/mol for UV is 300-600, for IR is 4.8-48, and for ${}^1\mathrm{H}$NMR is $8.0\times {10}^{-5}$ .

Thus the energy required for UV transition is greater than for IR or ${}^1\mathrm{H}$NMR transition