Chapter 20, Problem 43GQ

Interpretation Introduction

Interpretation: The wavelength of the radiation with sufficient energy to break $\text{C-Cl}$ bond should be calculated and the region where this falls in electromagnetic spectrum should be determined.

Concept introduction:

Electromagnetic radiations are a type of energy surrounding us. They are of different types like radio waves, IR, UV, X-ray etc.

Ultraviolet radiation lies between $200\text{nm}$ to $400\text{nm}$

Energy associated with a radiation,

$\begin{array}{l}\text{E}\text{=}\text{hγ}\\ \text{E}\text{=}\frac{\text{hc}}{\text{λ}}\text{where}\text{h}\text{(Plancks}\text{constant)}\text{=}\text{6}{\text{.626×10}}^{\text{-34}}\text{Js}\\ \text{c}\text{(speed}\text{of}\text{light)}\text{=}{\text{3×10}}^{\text{8}}\text{m}/\text{s}\\ \text{E}\text{is}\text{energy}\text{of}\text{the}\text{radiation}\\ \text{λ}\text{is}\text{the}\text{wavelength}\end{array}$

Answer to Problem 43GQ

The wavelength of the radiation is $3.53\times {10}^{-3}\text{m}$ and this is in the ultraviolet region.

Explanation of Solution

Given:

From the table 8.8, the average bond energy of $\text{C-Cl}$ bond is $\text{339}\text{kJ}/\text{mol}$

In-order to find the wavelength of the radiation we can use the equation

$\begin{array}{l}\text{E}\text{=}\text{hγ}\\ \text{E}\text{=}\frac{\text{hc}}{\text{λ}}\text{where}\text{h}\text{(Plancks}\text{constant)}\text{=}\text{6}{\text{.626×10}}^{\text{-34}}\text{Js}\\ \text{c}\text{(speed}\text{of}\text{light)}\text{=}{\text{3×10}}^{\text{8}}\text{m}/\text{s}\\ \end{array}$

Substituting the values

$\begin{array}{l}\text{λ}\text{=}\frac{\text{hc}}{\text{E}}\\ \text{=}\frac{\text{6}{\text{.626×10}}^{\text{-34}}{\text{Js×3×10}}^{\text{8}}\text{m}/\text{s}}{{\text{339×10}}^{\text{3}}\text{J}/\text{mol}}\\ \text{=}\text{5}{\text{.863×10}}^{\text{-31}}\text{m}/\text{mol}\end{array}$

The wavelength of the radiation is $3.53\times {10}^{-3}\text{m}$

Therefore wavelength of the radiation in meter is calculated by multiplying the answer with Avogadro number.

$\begin{array}{l}\text{λ}\text{=}\text{5}{\text{.863×10}}^{\text{-31}}\text{m}/\text{mol}\text{×}\text{6}{\text{.022×10}}^{\text{23}}\\ \text{=}\text{3}{\text{.53×10}}^{\text{-7}}\text{m}\end{array}$

This wavelength corresponds to ultraviolet region in the electromagnetic spectrum.

Conclusion

The wavelength of the radiation with sufficient energy to break $\text{C-Cl}$ bond is calculated and found to be $\text{3}{\text{.53×10}}^{\text{-7}}\text{m}$.