Chapter 20, Problem 14P

Summary Introduction

To determine: The way in which single chlorophyll molecule absorb a photon.

Introduction:

Chlorophyll is a pigmented molecule present in green plants and algae. The chlorophyll molecules have an ability to absorb sunlight to drive photosynthesis process.

Explanation of Solution

“The leaves absorb light in the form of small energy packets or photons”. On the basis of wavelength, the absorption of energy by leaves vary from 170 kJ/mol to 300 kJ/mol. Thus, the rate of light absorption by leaf can be calculated as below,

$\begin{array}{c}\text{The}\text{rate}\text{of}\text{light}\text{absorption}=\frac{\text{50}}{\text{100}}\text{×}\text{5}\text{.4}{\text{(J/cm}}^{\text{2}}\text{×min)}\\ \text{=}\text{2}\text{.7}{\text{J/cm}}^{\text{2}}\cdot \text{min}\end{array}$

Assume an average energy of 270 kJ/mol. Thus, the rate of light absorption can be calculated by the given formula:

$\text{Rate}\text{of}\text{light}\text{absorption}\text{=}\frac{\text{amount}\text{of}\text{light}\text{absorbed}}{\text{total}\text{available}\text{energy}}$

In this, 2.7 J/cm² amount of light is absorbed by chlorophyll, and the total amount of available energy is given as 270 kJ/mol.

Now, from the above given formula, the rate of light absorption can be calculated as:

$\begin{array}{c}\text{Rate}\text{of}\text{light}\text{absorption}\text{=}\frac{\text{2}\text{.7}\text{×}{\text{10}}^{\text{-3}}{\text{kJ/cm}}^{\text{2}}\cdot \text{min}}{\text{2}\text{.7}\text{×}{\text{10}}^{\text{2}}\text{kJ/mol}}\\ =1\times {10}^{-3+(-2)}{\text{mol/cm}}^2\cdot \min \\ =\text{1}\text{×}{\text{10}}^{\text{-5}}{\text{mol/cm}}^2\cdot \min \end{array}$

Thus, the rate of light absorption by chlorophyll molecule is1×10^-5 mol/cm².

Now, to calculate rate of light absorption by single chlorophyll molecule, first the amount of chlorophyll present in spinach leaf is calculated. So, the content of chlorophyll in spinach leaf can be calculated by the given formula:

$\text{Content of chlorophyll in spinach leaf=}\frac{\text{Amount}\text{of}\text{chloropyll}\text{in}\text{spinach}\text{leaf}}{\text{Molecular}\text{weight}\text{of}\text{chlorophyll}}$

As the amount of chlorophyll present in spinach is given as 20×10^-6 g/cm² and molecular weight of chlorophyll is given as 892 mol/cm². Thus, the chlorophyll content in spinach leaf can be calculated by:

$\begin{array}{c}\text{Content of chlorophyll in spinach leaf=}\frac{\text{20}\text{×}{\text{10}}^{\text{-6}}{\text{g/cm}}^{\text{2}}}{\text{892}\text{g/mol}}\\ \text{=}\text{0}\text{.22}{\text{×10}}^{\text{-6}}{\text{mol/cm}}^{\text{2}}\\ \simeq \text{2}\text{.2}\text{×}{\text{10}}^{\text{-8}}{\text{mol/cm}}^{\text{2}}\end{array}$

Now, the rate of light absorption by single chlorophyll molecule can be calculated as below:

$\begin{array}{c}\text{Rate of light absorption by single chlorophyll molecule }\\ \text{= (2}\text{.2}\text{×}{\text{10}}^{\text{-8}}{\text{mol/cm}}^{\text{2}}\text{)}\text{×}\left(\text{1}\text{×}{\text{10}}^{\text{-5}}{\text{mol/cm}}^{\text{2}}\text{×min}\right)\\ \text{=}\text{2}\text{.2}\text{×}{\text{10}}^{\text{-3}}\text{min}\\ \text{=}\text{0}\text{.1s}\end{array}$

Thus, the rate of light absorption by single chlorophyll molecule is 0.1s.

Conclusion

The rate of absorption of light by single chlorophyll molecules is 0.1s.

Summary Introduction

To determine: The fraction of chlorophyll molecules that are excited at any one time.

Introduction:

Chlorophyll is a pigmented molecule present in green plants and algae. The chlorophyll molecules have an ability to absorb sunlight to drive the photosynthesis process.

Explanation of Solution

Given,

The average lifetime of an excited chlorophyll molecule =1 ns =1×10^-9 sec.

Thus, the excited fraction of the chlorophyll molecules at one time can be calculated as below,

$\begin{array}{c}\text{The fraction of chlorophyll molecules=}\left(\frac{\text{1}\text{×}{\text{10}}^{\text{-9}}\text{sec}}{\text{1}\text{×}{\text{10}}^{\text{-1}}\text{sec}}\right)\\ \text{=}\text{1}\text{×}{\text{10}}^{\text{-8}}\text{sec}\end{array}$

Hence, one in 10⁸ chlorophyll molecules are excited at any one given time.

Conclusion

In one chlorophyll molecule 10⁸ molecules are excited at any one time.