Chapter 15, Problem 3P

Interpretation Introduction

Interpretation:

The longest wavelength of light that could provide enough energy per photon to pump one proton against this gradient should be calculated at ${25}^{0}C$, assuming 20% efficiency in photosynthesis.

Concept introduction:

The energy required to move the proton against any gradient should be equal to the energy of the proton.

Energy of one proton is calculated as:

$E=\frac{h\times c}{\lambda }$

For one mole of proton, the energy should be calculated as:

$E=\frac{h\times c}{\lambda }\times N_A$

Where, h is Planck's constant, c is speed of light and λ is wavelength with the values as:

$\begin{array}{c}h=6.626\times {10}^{-34}J.s\\ c=3\times {10}^{8}m/s\\ \lambda =700nm=7\times {10}^{-7}m\\ N_A=6.02\times {10}^{23}/mol\end{array}$

Interpretation Introduction

Interpretation:

The standard free energy change $(\Delta G)$ per mol of $O_2$ produced should be calculated. The comparison of this energy should be done with the energy required to drive the synthesis of ATP.

Concept introduction:

The overall reaction for ATP synthesis in cyclic photophosphorylation is given as:

$2NAD{P}^{+}+3AD{P}^{3-}+3P{i}^{2-}+H^{+}\to O_2+2NADPH+3AT{P}^{4-}+H_{2}O$

Looking, at the reaction, it can be said that one mole of proton produces one mole of O₂.

But, the reaction of production of $O_2$ is given as:

$2NAD{P}^{+}+3ADP+3P{i}^{2-}+10H^{+}\to O_2+2NADPH+3ATP+12H^{+}$

Here, 12 moles of protons are produced with one mole of $O_2$ which confirms that energy change in production of 12 moles of protons will be the energy change per mole of $O_2$.

Interpretation Introduction

Interpretation:

The maximum number of moles of protons should be calculated that could be pumped against the gradient by the energy in a mole of photon of 650nm wavelength.

Concept introduction:

The energy required to move the proton against any gradient should be equal to the energy of the proton.

Energy of one proton is calculated as:

$E=\frac{h\times c}{\lambda }$

For one mole of proton, the energy should be calculated as:

$E=\frac{h\times c}{\lambda }\times N_A$

Where, h is Planck's constant, c is speed of light and λ is wavelength with the values as:

$\begin{array}{c}h=6.626\times {10}^{-34}J.s\\ c=3\times {10}^{8}m/s\\ \lambda =700nm=7\times {10}^{-7}m\\ N_A=6.02\times {10}^{23}/mol\end{array}$