Question

One way in which photosynthetic bacteria store chemical energy is through the conversion of a compound called adenosine diphosphate (ADP), together with hydrogen phosphate ion, to adenosine triphosphate (ATP):

$$\begin{gathered} \mathit{A}\mathit{D}{\mathit{P}}^{\mathbf{3}\mathbf{-}}\mathbf{+}\mathit{H}\mathit{P}{\mathit{O}}_{\mathbf{4}}^{\mathbf{2}\mathbf{-}}\mathbf{+}{\mathit{H}}_{\mathbf{3}}{\mathit{O}}^{\mathbf{+}}\mathbf{\to }\mathit{A}\mathit{T}{\mathit{P}}^{\mathbf{4}\mathbf{-}}\mathbf{+}\mathbf{2}{\mathit{H}}_{\mathbf{2}}\mathit{O} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{∆}\mathit{G}\mathbf{=}\mathbf{+}\mathbf{34}\mathbf{.}\mathbf{5}\mathit{K}\mathit{J}\left(\mathit{p}\mathit{H}=7\right) \end{gathered}$$

Suppose some chlorophyll molecules absorb 1.00 mol of photons of blue light with wavelength 430nm. If all this energy could be used to convert ADP to ATP at room conditions and pH 7, how many molecules of ATP would be produced per photon absorbed? (The actual number is smaller because the conversion is not 100% efficient.)

Short answer

The total number of molecules of ATP produced will be 8N_A.

Step-by-step solution

Definition of photoelectric effect

When light shines on a metal, the photoelectric effect results in the “expulsion of electrons” from the metal's surface termed as photoelectrons. This complete process is also known as photoemission.

Calculation of total energy

Given that, wavelength (λ) is 430nm at room temperature and under neutral pH.

According to photoelectric equation,

$E=\frac{hc}{\lambda }{N}_A$

Where, h = Planck’s constant, c = speed of light, and ${\text{N}}_{\text{A}}$= Avogadro’s number.

The known values are substituted.

$$\begin{gathered} E=\frac{hc}{\lambda }{N}_A \\ E=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{430\times {10}^{-9}}\times 6.023\times {10}^{23} \\ \mathrm{E}=278.598\mathrm{kJ}{\mathrm{mol}}^{-1} \end{gathered}$$

Calculation of total number of ATP molecules

According to given information, for formation of one molecule of ATP 34.5kJ energy is required.

So, number of molecules formed due to 1 mol of photons can be given by-

$n=\frac{E}{\Delta G}{N}_A$

Where,

• n is number of molecules
• E is energy of 1 mole of photons
• ΔG is energy of formation of one mole of ATP

Then,

$$\begin{gathered} n=\frac{278.598}{34.5}{N}_A \\ n=8.07 \\ n\approx 8N_A \end{gathered}$$

Hence, 8N_A of ATP can be formed.