Step 1: Understanding the Concept:
Non-cyclic photophosphorylation (Z-scheme) is the light-driven process in photosynthesis where electrons flow from water to NADP${}^+$.
This process generates both ATP (via a proton motive force across the thylakoid membrane) and NADPH, storing energy for carbon fixation.
Key Formula or Approach:
To calculate the energetic efficiency in terms of ATP equivalents per absorbed photon, we use the stoichiometry of non-cyclic electron transport:
\[ \text{Efficiency} = \frac{\text{Direct ATP Produced} + \text{ATP Equivalent of NADPH}}{\text{Total Photons Absorbed}} \]
Step 2: Detailed Explanation:
Let us determine the stoichiometry of non-cyclic electron flow:
1. Photons absorbed: The transfer of 4 electrons from 2 $\text{H}_2\text{O}$ to produce 1 $\text{O}_2$ and 2 NADPH requires the absorption of 8 photons (4 by Photosystem II and 4 by Photosystem I).
2. Proton translocation: The flow of these 4 electrons leads to the translocation of 12 protons into the thylakoid lumen (8 protons via the Q-cycle and plastoquinol oxidation, plus 4 protons released directly from water splitting).
3. Direct ATP synthesis: The chloroplast ATP synthase requires approximately $4$ protons ($\text{H}^+$) to synthesize 1 ATP.
Thus, the 12 protons translocated can drive the synthesis of:
\[ 12 \text{ H}^+ / 4 \text{ H}^+ \text{ per ATP} = 3 \text{ ATP} \]
4. NADPH to ATP conversion: Each NADPH molecule has high reducing power, equivalent to approximately $3.5$ ATP molecules in terms of energetic value (or $3$ to $4$ ATP equivalents in metabolic calculations).
For 2 NADPH produced:
\[ 2 \text{ NADPH} \times 3.5 \text{ ATP equivalents} = 7 \text{ ATP} \]
5. Total ATP equivalents:
\[ \text{Total ATP equivalents} = 3 \text{ ATP (direct)} + 7 \text{ ATP (from NADPH)} = 10 \text{ ATP} \]
6. Efficiency:
\[ \text{Efficiency} = \frac{10 \text{ ATP equivalents}}{8 \text{ photons}} = 1.25 \text{ ATP per photon} \]
Step 3: Final Answer:
The energetic efficiency of the non-cyclic electron transport process is 1.25 ATP equivalents per absorbed photon, which corresponds to option (C).