biochemistry - How many ATP molecules are formed?

What is the number of ATP molecules formed during the photosynthetic processes which consume 8 molecules of $\text{H}_2\text{O}$ due to noncyclic electron transport and subsequent photophosphorylation?

Assume that quinone cycle facilitates the transfer 4H⁺ to the lumen of thylakoid membrane for every two electrons passing through electron transport system and one ATP is formed for every 3H⁺ moving down the proton gradient by the mediation of F₀F₁-ATPase

MY ATTEMPT: In the lumen, due to hydrolysis 16 H⁺ are formed. Due to quinone cycle 32 H⁺ are taken from stroma and transferred to the lumen and NADP⁺ takes 48 H⁺ so in stroma there is deficiency of 80 and there are only 48 H⁺ in the lumen. If I assume that if there were initially hundred H⁺ on both sides then after non cyclic transport inside the lumen there are 148 H⁺ and in stroma there are 20 H⁺ so to have equilibrium then there should be 84 H⁺ on both side so total 64 H⁺ should travel then I am getting 64/3 ATP which is wrong. Where I am going wrong?

Screenshot of question paper

Answer

Sorry for the poor quality of the image, but its just as a reference for my answer.

You have made the question too complex. From the figure, we find that 1 H₂O gives 2 H⁺ and 2 e^-. 2 e^-, through quinone cycle, provide 4 H⁺ i.e. total 6 H⁺ which form 6/3 = 2 ATP i.e.

1 H₂O => 6 H⁺ => 2 ATP

Multiply this equation by 8 and you get:

8 H₂O => 48 H⁺ => 16 ATP

So, 16 ATP should be the answer.

Reference:

Pradeep's: A textbook of Biology for Class XI, 2015, Vol. II, page IV/106