The sodium-potassium pump in animal cells requires cytoplasmic ATP to pump ions across the plasma membrane. When the proteins of the pump are first synthesized in the rough ER, what side of the ER membrane will the ATP binding site be on?

It will be on the cytoplasmic side of the endoplasmic reticulum

Explanation:

The inner mitochondria protein called  Adenine Nucleotide Translocator or ADP/ATP carrier protein, maintains  the transport of  ADP into the matrix of the mitochondria  from the cytoplasm for ADP to be available for  ATPase synthesis of ATP, from ADP and Pi(inorganic phosphate ion) during  chemiosmosis of oxidative phosphorylation in the mitochondria.

The same carrier proetin also convey  the synthesized  ATPs  back to  the Cytoplasm for cellular utilization.

Therefore the ATP binding site should at the cytoplasmic side of the E.R, because  the cytoplasm of the E.R is the site of deposits of synthesized ATP s, thus proximity of the  ATP-binding site to it is needed.