The ground state of hydrogen is nondegenerate, so the first-order correction to the ground state energy is given by
where we have taken the electric field to be in the positive direction for convenience. Recall the function form of the ground state of hydrogen
This function is symmetric about the x-y plane (i.e. ). Therefore, the integral in equation (1) must be zero, because is antisymmetric with respect to the x-y plane, so the integral will be an integral of an odd function over the symmetric interval . Therefore, answer (A) is correct.