Answer
$6.0\times10^{26}$ nucleons. The composition of the object doesn't matter.
Work Step by Step
The mass of an electron is negligible compared to the mass of a nucleon. (It was calculated in problem 10 that over 99.95 percent of a hydrogen atom’s mass is in the nucleus.)
One nucleon has a mass approximately equal to a proton's mass or a neutron's mass. Find the number of nucleons in a 1.0-kg object.
$$N=\frac{1.0\;kg}{1.67\times10^{-27}kg/nucleon}=6.0\times10^{26}\;nucleons$$
The composition of the object doesn't affect the answer, because the mass of a nucleon is about the same for all materials.