The difference in masses of 10³ moles each of magnesium atoms and magnesium ions is. (Mass of an electron = 9.1×10^-31kg).

10³ moles of Mg²⁺ and Mg atoms would differ by 10³ × 2 moles of electrons
Mass of 2 ×10³  moles of electrons 
$\Rightarrow$2× 10³× 6.023 ×10²³× 9.1 × 10^-31kg 
$\Rightarrow$ 2 × 6.023 × 9.1 × 10^-5kg 
$\Rightarrow$109.6004 ×10^-5 kg

Therefore, the difference in masses of 10³ moles each of magnesium atoms and magnesium ions is 1.096004 ×10^-3 kg $\approx$ 1.096×10^-3 kg