The nucleus of an atom is approximately

According Rutherford’s model of an atom the size of nucleus should be smaller than the size of an atom in the order of ${10}^{-3}$  m to ${10}^{-5}$m

Size of nucleus of an atom is ${10}^{-13}\mathrm{cm}\left(\mathrm{or}\right) {10}^{-15}\mathrm{m}$

Size of the atom is ${10}^{-8}\mathrm{cm} \mathrm{or} {10}^{-10}\mathrm{m}=1{\mathrm{A}}^0$