Why is the second ionization energy greater

The ionization of atoms takes place by withdrawing an electron from the outermost shell, and probably from the inner shells. Withdrawing of a second electron can take place from the similar outermost shell, or from an inner shell. The energy to withdraw one electron from a neutral atom is known as the first ionization energy, and the energy needed to withdraw the second electron is known as the second ionization energy. Generally, the second ionization energy is greater in comparison to the first ionization energy.  

Withdrawing one electron from the neutral atom's outermost shell leads to the formation of an ion with a +1 charge. However, withdrawing a second electron needs more energy, in comparison to the withdrawal of the first electron, as this second electron experiences a +1 charge, and encounters with a larger electrostatic attraction from an atom possessing a net charge, in comparison to a neutral atom.  

In supplementation to this effect, if the second electron must be withdrawn from an inner shell, the second ionization energy is also made larger. Also, in case of withdrawing an electron from an inner shell, the electrons in the inner shells experience greater nuclear attraction as they are closer to the atomic nucleus.  

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3