Metals have free electrons due to the bonding in metallic substances.
In a metal there are strong attractive forces between the nuclei and the valance electrons.
Positively charged metal nuclei form a lattice (a cube like structure) each metal atom provides one or more valance electrons <u>that are free to move throughout the lattice</u> The electrons are attracted to the positively charged nuclei but not one individual nuclei, this is called non-directional bonding since it occurs in all directions.
Now all metals are conductive becuase of the free to move (delocalised) electrons. Since the valance electrons are free to move throughout the lattice they are able to carry a charge. (Ionic solids cannot since the ionic solids form a tightly packed lattice with cations and anions which have no free moving electrons, electrons have to be able to move to carry a charge)
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To solve this problem, it is necessary to take into account the concepts of the number of vacations N_v at a given temperature as well as the calculation of the number of atom sites per cubic meter.
For definition the number of atomic sites per cubic meter is given as,
Where,
Avogadro's number
density
A = Atomic weight
Replacing with our values we have
At the same time we know that the number of vacancies 
is defined as,
![[tex]N_v = Ne^{-\frac{Q_v}{KT}}](https://tex.z-dn.net/?f=%5Btex%5DN_v%20%3D%20Ne%5E%7B-%5Cfrac%7BQ_v%7D%7BKT%7D%7D)
[/tex]
Where,
Energy of vacancy
Boltzman constant
T = Temperature
Replacing with the values given we have
Therefore the number of vacancies per cubit meter at 1000°C is
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It’s a I hope this helps you out
