1 m3 of nickel is approximately 8,800 kg of metal. 1 mole of nickel weighs 0.059 kg. 8800/0.059 = 149152 moles. 1 mole = 6.023x1023 atoms. Thus 149,152 moles (1m3 of nickel) contain 8.98x1028 atoms. Each nickel atom has 2 valence electrons on its last shell. Therefore, in 1 m3 of nickel there are 1.8x1029 free electrons - the free electron density will be 1.8x1029 m-3.