An electric field of magnitude \(4.50 \times 10^{2} \mathrm{~V} / \mathrm{m}\) is created in a wire that is \(300 \mathrm{~mm}\) long and has a radius of \(1.00 \mathrm{~mm}\). The number density of the charge carriers in the wire is \(1.20 \times 10^{27}\) charge carriers \(/ \mathrm{m}^{3}\). How much energy is gained by the lattice of metal ions in the time interval it takes for the average electron to travel the length of the wire?