Niobium forms a substitutional solid solution with vanadium. Compute the number of niobium atoms per cubic centimeter for a niobium-vanadium alloy that contains 24 wt\% \(\mathrm{Nb}\) and \(76 \mathrm{wt} \% \mathrm{V}\). The densities of pure niobium and vanadium are 8.57 and 6.10 \(\mathrm{g} / \mathrm{cm}^{3},\) respectively .

Question: Calculate the number of niobium atoms in one cubic centimeter of a niobium-vanadium alloy containing 24 wt% niobium and 76 wt% vanadium. The densities of pure niobium and vanadium are 8.57 g/cm³ and 6.10 g/cm³ respectively. The molar mass of niobium is 92.906 g/mol and Avogadro's number is 6.022 × 10^23 mol^(-1). Answer: To calculate the number of niobium atoms in one cubic centimeter of the alloy, we first determine the mass of niobium and vanadium in one cubic centimeter of the alloy using the given densities and wt%. Then, we calculate the volume fractions of niobium and vanadium. Next, we find the mass of one cubic centimeter of the alloy. Finally, we divide the mass of niobium in one cubic centimeter of the alloy by the molar mass of niobium and multiply by Avogadro's number to obtain the number of niobium atoms per cubic centimeter of the alloy.