Final answer:
To calculate the spring stiffness for aluminum atoms modeled as being connected by springs, use Young's Modulus, the density of aluminum, and its molar mass to find the interatomic distance and cross-sectional area, and apply the formula relating these quantities.
Step-by-step explanation:
The question involves the calculation of the approximate spring stiffness (k) for a model where aluminum atoms are connected by springs. With Young's Modulus (E) for aluminum given as 6.2x10¹°N/m² and the atomic spacing for aluminum derived from its density (2.7 g/cm³) and molar mass (27 g/mol), we can estimate the spring stiffness using the equation E = k · L/A, where L is the interatomic distance and A is the cross-sectional area involved in the deformation.
The density information helps determine L by calculating the volume occupied by one mole of aluminum atoms. With Avogadro's number giving the number of atoms per mole, we can ascertain the spacing between atoms. Once L is known, assuming the deformation area A for a single atomic bond in a face-centered cubic structure, we can isolate k in the aforementioned equation to find the spring stiffness.