How Do You Determine Atomic Distance from Density and Molar Mass?

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To determine atomic distance from density and molar mass, first calculate the number of atoms in a mole using Avogadro's number. The density of lead (11.4 g/cm³) and the molar mass (207 g) allow for finding the volume occupied by one mole of lead. This volume can then be divided by the number of atoms to find the volume per atom, which can be related to atomic diameter. Young's modulus (1.6 x 10^10 N/m²) can be used alongside the calculated atomic distance to approximate the spring constant. Understanding these relationships simplifies the modeling of atomic interactions as springs.
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Heres my problem.
Youngs modulus for lead: 1.6exp10 N/m^2. Density of Lead: 11,4g/cm^3.
Mass of one mole lead: 207g
Model the interactions as if they were connected by springs.
Determine distance between lead atoms and approx spring constant.

Easy enough Y= K/d But what is bugging me is d. dia of atom
How do you determine d from density and the mass of one mole?
And how do u relate it to the distance between atoms?
It is keeping me up.
Probably very easy but just not seeing it.

PS: don't know if we use different notation is SA
 
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If you assume that each atom of lead is a point mass (has mass but zero volume), then the problem is greatly simplified.
 
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