The estimated atomic radius of sodium is approximately 1.86 angstroms.
To estimate the atomic radius of sodium, we can use the information provided about its crystal structure and density. Sodium adopts a body-centered cubic (BCC) structure, and its density is given as 0.97 g/cm³. In a BCC structure, each unit cell contains two atoms, and the volume of a unit cell is related to the atomic radius (r).
The density (ρ) is given by the mass per unit volume, where ρ= 2×atomic mass/Avogadro’s number×volume of a unit cell.
Rearranging this equation to solve for the atomic radius r=( 2×atomic mass/Avogadro’s number×density)^1/3.
Substituting the given values for sodium's atomic mass (22.99 g/mol), Avogadro's number (6.022×10^23 mol⁻¹), and density (0.97 g/cm³) into this equation yields an estimated atomic radius of approximately 1.86 angstroms. This value provides an approximation of the size of a sodium atom within its crystal lattice.