Based on the calculations, the radius of a tantalum (Ta) atom is equal to 0.143 nm.
Given the following data:
Density of tantalum (Ta) = 16.6 g/cm³.
Atomic weight of tantalum (Ta) = 180.9 g/mol.
Density can be defined as a ratio of mass to the volume of a physical object such as a tennis ball. Mathematically, the density of a physical object can be calculated by using this formula:
Density = Mass/Volume
For the mass of this unit cell, we have:
Mass = 2 atoms/unit-cell × 180.9 g/mol × 1 mol /6.022 x 10²³ atoms/mol
Mass = 6.01 x 10⁻²² g/unit-cell
Next, we would determine the volume and edge length of the cube:
Volume, V = 6.01 x 10⁻²²/16.6
Volume, V = 3.62 x 10⁻²³ cm³
For the edge length, we have:
V = a³
a = ∛V
a = ∛3.62 x 10⁻²³ cm
Edge length, a = 3.31 x 10⁻⁸ cm
Mathematically, the edge length of a body-centered cubic unit cell is given by this formula:
a = 4r/√3
r = a × √3/4
r = 3.31 x 10⁻⁸ × √3/4
Radius, r = 1.43 × 10⁻⁸ cm
Lastly, we would convert the value in cm to nm:
Radius, r = 1.43 × 10⁻⁸ × 1/100 × 1 × 10⁹
Radius, r = 0.143 nm.
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