Question

Calculate the radius of a tantalum (ta) atom, given that ta has a bcc crystal structure, a d ensity of 16.6 g/cm3, and an atomic weight of 180.9 g/mol.

Answer 1

solution:

$Ta is BCC, a=\frac{4}{\sqrt{3}r},n=2atoms/cell\\p=16.6gram/cm^3,A=180.9gram/mol\\P=\frac{A\times n}{N_{a}\times v}=\frac{180.9\frac{gram}{mol}\times 2 \frac{atom}{cell}}{6.023\times10^23\frac{atom}{mol}\times(\frac{4}{\sqrt{3}\times r})^3\frac{cm^3}{cell}}\\=16.6\frac{gram}{cm^3}\\r=(\frac{180.9\times2}{16.6\times6.023\times10^23\times(\frac{4}{\sqrt{3}})^3})^\frac{1}{3}\times10^8$