Question

The substance tantalum is found to crystallize in a body centered cubic unit cell and has a density of 17.01 g/cm3 using these data. Calculate the atomic radius of Tantalum in picometers

Answer 1

BCC unit cell -->

D = 17.01 g/cm3

calculate radius of Tantalum in pm

then..

recall that z = 2 for BCC

d = (z*MW) / (a^3 * N)

where:

MW = molar weight of element

a = lenght of unit cell

N = avogrados number = 6.022*10^23

d= density g/cm3

so...

substitute data

17.01 = (2*180.94788) / (a^3 * (6.022*10^23))

solve for a

a = 3.28*10^-8 cm

Note that this is NOT the radius

this is the lenght if the unit cell

the unit cell and radius can be related as:

r = sqrt(3) * a / 4

so

r = sqrt(3) * a / 4

r = sqrt(3)*(3.28*10^-8)/4

r = 1.420281*10^-8 cm

r = 1.420281*10^-10 m --> to pico by 10^12

r = 142.03 pm