What is the diameter of a spherical tungsten cluster (atomic radius Ra = 0.148 nm) that contains 106 atoms? With 0.250 nm radius?

diameter is 2.36 nm

Explanation:

given data

atomic radius Ra = 0.148 nm

no of atoms = 106

radius r = 0.250 nm

to find out

diameter

solution

we know that diameter = 2 R ... 1

so we find R first

we apply equation here

volume of cluster = 106 * atom volume

put here volume

4/3 * π*R³ = 106 * 4/3 * π*r³

R³ = 106 * (0.250) ³

R = 1.183

so from equation 1

diameter = 2 (1.183)

diameter = 2.36 nm