Calculating atomic radius from weight + density

[physicsnnewbie]

Homework Statement

Calculate the radius of a palladium atom, given that Pd has an FCC crystal structure, a density of 12.0g/cm3, and an atomic weight of 106.4g/mol

Homework Equations

Pd contains 4 atoms per unit cell.
unit cell edge lengh = 2*Radius*sqrt(2)

The Attempt at a Solution

calculate atom weight:
106.4/6.0221418e23 = 1.7668133e-22

calculate unit cell weight:
1.7668133e-22*4 = 7.0672532e-22

calculate unit cell volume in cm3:
7.0672532e-22/12 = 5.8893777e-23

convert to nm3:
5.8893777e-23*(10^7)^3 = 0.0588938

calculate edge length:
0.0588938^(1/3) = 0.3890659

calculate radius:
0.3890659/2 = 0.194533

my answer:
0.194533nm

correct answer:
0.138nm

I can't figure out what I've done wrong here.

 

[physicsnnewbie]

I figured it out. I got confused and thought 2*sqrt(2) was equal to 2. So silly!