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!

 

[Blueshift5]

Can you please provide some guidance?

Your calculations seem to be correct, however, it is important to note that the FCC crystal structure of Pd has a basis of 4 atoms per unit cell, not just 1. This means that the unit cell weight should be multiplied by 4, not the atomic weight. This will change your final answer to be closer to the correct value of 0.138nm. Additionally, it is important to be aware of any rounding or significant figure rules that may affect your final answer. Make sure to check your calculations and units carefully to ensure accuracy.