Calculating atomic radius from weight + density

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SUMMARY

The discussion focuses on calculating the atomic radius of a palladium (Pd) atom, given its face-centered cubic (FCC) crystal structure, density of 12.0 g/cm³, and atomic weight of 106.4 g/mol. The calculations involve determining the weight of a single palladium atom, the unit cell weight, and the unit cell volume, ultimately leading to the calculation of the atomic radius. The user initially calculated the radius as 0.194533 nm but later corrected it to the accurate value of 0.138 nm after realizing a miscalculation involving the unit cell edge length formula.

PREREQUISITES
  • Understanding of face-centered cubic (FCC) crystal structures
  • Knowledge of atomic weight and Avogadro's number (6.0221418e23)
  • Familiarity with unit cell volume calculations
  • Basic proficiency in dimensional analysis and unit conversions
NEXT STEPS
  • Study the relationship between atomic weight and density in crystal structures
  • Learn about the derivation of unit cell dimensions in FCC lattices
  • Explore advanced topics in crystallography, such as Bravais lattices
  • Investigate the significance of atomic radius in material properties
USEFUL FOR

This discussion is beneficial for chemistry students, materials scientists, and anyone involved in crystallography or solid-state physics, particularly those studying atomic structures and properties of metals like palladium.

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

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