Question

The density of palladium (Pd) is 12.0 g/mL and the cell volume is 5.89 ✕ 10^−23 mL. Determine the number of atoms in the unit cell. (Because there cannot be a part of an atom in a unit cell, we must round the number of atoms to the nearest whole number.)

Answer 1

atomic mass ... 106.4

moles per ml ... 106 / 12

6.02E23 * (12.0 / 106) * 5.89E-23

Answer 2

atomic mass ... 106.4

moles per ml ... 12.0 / 106 ...OOPS...

6.02E23 * (12.0 / 106) * 5.89E-23

Answer 3

atomic mass=106*1.6726E-27 kg

mass per cell= 12g/ml*5.89E-23 g
=

the number of atoms per cell:
number= mass per cell/atommassperatom
= 7.06800e-25kg/106*1.6726E-27 =3.98656255

number per cell = 4

Answer 4

It's hard (for me) to follow the post by Scott but solve what he has written and the answer is right. Here it is in what I hope is a little easier to follow. Let y = # atoms/unit cell.
mass unit cell = y*atomic mass/6.02E23
volume = mass/density; therefore.
5.89E-23 = y*106.42/12*6.02E23
y = 5.89E-23*12*6.02E23/106.42=3.998 which rounds to 4.0
Pd is a face centered cubic structure which has 4 atoms to the unit cell.