Question

1. Unit Cells

i. A certain metal crystallizes in a face-centered cubic unit cell. If the atomic radius is 150 pm, calculate the edge length (cm) and volume of the unit cell (cm3)?

ii. If said metal is Gold (Au), calculate the density.

Answer #1

Solution:

1) Convert pm to cm: 150 pm*(1cm/10^10pm) = 1.5*10^-8 cm =r

2) Edge length of the cell: From pythogorean theorm; r = a ÷ 2(√2)

1.5*10^-8 cm = a ÷ 2(√2)

a = 4.242*10^-8 cm

3) Volume of cell: V = a^3 = (4.242*10^-8 cm)^3 = 7.633*10^-23 cm^3

4) Mass of 4 unit cells in a unit cell:

At. wt of Au = 197g/mol

197g/mol/6.023x 10^{23} atoms/mol = 3.27*10^-22
g/atom

3.27*10^-22 g/atom times 4 atoms = 1.308*10^-21 g

5) Density of element= mass of unit cell/volume = 1.308*10^-21 g / 7.633*10^-23 cm^3 = 17.13 g/cm^3

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density of the metal is 8.908 g/cm3, what is the unit cell edge
length in pm?

Gold crystallizes is a face-centered cubic unit cell.
Its density is 19.3 g/cm3
. Calculate the atomic radius of
gold in picometer.

Copper crystallizes with a face-centered cubic lattice and has a
density of 8.93 g/cm3.
a.) Calculate the mass of one unit cell of copper (in grams) b.)
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Calculate the edge length of the unit cell (in cm). d.) Calculate
the radius of a copper atom (in pm).

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If the atomic radius of an Al is 1.43Angstroms, what is the density
of aluminum (in g/cm^3)

A certain metal crystallizes in a body centered cubic unit cell
with an edge length of 310 pm. What is the length in Angstroms of
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A hypothetical metal crystallizes with the face-centered cubic
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(a) What is the atomic radius (in Å) of chromium in this
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____ Å
(b) Calculate the density (in g/cm3) of chromium.
____ g/cm3

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The edge length of the unit cell was found by x-ray diffraction to
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Rhodium crystallizes in a face-centered cubic unit cell. The
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please show all work and units!

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