Question

Show if lead is an FCC or a BCC crystal structure.

**Lead (Pb) has an atomic radius of 0.175 nm and a density
of 11.35 g/cm3 . Use this information to determine whether it has
an FCC or a BCC crystal structure.**

**Please also provide the correct units.**

Answer #1

We know density , d = (Z x atomic mass) / ( No x a^{3} x
10^{-30} cm^{3} )

Where Z = No . of atoms in a unit cell = ?

atomic mass of lead = 207.2 g

N_{o} = avagadro number = 6.023x10^{23}

a = edge length = in pm

For fcc arrangement radius , r = (√2 / 4 ) a

a = 4r / √2 radius = r = 0.175 nm = 175 pm

= 495 pm

Plug these values in (1) we get

Z = d x No x a^{3} x 10^{-30} cm^{3} /
atomic mass

= 4

Since the number of atoms in a unit cell = 4 so it is an FCC structure

1) For a metal that has the face-centered cubic (FCC) crystal
structure, calculate the atomic radius if the metal has a density
of (8.000x10^0) g/cm3 and an atomic weight of
(5.80x10^1) g/mol. Express your answer in
nm.
2) Consider a copper-aluminum solid solution containing
(7.82x10^1) at% Al. How many atoms per cubic centimeter
(atoms/cm^3) of copper are there in this solution?
Take the density of copper to be 8.94 g/cm3 and the
density of aluminum to be 2.71 g/cm3.

Niobium (Nb) has an atomic radius of 0.1430 nm and a density of
8.57 g/cm^3. Determine whether it has an FCC or a BCC crystal
structure.

1. Aluminum and iron are both important structural metals.
Suppose they are processed into the FCC and BCC structures. Of
these four possible structures (FCC Al, BCC Al, FCC Fe, BCC Fe),
which one has the a) lowest unit cell volume, and b) lowest
theoretical density? The radius of Al is 0.1431 nm and the radius
of Fe is 0.1241 nm.
2. An unknown metal has a BCC structure, density of 7.25 g/cm3,
and atomic weight of 50.99 g/mol. Determine...

Below are listed the atomic weight, density, and atomic radius
for three hypothetical alloys at room temperature. For each
determine whether its crystal structure is FCC, BCC, or simple
cubic and then justify your answer.
Alloy
Atomic weight
Density
Atomic radius
(g/mol)
(g/cm3)
(nm)
A
195.08
21.45
0.139
B
209
9.32
0.335
C
55.85
7.87
0.124

BCC (body-centered cubic) crystal structure is one of common
crystal structuresfor metals. Please do the following
questions.
(a) Describe what is a BCC structure and draw a BCC unit
cell.
(b) Calculate the radius of a vanadium (V) atom, given that
V has a BCCcrystal structure, a density of 5.96 g/cm3,
and an atomic weight of 50.9 g/mol.

Niobium (Nb) has an atomic radios of 0.1430 nm and a density of
8.57 g/cm^3. Determine whether it has an FCC or a BCC crystal
structure.

Calculate the radius of an silver atom in cm, given that Ag has
an FCC crystal structure, a density of 10.5 g/cm3, and
an atomic weight of 107.87 g/mol.

The density of a uniform crystal structure can be estimated from
the crystal type and information about the lattice parameter and
atomic radii. Estimate the density of a material
(gram/cm3) for a material with these properties:
Atomic Radius = 0.1281 nm
Crystal Type = FCC
atomic Mass = 47 grams/mol
(Note: Avogadro's Number , 6.022x10^23 atoms/mol)

Given the information below, determine the crystal structure.
Consider only FCC and BCC structures as possibilities.
Lattice parameter a = 0.4997
nm
Powder x-ray: λ = 0.1542
nm
2θ (°) Constructive Interference
31.0, 36.0, 51.8, 61.6, 64.8

A certain material has a FCC crystal structure with an atomic
radius of 1.44 A° (1 A° = 10-8 cm), and an atomic mass of 197.
Calculate:
a) The lattice constant ‘a’ of unit cell in cm,
b) The atomic packing factor of the material.

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