1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
k0ka [10]
3 years ago
5

Assume that each atom is a sphere, and that the surface of each atom is in contact with its nearest neighbor. Determine the perc

entage of unit cell volume that is occupied in (a) a face- centered cubic lattice, (b) a body-centered cubic lattice, and (c) a diamond lattice.
Chemistry
1 answer:
tatiyna3 years ago
4 0

Answer:

  • The percentage of unit cell volume that is occupied by atoms in a face- centered cubic lattice is 74.05%
  • The percentage of unit cell volume that is occupied by atoms in a body-centered cubic lattice is 68.03%  
  • The percentage of unit cell volume that is occupied by atoms in a diamond lattice is 34.01%

Explanation:

The percentage of unit cell volume = Volume of atoms/Volume of unit cell

Volume of sphere = \frac{4 }{3} \pi r^2

a) Percentage of unit cell volume occupied by atoms in face- centered cubic lattice:

let the side of each cube = a

Volume of unit cell = Volume of cube = a³

Radius of atoms = \frac{a\sqrt{2} }{4}

Volume of each atom = \frac{4 }{3} \pi (\frac{a\sqrt{2}}{4})^3 = \frac{\pi *a^3\sqrt{2}}{24}

Number of atoms/unit cell = 4

Total volume of the atoms = 4 X \frac{\pi *a^3\sqrt{2}}{24} = \frac{\pi *a^3\sqrt{2}}{6}

The percentage of unit cell volume = \frac{\frac{\pi *a^3\sqrt{2}}{6}}{a^3} =\frac{\pi *a^3\sqrt{2}}{6a^3} = \frac{\pi \sqrt{2}}{6} = 0.7405

= 0.7405 X 100% = 74.05%

b) Percentage of unit cell volume occupied by atoms in a body-centered cubic lattice

Radius of atoms = \frac{a\sqrt{3} }{4}

Volume of each atom =\frac{4 }{3} \pi (\frac{a\sqrt{3}}{4})^3 =\frac{\pi *a^3\sqrt{3}}{16}

Number of atoms/unit cell = 2

Total volume of the atoms = 2X \frac{\pi *a^3\sqrt{3}}{16} = \frac{\pi *a^3\sqrt{3}}{8}

The percentage of unit cell volume = \frac{\frac{\pi *a^3\sqrt{3}}{8}}{a^3} =\frac{\pi *a^3\sqrt{3}}{8a^3} = \frac{\pi \sqrt{3}}{8} = 0.6803

= 0.6803 X 100% = 68.03%

c) Percentage of unit cell volume occupied by atoms in a diamond lattice

Radius of atoms = \frac{a\sqrt{3} }{8}

Volume of each atom = \frac{4 }{3} \pi (\frac{a\sqrt{3}}{8})^3 = \frac{\pi *a^3\sqrt{3}}{128}

Number of atoms/unit cell = 8

Total volume of the atoms = 8X \frac{\pi *a^3\sqrt{3}}{128} = \frac{\pi *a^3\sqrt{3}}{16}

The percentage of unit cell volume = \frac{\frac{\pi *a^3\sqrt{3}}{16}}{a^3} =\frac{\pi *a^3\sqrt{3}}{16a^3} = \frac{\pi \sqrt{3}}{16} = 0.3401

= 0.3401  X 100% = 34.01%

You might be interested in
Technetium 99 releases a gamma ray
GenaCL600 [577]

what?? please reword this

6 0
3 years ago
What factors affect the temperature of sea water
Gelneren [198K]
The two main factors the temperature of seawater are density and the salinity of the water.
8 0
3 years ago
What is the chemical formula for a compound between Li and Br?
natima [27]

LiBr.

<h3>Explanation</h3>

Note that the group number in this answer refers to the new IUPAC group number, which ranges from 1 to 18. Counts from the left. Start with the first two column (group 1 and 2), go on to the transition elements (Sc, Ti, etc. in group 3 through 12), and continue with the nonmetals (group 13 through 18).  

Li is a group 1 metal. As a metal, it tends to form positive ions ("cations"). Metals in group 1 and 2 are <em>main group</em> metals. The charge on main group metal ions tends to be the same as the group number of the metal. Li is in group 1. The charge on an Li ion will be +1. Formula of the Li ion will be \text{Li}^{+}.

Br is a group 17 nonmetal. As a nonmetal, it tends to form negative ions ("anions"). The charge on nonmetal ions excepting for H tends to equal the group number of the nonmetal minus 18. Br is in group 17. The charge on a Br ion will be 17 - 18 = -1. Formula of the Br ion will be \text{Br}^{-}

All the ions in an ionic compound carry charge. However, some of the ions like \text{Li}^+ are positive. Others ions like \text{Br}^{-} are negative. Charge on the two types of ions balance each other. As a result, the compound is <em>overall</em> neutral.

1 × (+1) + 1 × (-1) = 0. The positive charge on one \text{Li}^{+} ion balances the negative charge on one \text{Br}^{-} ion. The two ions would pair up at a 1:1 ratio.

The empirical formula for an ionic compound shows all the ions in the compound. Positive ions are written in front of negative ions. \text{Li}^{+} is positive and \text{Br}^{-} is negative. The formula shall also show the simplest ratio between the ions. For the compound between Li and Br, a 1:1 ratio will be the simplest. The "1" subscript in an empirical formula can be omitted. Hence the formula: LiBr.

5 0
3 years ago
Abbrevation of mass in the si unit
Leno4ka [110]
The SI unit for mass is Kilogram (kg).
3 0
3 years ago
Which of these is the best definition of a fuel cell?
oksian1 [2.3K]

Answer:

A voltaic cell that uses the oxidation of a fuel to produce electricity  

Explanation:

A fuel cell is a voltaic cell that converts the chemical energy of a fuel and an oxidizing agent into electricity.

A. is wrong. This definition is so broad that it could include a candle in a cup.

C is wrong. The batteries in flashlights and cell phones are not fuel cells.

 

3 0
2 years ago
Other questions:
  • How is burning methane similar to burning magnesium?
    13·2 answers
  • Nncncncncncncncaaaaaaa
    6·2 answers
  • What is the largest body in our solar system
    5·2 answers
  • I need to know all the answers for this homework!!!!
    10·1 answer
  • Please use the values in the resources listed below instead of the textbook values. Under certain conditions the decomposition o
    14·1 answer
  • You have a 5-liter container with 2.00 x 1023 molecules of ammonia gas (NH3) at STP
    11·1 answer
  • This is a mixture that has the same composition throughout.
    11·1 answer
  • When 40g of ammonium nitrate explode 14g of nitrogen and 8g of oxygen form. How many grams of water form?
    9·1 answer
  • How many grams are in 1.2 moles of neon
    6·1 answer
  • A physical change is ...
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!