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Test: Packing Efficiency - Chemistry MCQ


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10 Questions MCQ Test - Test: Packing Efficiency

Test: Packing Efficiency for Chemistry 2024 is part of Chemistry preparation. The Test: Packing Efficiency questions and answers have been prepared according to the Chemistry exam syllabus.The Test: Packing Efficiency MCQs are made for Chemistry 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Packing Efficiency below.
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Test: Packing Efficiency - Question 1

If copper, density = 9.0 g/cm3 and atomic mass 63.5, bears face-centered unit cells then what is the ratio of surface area to volume of each copper atom?

Detailed Solution for Test: Packing Efficiency - Question 1

Density, d of unit cell is given by d = 
Given,
Density, d = 9.0 g/cm3
Atomic mass, M = 63.5 g/mole
Edge length = a
NA = Avogadro’s number = 6.022 x 1023
z = 4 atoms/cell
On rearranging the equation for density we get a3
Substituting the given values:

Therefore, a = 360.5 pm
The relation of edge length ‘a’ and radius of particle ‘r’ for FCC packing i.e. a = 2√2r.
On substituting the value of ‘a’ in the given relation, r = =127.46 pm
Now, for spherical particles volume, V = 4πr3/3 and surface area, S = 4πr2
Required ratio = S/V=4πr2/(4πr3/3) = 3/r (after simplifying)
Thus, S/V = 3/127.46 = 0.0235.

Test: Packing Efficiency - Question 2

How many atoms surround the central atom present in a unit cell with the least free space available?

Detailed Solution for Test: Packing Efficiency - Question 2

FCC, CCP and HCP are unit cells with least free space available i.e. highest packing efficiency. The coordination number of given cells are 12.

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Test: Packing Efficiency - Question 3

“The packing efficiency can never be 100%”. Is this true or false?

Detailed Solution for Test: Packing Efficiency - Question 3

Packing efficiency can never be 100% because in packing calculations all constituent particles filling up the cubical unit cell are assumed to be spheres

Test: Packing Efficiency - Question 4

If the body-centered unit cell is assumed to be a cube of edge length ‘a’ with spherical particles of radius ‘r’ then how is the diameter, d of particle and surface area, S of the cell related?

Detailed Solution for Test: Packing Efficiency - Question 4

For BCC unit cell the relation between radius of a particle ‘r’ and edge length of unit cell, a, is r = 
We know that diameter, d = 2r =
Implying d2 =
Therefore, 4d2/3=a2
Multiplying by 6 on both sides gives S = 6a2 = 8d2, where S is the surface area of the cube = 6a2.

Test: Packing Efficiency - Question 5

What is the dimensional formula of packing fraction?

Detailed Solution for Test: Packing Efficiency - Question 5

Packing fraction is a dimensionless quantity which is the ratio of space occupied to total crystal space available. Since both the quantities have the same units the ratio renders dimensionless.

Test: Packing Efficiency - Question 6

If metallic atoms of mass 197 and radius 166 pm are arranged in ABCABC fashion then what is the surface area of each unit cell?

Detailed Solution for Test: Packing Efficiency - Question 6

ABCABC arrangement is found in CCP.
In closed cubic packing, relation between edge length of unit cell, a, and radius of particle, r, is given as a=2√2r.
Surface area (S.A.) = 6a2
From the relationship,
a2 = 8r2
S.A. = 6a2 = 48r2
When r = 166 pm, S.A. = 48(166pm) = 1.32 x 106 pm2.

Test: Packing Efficiency - Question 7

What are the percentages of free space in a CCP and simple cubic lattice?

Detailed Solution for Test: Packing Efficiency - Question 7

The packing efficiency in CCP and simple cubic lattice are 74% and 52%, respectively. Hence the corresponding free spaces will be 100% – 74% = 26% and 100% – 52% = 48%.

Test: Packing Efficiency - Question 8

Which of the following metals would have the highest packing efficiency?

Detailed Solution for Test: Packing Efficiency - Question 8

Copper metal bears face-centered unit cells in its crystal structure. Potassium and chromium both have body-centered unit cells whereas polonium is the only known metal to bear a simple cubic structure. FCC structure has the highest efficiency.

Test: Packing Efficiency - Question 9

Arrange the types of arrangement in terms of decreasing packing efficiency.

Detailed Solution for Test: Packing Efficiency - Question 9

HCP and CCP have the highest packing efficiency of 74% followed by BCC which is 68%. The simple cubic structure has a packing efficiency of 54%.

Test: Packing Efficiency - Question 10

What does the ratio ‘space occupied/total space’ denote?

Detailed Solution for Test: Packing Efficiency - Question 10

Packing factor is a fraction of total space of the unit cell occupied by the constituent particles.

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