А. this question. Sketch one 'face' of a unit cell for SC, FCC and BCC. A total of 3 sketches are required for В. Calculate the percent empty space in each of the unit cells, SC, BCC and FCC. This is the ratio of space filled by atoms inside the unit cell to the total volume of the unit cell, given as a percentage. Remember that the volume of a sphere with radius, r, is ar³. (volume of unit cell – volume of atoms inside unit cell) volume of unit cell % Empty space x 100% a) Calculate the volume of ONE unit cell, keep the 'r' term in your result. b) Calculate the volume of all atoms inside ONE unit cell, again keep the 'r' term in your result. c) Use the equation above and your previous two answers to calculate the % empty space in the unit cell. You should find the r' terms cancel! Simplify and report your answer to 3 sig. figs. C. Density is an intensive property, meaning any sample size will give the same value. Hence, even a sample as small as a unit cell can be used to determine a substance's density: mass of atoms inside unit cell (in grams) density (using unit cell) = volume of the unit cell, a³ (in cm³) Using the density formula above, calculate the density (in g/cm³) for each of the three crystal structures (SC, FCC, & BCC) when they contain atoms with a mass of 105.00 amu and a radius of 0.125 nm. For each unit cell type, label and show how a calculation for the mass of the unit cell, the volume of the unit cell and the density of the unit cell. Show all necessary work, including units for each numeric value used in these calculations! HINT: Be careful with your unit conversions.if your density values are not between 0.5 and 30 g/cm³, you've likely made a unit conversion error. Which one of the three types of cubic unit cells (SC, BCC, FCC) corresponds to what is called "cubic closest packing"? Use two pieces of evidence from Table 1 and the previous questions to explain and support your selection. (just listing them is not an explanation and earns no points)

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
icon
Related questions
icon
Concept explainers
Question
100%

pls help q(A) and (D)

Table 1: Cubic Unit Cell System
Simple
Body
Face
Description of table entry
Cubic
Centered
Centered
(1) # of corner atoms in one unit cell
8
8.
(2) Fraction of a single corner atom inside one unit cell 1/8
1/8
1/8
Total # of 'equivalent corner atoms inside one unit cell
Hint: multiple (1) x (2)
(3) # of atoms in the center (body) of one unit cell 0
1
1.
1
1
(4) Fraction of a single body atom inside one unit cell
1.
Total # of 'equivalent body atoms inside one unit cell
1
Hint: multiple (3) x (4)
(5) # of atoms in all faces of one unit cell
6
(6) Fraction of each face atom inside one unit cell
Total # of 'equivalent face atoms inside one unit cell.
Hint: multiple (5) x (6)
1/2
3
a) Find the total # of 'equivalent atoms in each unit cell (sum
1.
2
4
equivalent # of corner, body, and face atoms)
b) Coordination number for an atom in this unit cell
6.
8
12
c) Along which length do atoms touch in this unit cell, a, c or d?
la
d.
d) Express the above length in terms of atomic radius, 'T'
Keep 'r' as a variable in your answer (e.g., '2r')
a= 2r
d=4r
c=4r
e) Use the answer above to find the unit cell edge length, a in terms of
Tr'. Round to 3 sig figs & keep 'r' as a variable, e.g. "3.14r". Show
2.00r
2.31r
2.83r
your
work
f) Using the answer above for 'a', determine the unit cell volume (a®) in 8.00r^3
12.3г^3
22.6r^3
terms of atomic radius, 'r³'. Round your answer to 3 sig figs and
keep 'r' as a variable. Show
your .
work
Transcribed Image Text:Table 1: Cubic Unit Cell System Simple Body Face Description of table entry Cubic Centered Centered (1) # of corner atoms in one unit cell 8 8. (2) Fraction of a single corner atom inside one unit cell 1/8 1/8 1/8 Total # of 'equivalent corner atoms inside one unit cell Hint: multiple (1) x (2) (3) # of atoms in the center (body) of one unit cell 0 1 1. 1 1 (4) Fraction of a single body atom inside one unit cell 1. Total # of 'equivalent body atoms inside one unit cell 1 Hint: multiple (3) x (4) (5) # of atoms in all faces of one unit cell 6 (6) Fraction of each face atom inside one unit cell Total # of 'equivalent face atoms inside one unit cell. Hint: multiple (5) x (6) 1/2 3 a) Find the total # of 'equivalent atoms in each unit cell (sum 1. 2 4 equivalent # of corner, body, and face atoms) b) Coordination number for an atom in this unit cell 6. 8 12 c) Along which length do atoms touch in this unit cell, a, c or d? la d. d) Express the above length in terms of atomic radius, 'T' Keep 'r' as a variable in your answer (e.g., '2r') a= 2r d=4r c=4r e) Use the answer above to find the unit cell edge length, a in terms of Tr'. Round to 3 sig figs & keep 'r' as a variable, e.g. "3.14r". Show 2.00r 2.31r 2.83r your work f) Using the answer above for 'a', determine the unit cell volume (a®) in 8.00r^3 12.3г^3 22.6r^3 terms of atomic radius, 'r³'. Round your answer to 3 sig figs and keep 'r' as a variable. Show your . work
Sketch one 'face' of a unit cell for SC, FCC and BCC. A total of 3 sketches are required for
this question.
Calculate the percent empty space in each of the unit cells, SC, BCC and FCC. This is the ratio
of space filled by atoms inside the unit cell to the total volume of the unit cell, given as a percentage.
Remember that the volume of a sphere with radius, r, is tr³.
А.
В.
(volume of unit cell – volume of atoms inside unit cell)
volume of unit cell
% Empty space
x 100%
a) Calculate the volume of ONE unit cell, keep the 'r' term in your result.
b) Calculate the volume of all atoms inside ONE unit cell, again keep the 'r term in your result.
c) Use the equation above and your previous two answers to calculate the % empty space in the
unit cell. You should find the r' terms cancel! Simplify and report your answer to 3 sig. figs.
С.
Density is an intensive property, meaning any sample size will give the same value. Hence,
even a sample as small as a unit cell can be used to determine a substance's density:
mass of atoms inside unit cell (in grams)
volume of the unit cell, a³ (in cm³)
density (using unit cell)
Using the density formula above, calculate the density (in g/cm³) for each of the three crystal
structures (SC, FcC, & BCC) when they contain atoms with a mass of 105.00 amu and a radius of
0.125 nm.
For each unit cell type, label and show how a calculation for the mass of the unit cell, the
volume of the unit cell and the density of the unit cell.
Show all necessary work, including units for each numeric value used in these calculations!
HINT: Be careful with your unit conversions.if your density values are not between 0.5 and
30 g/cm?, you've likely made a unit conversion error.
Which one of the three types of cubic unit cells (SC, BCC, FCC) corresponds to what is called
"cubic closest packing"? Use two pieces of evidence from Table 1 and the previous questions to
explain and support your selection. (just listing them is not an explanation and earns no points)
Transcribed Image Text:Sketch one 'face' of a unit cell for SC, FCC and BCC. A total of 3 sketches are required for this question. Calculate the percent empty space in each of the unit cells, SC, BCC and FCC. This is the ratio of space filled by atoms inside the unit cell to the total volume of the unit cell, given as a percentage. Remember that the volume of a sphere with radius, r, is tr³. А. В. (volume of unit cell – volume of atoms inside unit cell) volume of unit cell % Empty space x 100% a) Calculate the volume of ONE unit cell, keep the 'r' term in your result. b) Calculate the volume of all atoms inside ONE unit cell, again keep the 'r term in your result. c) Use the equation above and your previous two answers to calculate the % empty space in the unit cell. You should find the r' terms cancel! Simplify and report your answer to 3 sig. figs. С. Density is an intensive property, meaning any sample size will give the same value. Hence, even a sample as small as a unit cell can be used to determine a substance's density: mass of atoms inside unit cell (in grams) volume of the unit cell, a³ (in cm³) density (using unit cell) Using the density formula above, calculate the density (in g/cm³) for each of the three crystal structures (SC, FcC, & BCC) when they contain atoms with a mass of 105.00 amu and a radius of 0.125 nm. For each unit cell type, label and show how a calculation for the mass of the unit cell, the volume of the unit cell and the density of the unit cell. Show all necessary work, including units for each numeric value used in these calculations! HINT: Be careful with your unit conversions.if your density values are not between 0.5 and 30 g/cm?, you've likely made a unit conversion error. Which one of the three types of cubic unit cells (SC, BCC, FCC) corresponds to what is called "cubic closest packing"? Use two pieces of evidence from Table 1 and the previous questions to explain and support your selection. (just listing them is not an explanation and earns no points)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 6 images

Blurred answer
Knowledge Booster
Basics in Organic Reaction Mechanisms
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY