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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)

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)

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Chemistry
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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
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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)
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