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2. Body-Centered Unit Cell a. How many unit cells share the center atom of the body-centered unit cell? b. How many total atoms are there in a body centered cubic cell? c. What is the coordination number of the atom at the center of the body centered unit cell? How about the coordination number of an atom at the corner of this unit cell? Coordination number is defined as the number of nearest neighbors of an atom or ion.

2. Body-Centered Unit Cell a. How many unit cells share the center atom of the body-centered unit cell? b. How many total atoms are there in a body centered cubic cell? c. What is the coordination number of the atom at the center of the body centered unit cell? How about the coordination number of an atom at the corner of this unit cell? Coordination number is defined as the number of nearest neighbors of an atom or ion.

Chemistry
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...
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2. Body-Centered Unit Cell a. How many unit cells share the center atom of the body-centered unit cell? b. How many total atoms are there in a body centered cubic cell? c. What is the coordination number of the atom at the center of the body centered unit cell? How about the coordination number of an atom at the comer of this unit cell? Coordination number is defined as the number of nearest neighbors of an atom or ion. d. Below is a body centered unit cell, write the letter "a" along the edge length. Calculate the length of the diagonal if all sides are "a". The dotted line refers to the diagonal of the cubes body. Use the Pythagorean relationship e = a+ b? e. Notice that the center atom and the two corner atoms along a diagonal all touch. What is the length of the diagonal in terms of "r" the radius of the atom? f. Since question 2d and 2e express the length of the diagonal when the side is “a" set them equal and solve for "a", the side of length of a body centered unit cube. g. Find the total volume of atoms in this unit cell expressed in terms of "r". To do this, multiply the number of atoms in this unit cell by the volume of a single atom with radius "". h. Find the volume of the entire unit cell including the empty space in terms of r. Remember for a cube the volume, V=1xw xh. You already know the edge length of the side in terms of "r" based in the earlier questions. i. Calculate the fraction of the total volume of the cube occupied by atoms. Express your answer in percent.
Transcribed Image Text:2. Body-Centered Unit Cell a. How many unit cells share the center atom of the body-centered unit cell? b. How many total atoms are there in a body centered cubic cell? c. What is the coordination number of the atom at the center of the body centered unit cell? How about the coordination number of an atom at the comer of this unit cell? Coordination number is defined as the number of nearest neighbors of an atom or ion. d. Below is a body centered unit cell, write the letter "a" along the edge length. Calculate the length of the diagonal if all sides are "a". The dotted line refers to the diagonal of the cubes body. Use the Pythagorean relationship e = a+ b? e. Notice that the center atom and the two corner atoms along a diagonal all touch. What is the length of the diagonal in terms of "r" the radius of the atom? f. Since question 2d and 2e express the length of the diagonal when the side is “a" set them equal and solve for "a", the side of length of a body centered unit cube. g. Find the total volume of atoms in this unit cell expressed in terms of "r". To do this, multiply the number of atoms in this unit cell by the volume of a single atom with radius "". h. Find the volume of the entire unit cell including the empty space in terms of r. Remember for a cube the volume, V=1xw xh. You already know the edge length of the side in terms of "r" based in the earlier questions. i. Calculate the fraction of the total volume of the cube occupied by atoms. Express your answer in percent.
1. Simple Cubic Unit Cell a. Each corner atom of the unit cell would be shared by how many unit cells? b. Assuming the atoms as perfect spheres, how much of a corner atom is used by just a single unit cell? c. If there are atoms at the eight corners of a simple cubic cell and each atom is shared by eight-unit cells, how many total atoms are there per simple cubic unit cell? d. What is the coordination number of each atom? Coordination number is defined as the number of nearest neighbors of an atom or ion. e. Consider one unit cell and assume the length of the side of the cube is "a". Remember that "a" is the distance between the centers of two adjacent atoms. How long is “a", the edge of a unit cell, in terms of radius, r, of an atom? f. Based in the earlier questions, a simple cubic cell has the equivalent of only 1 atom. Recall the volume of sphere with radius, r, is expressed as V= 4/3 ưr. With this information, find the total volume of all the spheres in this unit cell, expressed in terms of r. To do this, take the total number of atoms and multiply it by the volume of one atom, with radius, r) g. Find the volume of the entire unit cell including the empty space in terms of r. Remember for a cube the volume, V=1xw xh. You already know the edge length of the side in terms of "r" based in the earlier questions. h. Find the fraction of the total volume of the cube (which is the unit cell's volume) is occupied by the atoms. Express this as percent
Transcribed Image Text:1. Simple Cubic Unit Cell a. Each corner atom of the unit cell would be shared by how many unit cells? b. Assuming the atoms as perfect spheres, how much of a corner atom is used by just a single unit cell? c. If there are atoms at the eight corners of a simple cubic cell and each atom is shared by eight-unit cells, how many total atoms are there per simple cubic unit cell? d. What is the coordination number of each atom? Coordination number is defined as the number of nearest neighbors of an atom or ion. e. Consider one unit cell and assume the length of the side of the cube is "a". Remember that "a" is the distance between the centers of two adjacent atoms. How long is “a", the edge of a unit cell, in terms of radius, r, of an atom? f. Based in the earlier questions, a simple cubic cell has the equivalent of only 1 atom. Recall the volume of sphere with radius, r, is expressed as V= 4/3 ưr. With this information, find the total volume of all the spheres in this unit cell, expressed in terms of r. To do this, take the total number of atoms and multiply it by the volume of one atom, with radius, r) g. Find the volume of the entire unit cell including the empty space in terms of r. Remember for a cube the volume, V=1xw xh. You already know the edge length of the side in terms of "r" based in the earlier questions. h. Find the fraction of the total volume of the cube (which is the unit cell's volume) is occupied by the atoms. Express this as percent
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