chemistry
posted by ali .
Sketch one face of a simple cubic unit cell of side a for the case when the maximum fraction of the lattice in volume is filled with atoms, and each atom is approximated by a hard sphere.
(ii) What is the radius of each atom in terms of a?
(iii) What is the volume of each atom in terms of a?
(iv) How many corner atoms contribute volume to the unit cell?
(v) What volumefraction of each corner atom is inside the unit cell?
(vi) In terms of a, how much of the volume of the unit cell is filled by all of the corner
atoms?
(vii) What is the total volume of the unit cell?
(viii) Calculate the maximum fraction of the lattice volume filled with atoms.

. (i) Sketch one face of a simple cubic unit cell of side a for the case when the maximum fraction of the lattice in volume is filled with atoms, and each atom is approximated by a hard sphere. [5 marks]
(ii) What is the radius of each atom in terms of a? [4 marks]
a/2
(iii) What is the volume of each atom in terms of a? [4 marks]
(4/3)pi r3 = (4/3)pi (a/2)3
=(pi a3)/6
(iv) How many corner atoms contribute volume to the unit cell? [4 marks]
Corner atoms contribute volume to the unit cell is one from eight corners.
(v) What volumefraction of each corner atom is inside the unit cell? [4 marks]
volume atom/volume unit cell
=[(pi a3)/6]/ a3
=pi/6
=0.5233 x 100% = 52.33%
(vi) In terms of a, how much of the volume of the unit cell is filled by all of the corner atoms? [5 marks]
Volume of the unit cell is filled by all of the corner atoms is due to its got 8 corners.
(vii) What is the total volume of the unit cell? [4 marks]
Total volume of the unit cell = a3
(viii) Calculate the maximum fraction of the lattice volume filled with atoms. [5 marks]
Maximum fraction of the lattice volume filled with atoms:
8 corners:
=[(pi a3)/6]/ 8a3
=pi/48
=0.0654 x 100% = 6.54%
Respond to this Question
Similar Questions

CHEM****
Initial info: The atoms of crystalline solid pack together into a threedimensional array of many small repeating units called unit cells. The simplest of the unit cells are those that have cubic symmetry, with atoms positioned at … 
Chemistry
what is the volume of the unit cell? A metal crystallizes in a facecentered cubic lattice. The radius of the atom is 0.197 nm. The density of the element is 1.54 g/cm^3 
chemistry help!
Hello, I am having problem with two lab questions and was wondering if someone can help! 1. Calculate the percentage of the empty space in a facecentered cubic lattice, and show that it does not depend on the edge length of the unit … 
chemistry
Hello, I am having problem with two lab questions and was wondering if someone can help! 1. Calculate the percentage of the empty space in a facecentered cubic lattice, and show that it does not depend on the edge length of the unit … 
chemistry
This problem is from my chemistry book and I am having a little trouble with the intermediary steps: Barium metal crystallizes in a body centered cubic lattice (atoms at lattice points only) The unit cell edge length is 502 pm, and … 
engineering
Sketch one face of a simple cubic unit cell of side a for the case when the maximum fraction of the lattice in volume is filled with atoms, and each atom is approximated by a hard sphere. (ii) What is the radius of each atom in terms … 
Chemistry
Boron Phosphide, BP, is a semiconductor, and a hard, abrasion resistant material. It is made by reacting Boron tribromide and phosphorus tribromide in a hydrogen atmosphere at high temperature (>750 degrees C) (a) Write a Balanced … 
Chemistry
1. The eleent gold, Au, has a facecentered cubic structure. (Density  19.3 g/cm^3) (a) What are the # of gold atoms in 1 unit cell? 
Science: Chemistry
1. The element gold, Au, has a facecentered cubic structure. (Density  19.3 g/cm^3) (a) What are the # of gold atoms in 1 unit cell? 
Chemistry
A mineral that contains iron and sulfur has the cubic unit cell pictured below. What is the empirical formula for this mineral?