Kaplan's Chem question

[DATkiller]

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Hey guys. I just saw this and I have no idea what the question is asking for.

How many atoms are there, respectively, in the body-centered cubic, face-centered cubic, and simple cubic unit cells?

the answer is 2,4,1

 

[Ibraiz]

Look this up: http://en.wikipedia.org/wiki/Cubic_crystal_system

 

[305602]

There was a pretty detailed section of my gchem textbook outlining what these are and how to do some calculations for the density of a substance given its structure:
Body-centered: http://www.google.com/imgres?imgurl=http://mrsec.wisc.edu/Edetc/SlideShow/images/unit_cells/body_centered_cubic2.jpg&imgrefurl=http://mrsec.wisc.edu/Edetc/SlideShow/slides/unit_cells/body_centered_cubic.html&h=336&w=320&sz=32&tbnid=d4zt8lnJ5tYkYM:&tbnh=119&tbnw=113&prev=/images%3Fq%3Dbody-centered%2Bcubic&usg=__29qgtoZ0vTi_q66kcUArlZW2Sos=&sa=X&ei=mOwcTIuGGoH6lwfnxcC8Dg&ved=0CCoQ9QEwBw
Face-centered: http://mrsec.wisc.edu/Edetc/SlideShow/slides/unit_cells/face_centered_cubic.jpg
Simple cubic: http://www.seas.upenn.edu/~chem101/sschem/simplecubic.JPG

To figure out how many atoms there are within a unit cell, imagine a cube. Add of the "fractions" of the atoms (imagine a sphere). For example, atoms fully inside the cube count as 1, atoms on one of the faces of the cube count as 1/2, and atoms located on the corners of the cube count as 1/8.

 

[DATkiller]

Look this up: http://en.wikipedia.org/wiki/Cubic_crystal_system

Interesting. I have never seen these stuff in my college gen chem. What is a lattice point btw?

 

[nze82]

Hey guys. I just saw this and I have no idea what the question is asking for.

How many atoms are there, respectively, in the body-centered cubic, face-centered cubic, and simple cubic unit cells?

the answer is 2,4,1

Only 1/8 of the atoms at the corners of each cell belong to that cell..
Only 1/2 of the atoms on each face of the cell belong to that cell..
The atom at the center of each cell completely belongs to that cell...

In a body centered cell, you have 8 corner atoms and one center atom, so:
Total # of atoms = 8(1/8) + 1 = 2

In a face centered cell you have 8 corner atoms and 6 face atoms, so:
Total # of atoms = 8(1/8) + 6(1/2) = 4

In a simple centered cell you only have 8 corner atoms, so:
Total # of atoms = 8(1/8) = 1