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Carbon atoms in a hexagonal structure

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    Consider carbon atoms arranged in interconnecting regular hexagons (shown below);




    I'm asked to find how many atoms there would be per m^3. I would find the area of the hexagon, divide 1 by it and times that number by how many atoms there are per hexagon.

    However, the answer confuses me. It says "Since each carbon atom is shared between three hexagons, there are effectively two full carbon atoms per hexagon".

    I'm not sure how to make this link. I understand every atom is shared between three hexagons, but I'm having a hard time visualising how that equates to 2 atoms per hexagon, can anyone help?
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    How would you go about adding a hexagon to the top of that image?
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    Well the way I would look at it is that if you look at any vertex of the central hexagon, you see that it is shared with an additional two hexagons. Thus this hexagon 'owns'  \frac{1}{3} of the vertex, or,  \frac{1}{3} of an atom. This can also be said of each of the vertices in the hexagon. So, to count up the number of atoms in the hexagon we need to take into account that the atoms are shared, so the total number of atoms in the hexagon is  6\frac{1}{3}=2

    Hope this helped
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    (Original post by Sasukekun)
    Consider carbon atoms arranged in interconnecting regular hexagons (shown below);




    I'm asked to find how many atoms there would be per m^3. I would find the area of the hexagon, divide 1 by it and times that number by how many atoms there are per hexagon.

    However, the answer confuses me. It says "Since each carbon atom is shared between three hexagons, there are effectively two full carbon atoms per hexagon".

    I'm not sure how to make this link. I understand every atom is shared between three hexagons, but I'm having a hard time visualising how that equates to 2 atoms per hexagon, can anyone help?
    Hey, the diagram you have there isn't that good for showing what you want to show; it's a bit confusing.

    The diagram you want is this one:

    Spoiler:
    Show


    Can you see that each carbon is bonded to three others, with 120o C-C-C bond angles?

    Each hexagon has 6 carbon atoms. Each carbon atom is at the centre of three hexagons. Therefore, you do 6 / 3 = 2 carbon atoms per hexagon.

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Updated: May 27, 2012
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