Anonymous
Anonymous asked in Science & MathematicsChemistry · 4 months ago

How do I find the radius of this?

Chromium forms a body centered cubic crystal. If the length of an edge is 2.884 angstroms, and the density is 7.20 g/cm^3 , what is the radius of a chromium atom in angstroms?

1 Answer

Relevance
  • Dr W
    Lv 7
    4 months ago
    Favourite answer

    I cover all the variations of these crystal cell problems in my answer here

    https://answers.yahoo.com/question/index?qid=20160...

    spend some time and sort through it.

    ***********

    this problem.  see the image I've attached

    in image #1.. note the edges of the cell start in the CENTER of each corner atom

    in image #2.. note how the corner atom exists in 8 adjacent cells

    in image #3.. note how 1/8th of each corner atom is in any given cell and how the central atom is entirely in the cell

    in image #4..

    .. (1)  note that for simple cubic cells, the atoms touch on an edge

    .. .. ... so that edge length = 2*r.  

    .. (2) For face centered cubic cells, the atoms touch on the diagonal

    .. .. .. of the face.  so that face diagonal length = 1r + 2r + 1r = 4r

    .. .. . .then using p-theorem

    .. .. .. ... . (edge length)² + (edge length)² = (face diagonal length)² 

    .. .. .. ... . 2*(edge length)² = (face diagonal length)² 

    .. .. .. ... . √ 2*(edge length) = (face diagonal length)

     .. .. .. ... .√ 2*(edge length) = (4r).

    .. .. .. .. ... edge length = 4r/√ 2

    .. (3) for body centered cubic cells, the atoms touch on the diagonal 

    .. .. . .of the CELL.  which has length = r+2r+r = 4r

    .. .. ...with legs of 1 edge and 1 face diagonal so that

    .. . . ...... . (edge length)² + (face diagonal length)² = (cell diagonal length)² 

    ... .. .. ... . 3*(edge length)² = (cell diagonal length)²

    .. .. .. ... . √3*(edge length) = (cell diagonal length)

     .. .. .. ... .√ 3*(edge length) = (4r).

    .. .. .. .. ... edge length = 4r/√ 3

    see the pics

    *************

    all that behind us, you don't need density to finish this

    .. r = √ 3 / 4 * (edge length) = √ 3 / 4 * (2.884Å ) = 1.249 Å

    Attachment image
    • Commenter avatarLog in to reply to the answers
Still have questions? Get answers by asking now.