The Solid State

  • Question 13
    CBSEENCH12005361

    Distinguish between Face-centred and end-centred unit cells.

    Solution

    (ii) Face centered unit cell

    End-centered unit cell

    It contains one particle present at the centre of its each face, besides the ones that are at its corners.

    In this unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners.

    Question 14
    CBSEENCH12005362

    Explain how much portion of an atom located at (i) corner and (ii) body-centre of a cubic unit cell is part of its neighbouring unit cell.

    Solution

    (i) Primitive cubic unit cell has atoms only at its corner. Each atom at a corner is shared between eight adjacent unit cells . four unit cells in the same layer and four unit cells of the upper (or lower) layer Therefore only 1/8th of an atom (molecule or ion) actually belongs to a particular unit cell.
    since each cubic unit cell has 8 atoms on its corners, the total number of atoms in one unit cell is 8×1/8 = 1 atom.
    (ii) The atom at the body centre wholly belongs to the unit cell in which it is present. Thus in a body-centered cubic (bcc) unit cell:
    (i) 8 corners×1/8 per corner atom =8×1/8 = 1 atom 
    (ii) 1 body centre atom =1×1=1
       therefore total number of atom per unit cell =2 atom.

    Question 15
    CBSEENCH12005363

    What is the two-dimensional coordination number of a molecule in square close packed layer ?

    Solution
    The co-ordination number is 4.
    Question 16
    CBSEENCH12005364

    A compound forms hexagonal closed-packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?

    Solution
    Number of closed packed particeles                          =0.5×6.022×1023=3.011×1023  
    therefore number of octhahedral voids                    =   3.011×1023
    and number oftetrahedral voids =2×3.011×1023=6.022×1023
    therefore total number of voids=3.011×1023 +6.022×1023 =9.033×1023.

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