Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atoms B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. What is the approximate packing efficiency in solid 2?

  • Option 1)

    45%

  • Option 2)

    75%

  • Option 3)

    90%

  • Option 4)

    65%

Answers (1)

 

length of body diagonal = \sqrt{3}a=r+r+2(2r)

                                      = \sqrt{3}a=6r

                                      = a=2\sqrt{3}r

Packing\; fraction=\frac{volume\; of \; particles}{volume\;of\; unit\; cell}

                                        =\frac{\frac{4}{3}\pi r^{3}+\frac{4}{3}\pi (2r)^{3}}{a^{3}}

                                        =\frac{\frac{4}{3}\pi r^{3}+\frac{4}{3}\pi (2r)^{3}}{\left (2\sqrt{3}r \right )^{3}}

                                         = 91.27%=90%

                                        


Option 1)

45%

Option 2)

75%

Option 3)

90%

Option 4)

65%

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