Grade 11Physical Chemistry

how to derive the height of a hcp unit cell? please discuss in detail.

tejaswini tummala

14 Years agoGrade 11

14 Years ago

Dear tejaswini tummala,

A,B,C,E (red dots) will represents the centres of sphere of atoms in HCP closed packing,

now, AB=BC=CA=EB = 2R (edge lengths of HCP)

$BD=\frac{2R}{\sqrt{3}}$ ,as BD divides the median through B in 2:1 ratio from B...

now EDB is rt. triangle,

by pythagores theorem :

$(\frac{2R}{\sqrt{3}})^2+h^2=(2R)^2$

=> $h=2R\sqrt{\frac{2}{3}}$

now, their will be another atom which will be mirror image of E on plane ABC

so, the height (c) of HCP will be 2h

$c=2h=4R\sqrt{\frac{2}{3}}$

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