Ga ( atomic mass 70 μ ) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is × 10 21 .(Round off to the Nearest Integer)

# Ga ( atomic mass $70\mu$ ) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is___ $×{10}^{21}$ .(Round off to the Nearest Integer)

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### Solution:

Ga Crystallizes as H.C.P

If number of Particles per unit cell = n ,  number. of Tetrahedron voids = 2n

number. of octahedron voids =   n,

Total = 3n

no. of Ga particles given $\frac{W}{GAW}×{N}_{A}=\frac{0.581}{70}×6.023×{10}^{23}=0.0499×{10}^{23}\text{\hspace{0.17em}}atom$

$=\frac{0.581}{70}×6.023×{10}^{23}=0.0499×{10}^{23}\text{\hspace{0.17em}}atom$

For one particles – 3 voids $\therefore \text{\hspace{0.17em}\hspace{0.17em}}0.0499×{10}^{23}\to \text{\hspace{0.17em}\hspace{0.17em}}?$

$\frac{0.0499×{10}^{23}}{1}×3=0.1499×{10}^{23}\text{\hspace{0.17em}}voids$

$\therefore \text{\hspace{0.17em}}14.99×{10}^{21}\cong 15×{10}^{21}\text{\hspace{0.17em}\hspace{0.17em}}voids\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}X=15$

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