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Question
Silver crystallizes in the fcc structure. If the edge length of the unit cell is 400 pm, calculate the density of silver (Atomic mass of Ag = 108).
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Solution
Given:
M = 108 g mol−1,
n = 4 atoms for fcc,
NA = 6.022 × 1023 atoms mol−1,
a = 400 pm = 4 × 10−8 cm,
ρ = ?
Formula:
ρ = `("M" xx "n")/("a"^3 xx "N"_"A")`
∴ ρ = `(108 xx 4)/((4 xx 10^-8)^3 xx 6.022 xx 10^23)`
= `432/(64 xx 10^-24 xx 6.022 xx 10^23)`
= `432/(385.408 xx 10^-1)`
∴ ρ = 11.21 g/cm3
∴ ρ = 11.21 × 103 kg/m3
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