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Question
The cubic unit cell of a metal (molar mass = 63.55g mol−1) has an edge length of 362 pm. Its density is 8.92g cm−3.
The type of unit cell is ______.
Options
primitive
face centered
body centered
end centered
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Solution
The cubic unit cell of a metal (molar mass = 63.55g mol−1) has an edge length of 362 pm. Its density is 8.92g cm−3.
The type of unit cell is face centered.
Explanation:
To determine the type of unit cell, we calculate the number of atoms per unit cell (Z) using the density formula:
`p = (Z xx M)/(a^3 xx N_A)`
Convert units:
The edge length a = 362 pm
= 3.62 × 10−8 cm.
Rearrange for Z:
`Z = (p . a^3 . N_A)/M`
Plug in values:
`Z = (8.92 xx (3.62xx10^-8)^3 xx 6.022 xx 10^23)/63.55`
= 4
Since a value of Z = 4 corresponds to a face-centered cubic (FCC) lattice, while primitive is 1 and body-centered is 2, the metal crystallizes in an FCC structure.
