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The density of lead is 11.35 g cm^(-3) a...

The density of lead is 11.35 g `cm^(-3)` and the metal crystallizes with fcc unit cell. Estimate the radius of lead atom.
[Atomic mass of lead = 207 g mol and `N_(A) = 6.02 xx 10^(23) mol^(-1)`]

Text Solution

Verified by Experts

`d = (Z xx M)/(a^(3) xx N_(A))`
`11.35 = (207 xx 4)/(a^(3) xx 6.023 xx 10^(23))`
`a^(3) = (828)/(6.023 xx 10^(23) xx 11.35)`
`a^(3) = (828 xx 10^(-23))/(68.361)`
`= 12.112 xx 10^(-23)`
`= 121.12 xx 10^(-24)`
or `a = (121.12)^(1//3) xx 10^(-8)`
`= 4.943.10^(-8)` cm
`= 494.3 xx 10^(-10)` cm
= 494.3 pm
for fcc `r = (a)/(2 sqrt(2))`
= 0.3535 a
= 0.3535 `xx` 494.3 pm
= 174.7 pm
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