a hypothetical alloy has a face-centered cubic unit cell. its density is 10.470 kg/m^3, and its atomic weight is 106.8 g/molw. a. what is the atomic radius of the alloy in cm? b. what is the volume of the single atom of the alloy in cm^3?
Convert the density into "g\/cm3"
D="10470kg\/m3"
D therefore=Â "10.47g\/cm3"
"d=(z\u00d7M)\/(a3\u00d7Na)"
For a FCCÂ "Z=4"
Therefore,
10.47g/cm3=Â "(4\u00d7106.8g\/mol)\u00f7(a3\u00d76.022\u00d710^23)\n\na3=6.776\u00d710^-22."
But volume"= l3"
L=Â "3\u221avol"
"L=3\u221a6.776\u00d710^-22\n\nL=8.79\u00d710^-8cm"
"=8.79\u00d710^-8\u00d7(10^10\/10^2cm)"
=8.79∆
But, "C^2=a^2+a^2\n,C^2=2a^2"
"C^2=2\u00d7(8.79)^2"
"C^=\u221a154.53"
"C=12.43\u2206"
And,
"r=c\/4"
r=12.43/4
Ans for part( a)
"r=3.12"Â ans.
(B)
Vol of a single atom "V=4\/3\u03c0r^3"
"V=4\/3\u00d722\/7\u00d73.12^3"
"V=127.27cm^3"Â Ans.
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