Ques.The density of copper metal is 8.95 g cm3. If the radius of copper atom is 127.8 pm, is the copper unit cell a simple cubic, a body-centred cubic or a face centred cubic structure? (Given: At. Mass of Cu = 63.54 g mol1and NA= 6.02 × 1023mol1)

can you please explain how it is fcc?d=M.z a3.NAOn substituting we get,8.95=z.63.54 6.022X1023X(1.27X10-8)3z=0.17.please help me out! where did i go wrong?

The density of metal is given as
d = z×Ma3×NA

For Simple cubic,
z = 1 and a = 2r

For BCC,
z = 2 and a = 43r

For FCC,
z = 4 and a = 42r

Substituting values of z and a in density formula and calculating density;
Given that-
Mass, M = 63.54 g/mol
Radius, r = 127.8 × 10-10 cm
Avagadro's number, NA = 6.02 ‚Äč× 1023

For simple cubic,
d = 1× 63.54(2×127.8×10-10)3 × 6.02 ×1023d = 6.31 g.cm-3

For BCC,
d = 2 × 63.54(43×127.8×10-10)3 ×6.02×1023d = 8.2 g.cm-3

For FCC,
d = 4 × 63.54(42×127.8×10-10)3 ×6.02×1023d = 8.92 g.cm-3

Given the density = 8.95 g.cm-3 , which is nearest for FCC. Hence copper unit cell is face centered cubic.
 

  • 53

sorry, its not the edge given its the atomic radius and hence we can find the volume.(4/3 pi r3

then we have mass =volumeX density.

mass = z. molar mass

NA

but still i get the answer as 0.72 and not 4.

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