Question

# At $$100^oC$$, copper $$(Cu)$$ has $$FCC$$ unit cell structure with cell edge length of $$x\,\mathring{A}$$. What is the approximate density of $$Cu$$ (in g.cm$$^{-3}$$) at this temperature?[Atomic mass of $$Cu =63.55\,u$$]

A
105x3
B
211x3
C
205x3
D
422x3

Solution

## The correct option is D $$\dfrac{422}{x^3}$$Density expression for unit cell,Density, $$d=\dfrac{Z\times M}{a^3\times N_A}$$where,$$d=$$ density of the unit cell$$M=$$ Molar mass of the molecule$$a^3=$$ volume of the unit cell$$N_A=$$ Avogadro numberHere, for FCC unit cell, $$Z=4$$Subsituting the values we get,Density, $$d=\dfrac{4\times 63.55}{6.02 \times10^{23}\times x^3 \times10^{-24}}g/cm^3$$            Note:  $$[1\mathring {A} = 10^{-8} cm]$$$$d=\dfrac{63.55\times 4\times10}{6.02\times x^3}g/cm^3$$$$d=\dfrac{422.26}{x^3} \simeq (\dfrac{422}{x^3})$$Chemistry

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