CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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
loader
B
211x3
loader
C
205x3
loader
D
422x3
loader

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 number

Here, 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

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image