Question

An element with molar mass 27g/mol
forms Cubic unit cell with edge length
of 405 pm. If density of the element
is 2.7 g/cm3. What is the nature of
cubic unit cell ? (fcc or ccp)​

Answer 1

Answer:

fcc is the nature of the cubic unit cell

Answer 2

$\huge\rm\underline\purple{Question :-}$

An element with molar mass 27 g/mol forms cubic unit cell with edge length of 405pm. If density of the element is 2.7g/cm³. What is the nature of cubic unit cell?

$\huge\rm\underline\purple{Answer :-}$

$\green{\underline\bold{Given,}}$

• Molar mass of the given element,m = 27 g/mol= 0.027 kg/mol
• Edge length,a = 4.05 × 10^-10m

$\red{\underline\bold{To\:find,}}$

• Nature of the cubic unit cell = ?

$\orange{\underline\bold{Applying\: the\: relation ,}}$

$\boxed{ \sf \blue{ d = \frac{z×m}{a3×Na}}}$

where, z is the number of atoms in the unit cell and Na is the avogadro number.

$\pink{\underline\bold{Thus,}}$

z = $\frac{d×a3×Na}{m}$

✏ After calculating, we get the value of z as,

z = 4

✏ Since, the number of atoms in the unit cell is 4, the given cubic unit cell has an fcc structure.

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