Question

How to calculate Density of tetragonal unit cell by formula?

Answer 1

Answer:

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

The formula of Density for a random unit cell is as follows -

$Density = \frac{ Z _{effective} \times M }{N _{a} \times a {}^{3} }$

where ,

★ $Z _{effective}$ = number of atoms in a unit cell

★ M = molar mass

★ $N _{a} = Avogadro's \: Number = 6 × 10^{23}$

★ a = edge length

now ,

In a tetragonal unit cell ,

the atoms are present over the corners as well as the at the body centre.

Therefore ,

$Z _{effective} = contribution \: by \: the \: 8 \: corners \: + contribution \: by \: the \: body \: centre$

$\implies \: (\frac{1}{8} \times 8) \: + \: 1 \\ \\ \implies \: 1 + 1 \\ \\ \implies2$

And ,

$N _{a} = 6 \times 10 {}^{23}$

Substituting the values of the following in the formula of Density , we get

$\bold\purple{Density = \frac{2 \times M}{6 \times 10 {}^{23} \times a {}^{3} }}$

hope helpful :D