Question

Number of unit cells in 10g NaCl is:
(a)- $\dfrac{1.5}{58.5}\text{x1}{{\text{0}}^{24}}$
(b)- $\dfrac{2.5}{58.5}\text{x1}{{\text{0}}^{23}}$
(c)- $\dfrac{5.6}{58.5}\text{x1}{{\text{0}}^{20}}$
(d)- $\dfrac{5.6}{58.5}\text{x1}{{\text{0}}^{21}}$

Answer 1

Hint: Given the amount of sodium chloride is 10g, so we can calculate the number of moles of sodium chloride by dividing the given value by the molecular mass. The sodium chloride has a face-centered cubic structure.

Complete step-by-step answer:We are given the amount of sodium chloride, i.e., 10 grams. Now, to find the number of moles of sodium chloride in 10 g, we have to divide the given value with the molecular mass of sodium chloride.
The molecular mass of sodium will be equal to the addition of mass of sodium and mass of chlorine. The mass of sodium is 23 and the mass of chlorine is 35.5. So, the mass will be 58.5.
The number of moles will be:
$Moles=\dfrac{10}{58.5}$
To find the total number of unit cells, we have to multiply the number of moles with the Avogadro’s number, its value is $6.022\text{ x 1}{{\text{0}}^{23}}$
So, the total number of unit cells will be:
$\dfrac{10}{58.5}\text{ x 6}\text{.022 x 1}{{\text{0}}^{23}}$
As we know that the sodium chloride units are present in the fcc structure, i.e., face-centered cubic structure. And there are a total of 4 atoms in one unit cell of fcc.
So, to find the number of unit cells, we have to divide the total number of unit cells by 4. The value will be:
$\dfrac{10}{58.5}\text{ x 6}\text{.022 x 1}{{\text{0}}^{23}}\text{ x}\dfrac{1}{4}=\dfrac{1.5}{58.5}\text{ x 1}{{\text{0}}^{24}}$
So, the number of unit cells are $\dfrac{1.5}{58.5}\text{ x 1}{{\text{0}}^{24}}$

Therefore, the correct answer is an option (a)- $\dfrac{1.5}{58.5}\text{ x 1}{{\text{0}}^{24}}$.

Note:When the structure of the crystal is simple cubic, then the number of atoms will be 1, when the structure of the crystal is a body-centered cubic structure, then the number of atoms will be 2.