A substance has a density of 2 g cm^{-3}. I | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The density of a unit cell is given by the formula: $d = \frac{Z 	imes M}{a^3 	imes N_A}$ For an $fcc$ crystal, the number of atoms per unit cel

Vedclass · Accepted Answer

$64.8$

Vedclass · Answer

(B) The density of a unit cell is given by the formula: $d = \frac{Z 	imes M}{a^3 	imes N_A}$ For an $fcc$ crystal, the number of atoms per unit cell, $Z = 4$. Given: $d = 2 \ g \ cm^{-3}$, $a = 600 \ pm = 600 	imes 10^{-10} \ cm = 6 	imes 10^{-8} \ cm$, $N_A = 6 	imes 10^{23} \ mol^{-1}$. Substituting the values: $2 = \frac{4 	imes M}{(6 	imes 10^{-8})^3 	imes 6 	imes 10^{23}}$ $2 = \frac{4 	imes M}{216 	imes 10^{-24} 	imes 6 	imes 10^{23}}$ $2 = \frac{4 	imes M}{216 	imes 0.1} = \frac{4 	imes M}{21.6}$ $M = \frac{2 	imes 21.6}{4} = 10.8 	imes 1 = 10.8$ Wait, recalculating: $2 = \frac{4 	imes M}{216 	imes 10^{-24} 	imes 6 	imes 10^{23}} = \frac{4 	imes M}{1296 	imes 10^{-1}} = \frac{4 	imes M}{129.6}$ $M = \frac{2 	imes 129.6}{4} = 64.8 \ g \ mol^{-1}$.

$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is
$(N_{A} = 6 \times 10^{23} \ mol^{-1})$

Similar Questions

$A$ metal crystallizes in a simple cubic lattice. The volume of one unit cell is $6.4 \times 10^7 \ pm^3$. What is the radius of the metal atom in $pm$?

The substance $CuCl$ has a $ZnS$ $(ccp)$ structure. If its density is $3.4 \ g \ cm^{-3}$, what is the edge length of the unit cell?

How many unit cells are present in a cube-shaped ideal crystal of $NaCl$ of mass $1 \ g$?

Calculate the density of an element having molar mass $63 \ g \ mol^{-1}$ that forms $FCC$ structure $\left[a^3 \times N_{A} = 28 \ cm^3 \ mol^{-1}\right]$ (in $g \ cm^{-3}$)

Calculate the radius of a metal atom in a $bcc$ unit cell having an edge length of $287 \ pm$. (in $pm$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$A$ substance has a density of $2 \ g \ cm^{-3}$. It crystallizes in the $fcc$ crystal with an edge length of $600 \ pm$. The molar mass of the substance (in $g \ mol^{-1}$) is $(N_{A} = 6 \times 10^{23} \ mol^{-1})$