If the density of a gold (Au) crystal crystal | vedclass

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

Question

(B) For a $ccp$ structure,the number of atoms per unit cell $Z = 4$. Density $d = \frac{Z 	imes M}{N_A 	imes a^3}$,where $M = 197 \, g/mol$ and $N_A

Vedclass · Accepted Answer

$1.439 	imes 10^{-8} \, cm$

Vedclass · Answer

(B) For a $ccp$ structure,the number of atoms per unit cell $Z = 4$. Density $d = \frac{Z 	imes M}{N_A 	imes a^3}$,where $M = 197 \, g/mol$ and $N_A = 6.022 	imes 10^{23} \, mol^{-1}$. $a^3 = \frac{Z 	imes M}{d 	imes N_A} = \frac{4 	imes 197}{19.3 	imes 6.022 	imes 10^{23}} = \frac{788}{116.22 	imes 10^{23}} \approx 6.78 	imes 10^{-23} \, cm^3 = 67.8 	imes 10^{-24} \, cm^3$. $a = \sqrt[3]{67.8 	imes 10^{-24}} \approx 4.078 	imes 10^{-8} \, cm$. For $ccp$ structure,$4r = \sqrt{2}a$,so $r = \frac{\sqrt{2} 	imes a}{4} = \frac{1.414 	imes 4.078 	imes 10^{-8}}{4} \approx 1.44 	imes 10^{-8} \, cm$.

If the density of a gold $(Au)$ crystal crystallizing in a $ccp$ structure is $19.3 \, g/cm^3$,what will be the radius of the atom? (Given: $Au = 197 \, amu$)

Similar Questions

An element crystallizes in a $bcc$ lattice. The atomic radius of the element is $2.598 \ \mathring{A}$. What is the volume (in $cm^3$) of one unit cell?

Calculate the number of atoms in $0.3 \ g$ of a metal if it forms a $bcc$ structure,given that $[\rho \times a^3 = 3 \times 10^{-22} \ g]$.

Calculate the molar mass of an element having a density of $8.6 \ g \ cm^{-3}$ if it forms a $bcc$ structure $[a^3 \times N_{A} = 22.0 \ cm^3 \ mol^{-1}]$.

$A$ solid having density of $9 \times 10^3 \ kg \ m^{-3}$ forms face-centred cubic crystals of edge length $200 \sqrt{2} \ pm$. What is the molar mass of the solid? [Avogadro constant $\cong 6 \times 10^{23} \ mol^{-1}$,$\pi \cong 3$]

An element has a body-centered cubic structure with a unit cell edge length of $400 \ pm$. The atomic mass of the element is $24 \ g \ mol^{-1}$. What is the density of the element (in $g \ cm^{-3}$)? $(N_{A} = 6 \times 10^{23} \ mol^{-1})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module