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

Potassium metal crystallizes in a face-centered cubic $(FCC)$ lattice. If the edge length of the unit cell is $0.574 \ nm$,what is the shortest distance between any two potassium nuclei (in $nm$)?

What is the atomic mass of an element with $BCC$ structure and density $10 \ g \ cm^{-3}$ having an edge length of $300 \ pm$?

Calculate the density of an element having molar mass $27 \ g \ mol^{-1}$ that forms $fcc$ unit cell. $[a^3 \cdot N_A = 38.5 \ cm^3 \ mol^{-1}]$ (in $g \ cm^{-3}$)

Silver crystallises in $fcc$ structure. If the edge length of the unit cell is $316.5 \text{ pm}$, what is the radius of the silver atom (in $\text{pm}$)?

Silver forms $ccp$ lattice and $X$-ray studies of its crystals show that the edge length of its unit cell is $408.6 \,pm$. Calculate the density of silver ( Atomic mass $= 107.9 \,u$ ).

Vedclass Test Series

Exam Paper Generator

Online Exam Module