The edge length of a unit cell of a metal hav | vedclass

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

Question

(C) The formula for density is $ho = \frac{Z 	imes M}{N_A 	imes a^3}$.Given: $ho = 2 \ g/cm^3$, $M = 75 \ g/mol$, $a = 5 \ \mathring{A} = 5 	im

Vedclass · Accepted Answer

$216.5$

Vedclass · Answer

(C) The formula for density is $ho = \frac{Z 	imes M}{N_A 	imes a^3}$.Given: $ho = 2 \ g/cm^3$, $M = 75 \ g/mol$, $a = 5 \ \mathring{A} = 5 	imes 10^{-8} \ cm$, $N_A = 6 	imes 10^{23}$.Calculating $Z$:$Z = \frac{ho 	imes N_A 	imes a^3}{M} = \frac{2 	imes 6 	imes 10^{23} 	imes (5 	imes 10^{-8})^3}{75} = \frac{12 	imes 10^{23} 	imes 125 	imes 10^{-24}}{75} = \frac{1500 	imes 10^{-1}}{75} = \frac{150}{75} = 2$.Since $Z = 2$, the crystal structure is Body-Centered Cubic $(BCC)$.For a $BCC$ structure, the relation between radius $r$ and edge length $a$ is $r = \frac{\sqrt{3}}{4} a$.$r = \frac{\sqrt{3}}{4} 	imes 5 \ \mathring{A} = 1.732 	imes 1.25 \ \mathring{A} = 2.165 \ \mathring{A}$.Converting to $pm$: $2.165 \ \mathring{A} = 2.165 	imes 100 \ pm = 216.5 \ pm$.

The edge length of a unit cell of a metal having a molar mass of $75 \ g/mol$ is $5 \ \mathring{A}$. It crystallizes in a cubic lattice. If the density is $2 \ g/cm^3$, find the radius of the metal atom in $pm$. (Given: $N_A = 6 \times 10^{23}$)

Similar Questions

Calculate the radius of an atom of metal if it forms a simple cubic unit cell with an edge length of $380 \ pm$. (in $pm$)

In an $NaCl$ crystal, the radii of $Na^{+}$ and $Cl^{-}$ ions are $95 \, pm$ and $180 \, pm$ respectively. The edge length of its unit cell is ........... $pm$.

$A$ metal crystallises with a face-centred cubic $(fcc)$ lattice. The edge length of the unit cell is $408 \, pm$. The diameter of the metal atom is ............. $pm$.

Select the $INCORRECT$ option regarding the cubic crystal system-

Copper (atomic mass $= 63.5$) crystallises in a $fcc$ lattice and has density $8.93 \, g \, cm^{-3}$. The radius of copper atom is closest to $.... \, pm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module