Relation Between r and a

Q. Copper crystallizes in a face-centered cubic lattice with a unit cell length of $361\text{pm}$. What is the radius of copper atoms in $\text{pm}$?

1. $157$
2. $181$
3. $108$
4. $128$

Q.

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Q. If the radius of a metal atom is \(2.00~\overset{\circ}{A}\) and its crystal structure is fcc lattice, what is the volume (in \(cm^3\)) of one unit cell?

Q. In an FCC unit cell, what fraction of the edge is not covered by atoms?

1. 0.134
2. 0.293
3. 0.26
4. 0.32

Q. For a tetrahedral void the correct relation between r and R is :
Here
\(r \text{ is radius of the tetrahedral void}\)
\(R \text{ is radius of the atoms in close packing}\)

Q. For 3-D hexagonal closed packing structure (with similar particles), the correct relation between radius of atoms (r) and height of unit cell (h) is :

1. $h=\sqrt{\frac{3}{2}}\times 4r$
2. $h=\sqrt{\frac{2}{3}}\times 4r$
3. $h=\sqrt{\frac{2}{3}}\times 2r$
4. $h=\sqrt{\frac{3}{2}}\times 2r$

Q. Which of the following is correct relation between radius of octahedral void (r) and radius of atom (R) in closed packed structure?

1. $R=0.732r$
2. $r=0.732R$
3. $R=0.414r$
4. $r=0.414R$

Q. Iron occurs as bcc as well as fcc unit cell. If the effective radius of an atom of iron is \(100~pm\), then choose the correct option regarding densities of unit cell :
Take \(\sqrt{\dfrac{2}{3}}\approx0.82\)

Q. The unit cell of a metallic element of atomic mass \(108~\text {g mol}^{-1}\)and density \(10.5~\text {g/cm}^3\) is a cube with edge length of \(410 ~\text {pm}\). The structure of the crystal lattice is:

Q. $CsCl$ crystallizes in body centred cubic lattice. If 'a' is its edge length then which of the following expressions is correct?

1. $r_{C{s}^{⨁}}+r_{C{I}^{\ominus }}=\frac{\sqrt{3}}{2}a$
   
2. $r_{C{s}^{⨁}}+r_{C{I}^{\ominus }}=\sqrt{3}a$
3. $r_{C{s}^{⨁}}+r_{C{I}^{\ominus }}=3a$
4. $r_{C{s}^{⨁}}+r_{C{I}^{\ominus }}=\frac{3a}{2}$

Q. The radius of a divalent cation $A^{2+}$ is $94pm$ and that of a divalent anion $B^{2-}$ is $146pm$. The coordination number of $AB$ is:

1. 6
2. 4
3. 8
4. 3

Q. In the crystals of which of the following ionic compounds would you expect maximum distance between centers of cations and anions

1. LiF
2. CsF
3. CsI
4. LiI

Q. In the crystals of which of the following ionic compounds would you expect maximum distance between centers of cations and anions

1. LiF
2. CsF
3. CsI
4. LiI

Q. Copper crystallizes in a face-centered cubic lattice with a unit cell length of $361\text{pm}$. What is the radius of copper atoms in $\text{pm}$?

1. $157$
2. $181$
3. $108$
4. $128$

Q. A compound forms cubic close packed structure. What is the total number of tetrahedral voids in $1.2mol$ of it?

1. $7.22\times {10}^{23}$
2. $21.68\times {10}^{23}$
3. $14.45\times {10}^{23}$
4. $10.83\times {10}^{22}$

Q. The unit cell of copper corresponds to a face centered cube of edge length $3.596\stackrel{\circ }{A}$ with one copper atom at each lattice point. The calculated density of copper in $kg/m^3$ is . [Molar mass of Cu: $63.54g:$, Avogadro number $=6.022\times {10}^{23}]$
(JEE Main 2021)

Q.

Find the relation between r and a in the following figure.

if a = x $\ast$ r , type 100x rounded off to 2 decimal places.

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Q. A metal 'X' forms a body centred cubic lattice whose unit cell edge length is $300\text{pm}$. Calculate the density of 'X'.
Given: $\text{Molar mass of metal 'X'}=78{\text{g mol}}^{-1}$

Q.

The edge length of a F.C.C. cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is

1. 288 pm

2. 398 pm

3. 618 pm

4. 144 pm

Q.

KCl crystallizes in the same type of lattice as does NACl. Given that $\frac{r_{N{a}^{+}}}{r_{C{l}^{-}}}=0.55$ and $\frac{r_{K^{+}}}{r_{C{l}^{-}}}=0.74$. Calculate the ratio of the side of the unit cell for KCl to that of NaCl.

1. 1.123

2. 0.891

3. 1.414

4. 0.414

Q.

The edge length of a unit cell of a metal whose molecular weight is 75 g/mol is 5 angstrom. This crystallises in a cubic lattice. If the density is 2 g/cc, find the radius of the metal atom. Give the answer in pm.

$N_A=6\times {10}^{2}3$

1. 457.8 pm

2. 216.5 pm

3. 789.5 pm

4. 257.8 pm

Q. Copper crystallizes in a face-centered cubic lattice with a unit cell length of $361pm$. What is the radius of copper atom in pm?
(AIPMT -2009)

Q.

RbCl has NaCl type lattice and its unit cell length is $0.30\stackrel{\circ }{A}$ greater than that for KCl. If $r_{k+}=1.33\stackrel{\circ }{A}$, the ionic radius of $R{b}^{+}$ is

1. $1.48\stackrel{\circ }{A}$

2. $1.63\stackrel{\circ }{A}$

3. $1.03\stackrel{\circ }{A}$

4. $Noneofthese$

Q. Two ionic solids $AB$ and $CB$ crystallize in the same lattice. If $\frac{r_{A^{+}}}{r_{B^{-}}}$ and $\frac{r_{C^{+}}}{r_{B^{-}}}$ are $0.50$ and $0.70$, respectively, then the ratio of edge length of $AB$ and $CB$ is

1. 0.69
2. 0.78
3. 0.88
4. 0.98

Q. Copper crystallises in a structure of face centred cubic unit cell. The atomic radius of copper is $1.28A^{\circ }$. What is the edge length of a unit cell of copper?

1. $2.16A^{\circ }$
2. $3.62A^{\circ }$
3. $3.94A^{\circ }$
4. $4.15A^{\circ }$

Q.

Sodium metal crystallises in a body-centred cubic lattice with the cell edge a = 4.29 Å . What is the radius of the sodium atom?

1. 2.45 Å 

2. 1.86 Å 

3. 3.56 Å 

4. 1.46 Å 

Q.

A given metal crystallizes out with a cubic structure having edge length of 361 pm. If there are four metal atoms in one unit cell, what is the radius of one atom?

1. 108 pm

2. 40 pm

3. 127 pm

4. 80 pm

Q. CsCl crystallizes in B.C.C lattice. If ‘a’ is its edge length then which of the following expressions is correct?

1. $r_{Cs}+r_{C{l}^{-}}=\frac{\sqrt{3}}{2}a$
2. $r_{C{l}^{-}}+r_{Cs}=\sqrt{3}a$
3. $r_{Cs}+r_{C{l}^{-}}=3a$
4. $r_{Cs}+r_{C{l}^{-}}=\frac{3a}{2}$

Q. Sodium metal crystallizes as a body centred cubic lattice with the cell edge 4.29 $\stackrel{\circ }{A}$. What is the radius of sodium atom

1. $1.857\times {10}^{-8}$
2. $2.371\times {10}^{-7}$
3. $3.817\times {10}^{-8}$
4. $9.312\times {10}^{-7}$

Q. Copper adopts fcc structure with edge length of unit cell equal to 0.361 nm. The value of $r_{metallic}$ :-

1. 0.128 nm
   
2. 0.091 nm
   
3. 0.180 nm
   
4. 0.64 nm