$(A)$ For a $BCC$ lattice, the relationship between the edge length $(a)$ and the ionic radii ($r^+$ and $r^-$) along the body diagonal is given by: $

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$(A)$ For a $BCC$ lattice, the relationship between the edge length $(a)$ and the ionic radii ($r^+$ and $r^-$) along the body diagonal is given by: $2(r^+ + r^-) = \sqrt{3}a$ $r^+ + r^- = \frac{\sqrt{3}a}{2}$ Given $a = 390 \ pm$ and $r^- = 180 \ pm$: $r^+ + 180 = \frac{1.732 \times 390}{2}$ $r^+ + 180 = 1.732 \times 195$ $r^+ + 180 = 337.74$ $r^+ = 337.74 - 180 = 157.74 \ pm \approx 158 \ pm$ Therefore, the correct option is $A$.

Class 12 Chemistry Solid State Mathematical analysis of cubic system and Bragg’s equation

Medium

Ammonium chloride crystallizes in a body-centered cubic $(BCC)$ lattice with a unit cell edge length of $390 \ pm$. If the radius of the chloride ion is $180 \ pm$, what is the radius of the ammonium ion in $pm$?

A
$158$
B
$174$
C
$142$
D
$126$

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Mathematical analysis of cubic system and Bragg’s equation

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Ammonium chloride crystallizes in a body-centered cubic $(BCC)$ lattice with a unit cell edge length of $390 \ pm$. If the radius of the chloride ion is $180 \ pm$, what is the radius of the ammonium ion in $pm$?

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Aluminium crystallises in a cubic close-packed structure. Its metallic radius is $125 \ pm$.$(i)$ What is the length of the side of the unit cell?$(ii)$ How many unit cells are there in $1.00 \ cm^3$ of aluminium?

If the density of a $CsCl$ crystal,which crystallizes in a $bcc$ structure,is $3.988 \, g/cm^3$,then the edge length of the unit cell will be ........ $(CsCl = 168.4 \, g/mol)$.

An element crystallizes in an $fcc$ unit cell structure with an edge length of $200 \, pm$. If $200 \, g$ of the element contains $24 \times 10^{23}$ atoms, what is its density in $g/cm^3$?

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Calculate the number of unit cells present in $1 \text{ g}$ of a metal if the product of the density of the metal and the volume of the unit cell is $2.5 \times 10^{-22} \text{ g}$.

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Aluminium crystallises in a cubic close-packed structure. Its metallic radius is $125 \ pm$.
$(i)$ What is the length of the side of the unit cell?
$(ii)$ How many unit cells are there in $1.00 \ cm^3$ of aluminium?