$(A)$ The formula for density is $d = \frac{n \times M}{a^3 \times N_A}$.Given: $a = 288 \, pm = 288 \times 10^{-10} \, cm$, $d = 7.2 \, g \, cm^{-3}$

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$(A)$ The formula for density is $d = \frac{n \times M}{a^3 \times N_A}$.Given: $a = 288 \, pm = 288 \times 10^{-10} \, cm$, $d = 7.2 \, g \, cm^{-3}$, $n = 2$ (for $BCC$ structure), and $N_A = 6.022 \times 10^{23} \, mol^{-1}$.Substituting the values: $7.2 = \frac{2 \times M}{(288 \times 10^{-10})^3 \times 6.022 \times 10^{23}}$.$M = \frac{7.2 \times (288 \times 10^{-10})^3 \times 6.022 \times 10^{23}}{2}$.$M \approx 51.8 \, g \, mol^{-1}$.

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

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An element has a $BCC$ structure. The edge length of the unit cell is $288 \, pm$. If the density of the crystal is $7.2 \, g \, cm^{-3}$, what is the atomic mass of the element?

A
$51.8$
B
$103.6$
C
$25.9$
D
$207.2$

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Mathematical analysis of cubic system and Bragg’s equation

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The edge length of a body-centered cubic $(BCC)$ unit cell is $390 \ pm$. If the radius of the cation is $150 \ pm$, what is the radius of the anion? (in $pm$)

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An element crystallizes in an $f.c.c.$ structure with a unit cell edge length of $200 \, pm$. If $200 \, g$ of this element contains $24 \times 10^{23}$ atoms,calculate its density in $\text{g cm}^{-3}$.

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An element has a $BCC$ structure. The edge length of the unit cell is $288 \, pm$. If the density of the crystal is $7.2 \, g \, cm^{-3}$, what is the atomic mass of the element?

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If the radius of an atom of an element which forms a body centered cubic unit cell is $173.2 \ pm$, the volume of the unit cell in $cm^3$ is:

For a crystal, the angle of diffraction $(2 \theta)$ is $90^{\circ}$ and the second order line has a $d$ value of $2.28 \ \text{Å}$. The wavelength (in $\text{Å}$) of $X$-rays used for Bragg's diffraction is

The edge length of a body-centered cubic $(BCC)$ unit cell is $390 \ pm$. If the radius of the cation is $150 \ pm$, what is the radius of the anion? (in $pm$)

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