(B) According to Bragg's Law: $n \lambda = 2d \sin \theta$ Given: $n = 1$,$\lambda = 2.29 \times 10^{-10} \ m$,$\theta = 27^\circ 8'$. Since $27^\circ

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(B) According to Bragg's Law: $n \lambda = 2d \sin \theta$ Given: $n = 1$,$\lambda = 2.29 \times 10^{-10} \ m$,$\theta = 27^\circ 8'$. Since $27^\circ 8' \approx 27.13^\circ$,$\sin(27.13^\circ) \approx 0.456$. Using the provided approximation $\sin(27^\circ 8') \approx 0.45$: $d = \frac{n \lambda}{2 \sin \theta} = \frac{1 \times 2.29 \times 10^{-10}}{2 \times 0.45}$ $d = \frac{2.29 \times 10^{-10}}{0.9} \approx 2.54 \times 10^{-10} \ m$. Rounding to the nearest option,$d = 2.5 \times 10^{-10} \ m$.

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

Medium

For a crystal,the first-order Bragg reflection of $X$-rays with a wavelength of $2.29 \times 10^{-10} \ m$ occurs at an angle of $27^\circ 8'$. Calculate the distance between two parallel planes.

A
$2.5 \times 10^{-8} \ m$
B
$2.5 \times 10^{-10} \ m$
C
$3.5 \times 10^{-10} \ m$
D
$4.5 \times 10^{-10} \ m$

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Class 12

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Solid State

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Mathematical analysis of cubic system and Bragg’s equation

If the crystal structure of $KCl$ is the same as that of $NaCl$,and the radius ratios are $r_{Na^+}/r_{Cl^-} = 0.55$ and $r_{K^+}/r_{Cl^-} = 0.74$,calculate the ratio of the edge lengths of the unit cells of $KCl$ and $NaCl$.

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$A$ face-centered cubic $(FCC)$ solid of an element (atomic mass $60$) has a cubic edge length of $4 \times 10^{-8} \, cm$. If Avogadro's number is $6 \times 10^{23} \, mol^{-1}$,then the density of the solid is:

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An element is found to crystallize with $BCC$ structure having density $8.55 \ g \ cm^{-3}$. What is the edge length of the unit cell? (Atomic mass of element $= 93$)

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An ionic compound $X^{+}Y^{-}$ has a $bcc$ structure. The distance between two nearest ions is $1.73 \, \mathring{A}$. What would be the edge length of the unit cell in $pm$?

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$A$ metal crystallizes in two cubic phases,$fcc$ and $bcc$,whose unit cell edge lengths are $3.5 \ \mathring{A}$ and $3.0 \ \mathring{A}$ respectively. Calculate the ratio of the densities of $fcc$ and $bcc$ phases.

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For a crystal,the first-order Bragg reflection of $X$-rays with a wavelength of $2.29 \times 10^{-10} \ m$ occurs at an angle of $27^\circ 8'$. Calculate the distance between two parallel planes.

Similar Questions

If the crystal structure of $KCl$ is the same as that of $NaCl$,and the radius ratios are $r_{Na^+}/r_{Cl^-} = 0.55$ and $r_{K^+}/r_{Cl^-} = 0.74$,calculate the ratio of the edge lengths of the unit cells of $KCl$ and $NaCl$.

$A$ face-centered cubic $(FCC)$ solid of an element (atomic mass $60$) has a cubic edge length of $4 \times 10^{-8} \, cm$. If Avogadro's number is $6 \times 10^{23} \, mol^{-1}$,then the density of the solid is:

An element is found to crystallize with $BCC$ structure having density $8.55 \ g \ cm^{-3}$. What is the edge length of the unit cell? (Atomic mass of element $= 93$)

An ionic compound $X^{+}Y^{-}$ has a $bcc$ structure. The distance between two nearest ions is $1.73 \, \mathring{A}$. What would be the edge length of the unit cell in $pm$?

$A$ metal crystallizes in two cubic phases,$fcc$ and $bcc$,whose unit cell edge lengths are $3.5 \ \mathring{A}$ and $3.0 \ \mathring{A}$ respectively. Calculate the ratio of the densities of $fcc$ and $bcc$ phases.

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