(B) Using Bragg's Law for first-order diffraction $(n=1)$: $n \lambda = 2d \sin \theta$ $\lambda = 2 \times (2.64 \times 10^{-10} \ m) \times \sin(7.7

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(B) Using Bragg's Law for first-order diffraction $(n=1)$: $n \lambda = 2d \sin \theta$ $\lambda = 2 \times (2.64 \times 10^{-10} \ m) \times \sin(7.75^{\circ})$ $\lambda = 5.28 \times 10^{-10} \times 0.1349 \approx 7.123 \times 10^{-11} \ m$ The energy difference $\Delta E$ is given by: $\Delta E = \frac{hc}{\lambda} = \frac{(6.626 \times 10^{-34} \ J \cdot s) \times (3 \times 10^8 \ m/s)}{7.123 \times 10^{-11} \ m}$ $\Delta E \approx 2.79 \times 10^{-15} \ J$ Thus,the closest option is $2.788 \times 10^{-15} \ J$.

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

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When an electron in an excited atom jumps from the $L$ shell to the $K$ shell,$X$-rays are emitted. These $X$-rays undergo first-order diffraction at an angle of $7.75^{\circ}$ by a crystal with an interplanar spacing of $2.64 \ \mathring{A}$. Calculate the energy difference between the $K$ shell and the $L$ shell. $(\sin \ 7.75^{\circ} = 0.1349)$

A
$2.788 \times 10^{-13} \ J$
B
$2.788 \times 10^{-15} \ J$
C
$3.586 \times 10^{12} \ J$
D
$1.075 \times 10^{13} \ J$

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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

$NaCl$ has $4$ formula units per unit cell. If the edge length of the unit cell is $0.564 \, nm$,then the density of the crystal is ............ $\text{g/cm}^3$. $(NaCl = 58.5 \, \text{g/mol})$

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If the edge length of a $bcc$ unit cell is $386 \ pm$, then the atomic radius will be ........... $pm$.

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The radius of $K^{+}$ is $133 \ pm$ and that of $Cl^{-}$ is $181 \ pm$. The volume of the unit cell of $KCl$ expressed in $10^{-22} \ cm^{3}$ is

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An element with molar mass $2.7 \times 10^{-2} \,kg \,mol^{-1}$ forms a cubic unit cell with edge length $405 \,pm$. If its density is $2.7 \times 10^{3} \,kg \,m^{-3}$, what is the nature of the cubic unit cell?

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The distance between two nearest $Ag$ atoms is $2.5 \times 10^{-8} \ cm$. The density of its crystal is .......... $g/cm^3$. $(Ag = 108 \ g/mol)$

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$NaCl$ has $4$ formula units per unit cell. If the edge length of the unit cell is $0.564 \, nm$,then the density of the crystal is ............ $\text{g/cm}^3$. $(NaCl = 58.5 \, \text{g/mol})$

If the edge length of a $bcc$ unit cell is $386 \ pm$, then the atomic radius will be ........... $pm$.

The radius of $K^{+}$ is $133 \ pm$ and that of $Cl^{-}$ is $181 \ pm$. The volume of the unit cell of $KCl$ expressed in $10^{-22} \ cm^{3}$ is

An element with molar mass $2.7 \times 10^{-2} \,kg \,mol^{-1}$ forms a cubic unit cell with edge length $405 \,pm$. If its density is $2.7 \times 10^{3} \,kg \,m^{-3}$, what is the nature of the cubic unit cell?

The distance between two nearest $Ag$ atoms is $2.5 \times 10^{-8} \ cm$. The density of its crystal is .......... $g/cm^3$. $(Ag = 108 \ g/mol)$

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