Which of the following relation is correct for first order Bragg's diffraction?

Question

Which of the following relation is correct for first order Bragg's diffraction? (A)  sin θ=(2 a/λ)(h2+k2+l2) (B)  sin θ=(2 a/λ)(h2+k2+l2)1 / 2 (C)  sin θ=(λ/2 a)(h2+k2+l2)1 / 2 (D)  sin θ=(λ/2 a)(h2+k2+l2)2

Tardigrade Admin · Accepted Answer

n λ=2 d sin θ d=(λ/2 sin θ)...(i) (for first order diffraction) d=(a/√h2+k2+l2)...(ii) Comparing equation (i) and (ii) (λ/2 sin θ)=(a/√h2+k2+l2) sin θ=(λ/2 a)( h 2+ k 2+l2)1 / 2

Q. Which of the following relation is correct for first order Bragg's diffraction?

$sin θ = \frac{2 a}{λ} (h^{2} + k^{2} + l^{2})$

$sin θ = \frac{2 a}{λ} (h^{2} + k^{2} + l^{2})^{1/2}$

$sin θ = \frac{λ}{2 a} (h^{2} + k^{2} + l^{2})^{1/2}$

$sin θ = \frac{λ}{2 a} (h^{2} + k^{2} + l^{2})^{2}$

$nλ = 2 d sin θ$

$d = \frac{λ}{2 s i n θ}$ ...(i) (for first order diffraction)

$d = \frac{a}{h ^{2} + k ^{2} + l ^{2}}$ ...(ii)

Comparing equation (i) and (ii)

$\frac{λ}{2 s i n θ} = \frac{a}{h ^{2} + k ^{2} + l ^{2}}$

$sin θ = \frac{λ}{2 a} (h^{2} + k^{2} + l^{2})^{1/2}$

Q. Which of the following relation is correct for first order Bragg's diffraction?

sinθ=λ2a​(h2+k2+l2)

sinθ=λ2a​(h2+k2+l2)1/2

sinθ=2aλ​(h2+k2+l2)1/2

sinθ=2aλ​(h2+k2+l2)2

nλ=2dsinθ d=2sinθλ​...(i) (for first order diffraction) d=h2+k2+l2​a​...(ii) Comparing equation (i) and (ii) 2sinθλ​=h2+k2+l2​a​ sinθ=2aλ​(h2+k2+l2)1/2

$sin θ = \frac{2 a}{λ} (h^{2} + k^{2} + l^{2})$

$sin θ = \frac{2 a}{λ} (h^{2} + k^{2} + l^{2})^{1/2}$

$sin θ = \frac{λ}{2 a} (h^{2} + k^{2} + l^{2})^{1/2}$

$sin θ = \frac{λ}{2 a} (h^{2} + k^{2} + l^{2})^{2}$

$nλ = 2 d sin θ$

$d = \frac{λ}{2 s i n θ}$ ...(i) (for first order diffraction)

$d = \frac{a}{h ^{2} + k ^{2} + l ^{2}}$ ...(ii)

Comparing equation (i) and (ii)

$\frac{λ}{2 s i n θ} = \frac{a}{h ^{2} + k ^{2} + l ^{2}}$

$sin θ = \frac{λ}{2 a} (h^{2} + k^{2} + l^{2})^{1/2}$