What will be the wavelength of the X-rays which give a diffraction angle $2 θ$ equal to ${16.80}^{o}$ for a crystal, if the inter planner distance in the crystal is 0.200 nm and only first order diffraction is observed $(sin {8.40}^{o} = 0.146) .$

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Solution

Using Bragg Equation
$n λ = 2 d sin θ$
$d = 0.200 n m$
$n = 1$
$2 θ = 16.80$
$θ = \frac{16.80}{2} = {8.40}^{o}$
angle given $\Rightarrow 20 = {16.80}^{o}$
$λ = ?$
$λ = 2 \times 0.200 \times 10^{- 9} m sin ({8.40}^{o})$
$= 2 \times 0.200 \times 10^{- 9} \times 0.146$
$= 0.0584 \times 10^{- 9} m$
$= 0.0584 \times 10^{- 9} \times 100 c m$
$= 5.84 \times 10^{- 9} c m$

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What will be the wavelength of the X-rays which give a diffraction angle 2θ equal to 16.80o for a crystal, if the inter planner distance in the crystal is 0.200 nm and only first order diffraction is observed (sin8.40o=0.146).

Using Bragg Equationnλ=2dsinθd=0.200nmn=12θ=16.80θ=16.802=8.40oangle given ⇒20=16.80oλ=?λ=2×0.200×10−9msin(8.40o)=2×0.200×10−9×0.146=0.0584×10−9m=0.0584×10−9×100cm=5.84×10−9cm

What will be the wavelength of the X-rays which give a diffraction angle $2 θ$ equal to ${16.80}^{o}$ for a crystal, if the inter planner distance in the crystal is 0.200 nm and only first order diffraction is observed $(sin {8.40}^{o} = 0.146) .$