The first order reflections of a beam of X - rays of wavelength of 1-54 - from the 100 face of a crystal of the simple cubic type occurs at an angle 11-29- Calculate the length of the unit cell-

Applying Bragg’s equation 2 d Sin θ = n λ Given θ = 11.29^∘,λ=1.54Ȧ= 1.54 × 10^ 8cm n=1 d =1.54 × 10^ 8/2 × Sin 11.29^∘ = 1.54 × 10^ 8/2 × 0.1957 = 3.93 × 10^ ...

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Standard XII

Physics

Angular Position of Fringes in Diffraction

The first ord...

Question

The first order reflections of a beam of X – rays of wavelength of $1.54 ˙ A$ from the (100) face of a crystal of the simple cubic type occurs at an angle ${11.29}^{\circ}$ . Calculate the length of the unit cell.

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Solution

Applying Bragg’s equation
$2 d S i n θ = n λ$
Given $θ = {11.29}^{\circ}, λ = 1.54 ˙ A = 1.54 \times 10^{- 8} c m$
n=1
$d = \frac{1.54 \times 10^{- 8}}{2 \times S i n {11.29}^{\circ}} = \frac{1.54 \times 10^{- 8}}{2 \times 0.1957} = 3.93 \times 10^{- 8} c m$
$d h k l = a \sqrt{h 2} + k_{2} + l_{2} = a$
$a = 3.93 \times 10^{- 8} c m$ (length of the unit cell)

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The first order reflections of a beam of X – rays of wavelength of 1.54˙A from the (100) face of a crystal of the simple cubic type occurs at an angle 11.29∘. Calculate the length of the unit cell.

Applying Bragg’s equation 2dSinθ=nλ Given θ=11.29∘,λ=1.54˙A=1.54×10−8cm n=1 d=1.54×10−82×Sin11.29∘=1.54×10−82×0.1957=3.93×10−8cm dhkl=a√h2+k2+l2=a a=3.93×10−8cm (length of the unit cell)

The first order reflections of a beam of X – rays of wavelength of $1.54 ˙ A$ from the (100) face of a crystal of the simple cubic type occurs at an angle ${11.29}^{\circ}$ . Calculate the length of the unit cell.