First slide

Diffraction

Question

The wavelength of 10 keV electron beam is 0.1227 A° When these waves are diffracted from a metal foil having d = 0.55 A°. At angle 𝜃 of first maxima will be present, then what will be the value of sin 𝜃:

Moderate

A

0.1116
B

0.2218
C

0.4464
D

0.8928

Solution

The wavelength associated with a particle is given by
$λ = \frac{h}{\sqrt{2 mE}}$
$λ = \frac{h}{\sqrt{2 meV}} = \sqrt{\frac{150}{V}} Å$
$for electron M = 9.11 \times 10^{- 31} kg)$
$λ = \sqrt{\frac{150}{10 \times 10^{3}}} = 0.122 A$
For minima,
$dsinθ = nλ$
For first minima, n = 1
$0 .55 sinθ = 0 .122$
$sinθ = \frac{0 .122}{0 .55} = 0 .2218$

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