Question

Find the glancing angle of the sylvine crystal in which a neutron beam of kinetic energy
0.04 eV is diffracted at the plane of (100). Here, the observed spectrum Bragg's first
order and the distance between the planes is 0.314 nm.
ert​

Answer 1

Given:

Kinetic energy of neutron $K = 0.04$ eV

Bragg's plane = (100)

Interplaner distance $d = 0.314 \times 10^{-9}$ m

Order of diffraction $n = 1$

To Find:

Glancing angle of the crystal,

First find wavelength from kinetic energy,

   $\lambda = \frac{0.286}{\sqrt{0.04} } \times 10^{-10}$

   $\lambda = 1.43 \times 10^{-10}$ m

From the formula of bragg diffraction,

   $2d\sin \theta = n \lambda$

Where $\sin \theta =$ glancing angle

   $\sin \theta = \frac{n\lambda }{2d}$

   $\sin \theta = \frac{1.43 \times 10^{-10} }{2 \times 0.314 \times 10^{-9} }$

   $\sin \theta = 0.2277$

        $\theta =$ 13.17°

Therefore, the glancing is 13.17°