Question

A cubic crystal with interatomic spacing of 0.28 nm is used to select y raysof energy 100 keV from a radioactive source containing a continuum of energies. If the incident beam is normal to the crystal, at what angle do do the 100 keV y rays appear?

Show work if possible.

Answer 1

According to Bragg's eauation , n = 2dsin

Where n = order = 1   ( since not specifing)

          d = interatomic spacing = 0.28 nm = 0.28x10^-9 m

         = angle = ?

          = wave length of X- rays = ?

We know that energy of rays is , E = hc /

Where

h = plank's constant = 6.625x 10^-34 Js

c = speed of light = 3x 10⁸ m/s

E = energy = 100 keV

                   = 100 x 1.6x10^-16 J

                  = 1.6x10^-14 J

Plug the values we get = hc / E

                                          = (6.625x 10^-34 Js x 3x 10⁸ m/s ) / (1.6x10^-14 J )

                                         = 1.24x10^-11 m

From    n = 2dsin

         sin = n / 2d

                 = ( 1x 1.24x10^-11 m ) ) / ( 2x0.28x10^-9 m)

                 = 0.022

            = sin^-10.022

                = 1.27 degrees