Advertisement Remove all ads

Derive Bragg'S Condition for X-ray Diffraction. Monochromatic X Rays Are Incident on a Crystal. If the First Order Rejection is Observed at an Angle of 3.4•, at What Angle Would Second Order Ref - Applied Physics 1

Answer in Brief

Derive Bragg's condition for X-ray diffraction. Monochromatic X rays are
incident on a crystal. If the first order rejection is observed at an angle of 3.4•, at
what angle would second order reflection expected.

Advertisement Remove all ads

Solution

W.L.Bragg's explained the phenomenon of X-ray diffractionn from a single crystal shown as
follows

When a beam of X-rays is incident on a crystal it is scattered by individual atoms of the rich
atomic planes. Thus,each atom become a source of scattered radiation. The atomic planes
responsible for the X-ray diffraction are called BRAGG'S PLANES. Therefore, the sets of
Braggs planes constitute the crystal grating. Bragg's scattering or Bragg's diffraction is also
referred as Braggs reflection. Bragg derived a law called Bragg's law to explain the X-ray
diffraction effect. Here a beam of X-ray is incident on a set of parallel planes of a crystal. The
rays makes glancing angle e and are practically reflected from different successive
planes. The phase relationship of the scattered rays can be determined from their path
differences. Here two parallel X-rays are reflected from two consecutive planes Pr and P. The
path differences between them as shown

6=MB+BN=2MB=2ABsin8.

Here AB = d,the interplanar spacing of the crystal

 Hence                  6=2dsine

The two diffracted rays reinforce each other when they interfere constructively when their
path
difference 6 is equal to n.A
Hence,                    2dsin8=n.A is called as Bragg's Law

Numericsl solution:

Date : ` theta_1  = 3.4°`

Fonnula: 2dsine = n.λ

Solution: From equation, sineΘ ∝ n

Hence,

`sintheta_1 / (sin theta_2) = n_1 /n_2`
sin(3.4) / `sintheta_2 = 1/2`
`sintheta_2 = 0.1186`

`theta_2 = 6.8113°`

Answer.· Hence, second order reflection is expected at 6. 8113°.

Concept: X-ray Diffraction
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×