X-rays of CuK_(a) (wavelength 154pm ) are diffracted by a set of atomic planes in a crystal in the following manner.The separation of the layers in the crystals is 404pm.Find the angle a along which the first-order reflection will occur.?

Question

Answer

Given data:
- Wavelength of X-rays (λ) = 154 pm = 154 x 10^(-12) m
- Separation of atomic planes (d) = 404 pm = 404 x 10^(-12) m

Calculating the angle of first-order reflection (a):

Step 1: Determine the Bragg's Law equation
The Bragg's Law equation is given by: nλ = 2d sinθ
Where:
- n = order of reflection (1 for first-order)
- λ = wavelength of X-rays
- d = separation of atomic planes
- θ = angle of reflection

Step 2: Substitute the given values into the equation
For first-order reflection (n = 1):
1 x 154 x 10^(-12) = 2 x 404 x 10^(-12) x sinθ

Step 3: Solve for the angle (θ)
sinθ = λ / (2d)
sinθ = 154 x 10^(-12) / (2 x 404 x 10^(-12))
sinθ = 0.1911
θ = sin^(-1)(0.1911)
θ ≈ 11.03 degrees

Therefore, the angle (a) along which the first-order reflection will occur is approximately 11.03 degrees. This angle represents the angle at which the X-rays will be diffracted by the set of atomic planes in the crystal.

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