Question

What is the wavelength of x-ray, if the interplanar distance of the crystal is 286 pm and the incident angle is ${15.8}^o$. Order of reflection is 2.

• A. 378 pm
• B. 154.2 pm
• C. 294.3 pm
• D. 77.8 pm

Answer 1

The correct option is D

77.8 pm

So, here we have been given interplanar distance (d) = 286 pm and incident angle (ɵ) which is ${15.8}^o$ We want wavelength of x-ray.

$\to$ Use Bragg’s equation.

$n\lambda =2dsin\theta$

If the order of reflection is not given,

take n = 1

But here order of reflection is second order.

Therefore n = 2.

$n\lambda =2dsin\theta$

$\to 2\times \lambda =2\times 286\times {10}^{-12}\times sin\left({15.8}^o\right)\to \lambda =\frac{2\times 286\times {10}^{-12}\times 0.272}{2}=77.792\times {10}^{-12}m\simeq 77.8pm$