Question

Monochromatic x rays are incident on a crystal for which the spacing of the atomic planes is 0.440 nm . The first-order maximum in the Bragg reflection occurs when the incident and reflected x rays make an angle of 39.4 â with the crystal planes.What is the wavelength of the x rays?

Answer 1

Answer:

Wavelength of the x rays is $\lambda=2.79\times 10^{-10}\ m$

Explanation:

It is given that,

The inter planer spacing between the crystal planes, $d=0.44\ nm=0.44\times 10^{-9}\ m$

The first-order maximum in the Bragg reflection occurs when the incident and reflected x rays make an angle of 39.4 degrees with the crystal planes. According to the Bragg's condition, the first-order maximum is given by :

$d\ sin\theta=n\lambda$

n = 1

$d\ sin\theta=\lambda$

$0.44\times 10^{-9}\times \ sin(39.4)=\lambda$

$\lambda=2.79\times 10^{-10}\ m$

So, the wavelength of the x rays is $2.79\times 10^{-10}\ m$. Hence, this is the required solution.