Question

If an X-ray beam of wavelength 1.4 × 10-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference, at what angle will the second order line appear?

Answer 1

43.16°

Step-by-step explanation:

λ = Wavelength = 1.4×10⁻¹⁰ m

θ₁ = 20°

n can be any integer

d = distance between the two slits

Since for the first bright fringe, n₁ = 1

n₂ = 2 for second order line

The relation between the distance of the slits and the angle through which it is passed is:

dsinθ=nλ

As d and λ are constant

`(n_1\lambda)/(sin \theta_1)=(n_2\lambda)/(sin \theta_2)\\\Rightarrow (1)/(sin20)=(2)/(sin\theta_2)\\\Rightarrow sin\theta_2=(2)/((1)/(sin20))\\\Rightarrow \theta_2=sin^(-1){(2)/((1)/(sin20))}\\\Rightarrow \theta_2=43.16^(\circ)`

∴ Angle by which the second order line appear is 43.16°