If the interplanar spacing of NaCl is 2.814 *10^-¹⁰ m,what is the predicted angle at which X-rays of wavelength 0.140 nm will be diffracted in a first-order maximum? A)31.3 $\degree$ B)7.20 $\degree$ C)20.5 $\degree$ D)14.4 $\degree$ E)29.8 $\degree$

Question

Quizplus · Accepted Answer

The Bragg's law states:

nλ = 2d sin θ

where n is the order of diffraction, λ is the wavelength of X-rays, d is the distance between planes (in this case, the interplanar spacing of NaCl), and θ is the angle of diffraction.

In this problem, we are given λ = 0.140 nm and d = 2.814 × 10^-10 m. To find θ, we rearrange the Bragg's law:

sin θ = nλ / 2d

For the first-order maximum, n = 1. Plugging in the values, we get:

sin θ = (1)(0.140 nm) / [2(2.814 × 10^-10 m)] = 0.251

Taking the inverse sine, we get:

θ = sin^-1(0.251) = 14.4°

Therefore, the predicted angle at which X-rays of wavelength 0.140 nm will be diffracted in a first-order maximum is 14.4°, which is answer choice D.

If the Interplanar Spacing of NaCl Is 2 °\degree° B)720 °\degree° C)205 °\degree°

If the Interplanar Spacing of NaCl Is 2 $\degree$ B)720 $\degree$ C)205 $\degree$