NaCl Crystal Reflection: Determining Wavelength & Sinus

[hcchong]

The distance between the primary planes of a NaCl crystal is 2.82 Å. It was found that the first order Bragg reflection of a monochromatic x-ray beam occurs at sinus= 10 degree. (i) Determine the wavelength of the x-ray. (ii) Determine the angle, sinus for a second order reflection.

 

[big man]

You have to post your attempt at the question. At least state the things that you know and what you find troubling. Even just post Bragg's law.

 

[kyle8921]

(i) To determine the wavelength of the x-ray, we can use the Bragg's Law equation: nλ = 2dsinθ, where n is the order of the reflection, λ is the wavelength, d is the distance between the primary planes, and θ is the angle of incidence. In this case, n = 1, d = 2.82 Å, and θ = 10 degrees. Plugging in these values, we get: 1λ = 2(2.82 Å)sin(10 degrees). Solving for λ, we get a wavelength of approximately 1.56 Å.

(ii) To determine the angle and sinus for a second order reflection, we can use the same equation, but with n = 2. Plugging in the same values for d and λ, we get: 2λ = 2(2.82 Å)sinθ. Solving for θ, we get an angle of approximately 19.4 degrees. To find the sinus, we can use the trigonometric identity sinθ = opposite/hypotenuse. In this case, the opposite side is the distance between the primary planes (2.82 Å) and the hypotenuse is the wavelength (1.56 Å). Therefore, the sinus for the second order reflection is approximately 1.81.