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The glancing angle (θ) of a Bragg reflection (n = 1) from a set of crystal planes separated by 99.3 pm is 10.42°. Calculate the wavelength of the X-rays used.

Answer :

The wavelength of the X-rays that is used is equal to 35.9 nanometers.

Given the following data:

  • Bragg reflection, n = 1
  • Glancing angle (θ) = 10.42°.
  • Distance between planes = 99.3 picometers.

To calculate the wavelength of the X-rays that is used, we would apply Bragg's law of reflection:

Mathematically, Bragg's law of reflection is given by the formula:

[tex]n\lambda = 2dsin\theta[/tex]

Where:

  • n is Bragg reflection.
  • d is the distance between crystal planes.
  • [tex]\lambda[/tex] is the wavelength.
  • [tex]\theta[/tex] is the reflection angle.

Substituting the given parameters into the formula, we have;

[tex]1 \times \lambda = 2 \times 99.3 \times 10^{-11} \times sin(10.42)\\\\ \lambda = 1.99 \times 10^{-9} \times 0.1809\\\\\lambda = 3.59 \times 10^{-10}[/tex]

Wavelength = 35.9 nanometers.

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Rewritten by : Barada

Answer:

wavelength λ = 35.92 pm

Explanation:

Given that:

The glancing angle (θ) = 10.42°

Bragg reflection n = 1

wavelength λ = ???

diameter d = 99.3 pm

Using the formula:

nλ = 2dsinθ

we have:

1 × λ = 2 × ( 99.3) × sin (10.42°)

λ = 198.6 × 0.18086

λ = 35.92 pm