X-rays with a wavelength of 1.70 Å scatter at an angle of 36.5° from a crystal. If \( n = 1 \), what is the distance between planes of atoms in the crystal that give rise to this scattering?

a) 2.45 Å
b) 3.10 Å
c) 1.70 Å
d) 2.95 Å

Question

29-06-2024
Chemistry

High School

Thank you for visiting X rays with a wavelength of 1 70 Å scatter at an angle of 36 5 from a crystal If n 1 what is the. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

X-rays with a wavelength of 1.70 Å scatter at an angle of 36.5° from a crystal. If \( n = 1 \), what is the distance between planes of atoms in the crystal that give rise to this scattering?

a) 2.45 Å
b) 3.10 Å
c) 1.70 Å
d) 2.95 Å

Answer :

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Final answer:

Using Bragg's Law, the correct distance between planes of atoms in the crystal that scatters X-rays at an angle of 36.5° is calculated to be 2.45 Å. Thus, the correct option is a) 2.45 Å.

Explanation:

To determine the distance between planes of atoms in a crystal that gives rise to scattering at a certain angle, we can use Bragg's Law, which is adapted for the fact that we are looking for the first-order (n=1) maximum. Bragg's Law is represented by the equation nλ = 2d • sin(θ), where n is the diffraction order, λ is the wavelength of the X-rays, d is the spacing between the planes in the crystal, and θ is the angle of scattering (half of the total diffraction angle).

In this scenario, given:

The wavelength λ = 1.70 Å
Scattering angle θ = 36.5°
Diffraction order n = 1

We can rearrange Bragg's Law to solve for d:

d = λ / (2 • sin(θ))

After plugging in the given values and executing the calculation, we can conclude:

d = 1.70 Å / (2 • sin(36.5°)) = 2.45 Å

Therefore, the correct distance between planes of atoms in the crystal is 2.45 Å, making option a) 2.45 Å the right answer to the student's question.

X-rays with a wavelength of 1.70 Å scatter at an angle of 36.5° from a crystal. If \( n = 1 \), what is the distance between planes of atoms in the crystal that give rise to this scattering?a) 2.45 Å b) 3.10 Å c) 1.70 Å d) 2.95 Å

Answer :

Final answer:

Explanation:

Other Questions

X-rays with a wavelength of 1.70 Å scatter at an angle of 36.5° from a crystal. If \( n = 1 \), what is the distance between planes of atoms in the crystal that give rise to this scattering?

a) 2.45 Å
b) 3.10 Å
c) 1.70 Å
d) 2.95 Å