**Determining the Wavelength of X-rays Using Crystallography** Cristian determines that the spacing between the planes of a crystalline material is 2.46 x 10-10 meters. When a beam of x-rays makes an angle of 15.20° with the planes of the crystal, first order constructive interference occurs. Determine the wavelength of the x-rays in nanometers with two decimal places please.*Explanation:** Given: - Spacing between planes (d): \( 2.46 \times 10^{-10} \) meters. - Angle of incidence (\( \theta \)): 15.20° - First order constructive interference: n = 1* Formula: \( n \lambda = 2d \sin(\theta) \) Where: - \( n \) is the order of constructive interference - \( \lambda \) is the wavelength of the x-rays - \( d \) is the spacing between planes - \( \theta \) is the angle of incidence* Steps to Solve: - Convert the angle from degrees to radians if necessary. - Substitute the given values into the formula and solve for \( \lambda \). - Convert the wavelength from meters to nanometers.* Additional Notes: - Ensure precise calculations to obtain the wavelength accurate to two decimal places. - Remember that 1 meter = \( 10^9 \) nanometers.

Given that Spacing between the planes of crystal matarial(d)=2.46×10^-10 m Angle(θ)=15.20o first…

Cristian determines that the spacing between the planes of a crystalline material is 2.46x10-10 m. When a beam of x-rays makes an angle of 1520° with the planes of the crystal, first order constructive interference occurs. Determine the wavelength of the x-rays in nanometers with two decimal places please.

Cristian determines that the spacing between the planes of a crystalline material is 2.46x10-10 m. When a beam of x-rays makes an angle of 1520° with the planes of the crystal, first order constructive interference occurs. Determine the wavelength of the x-rays in nanometers with two decimal places please.

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Determining the Wavelength of X-rays Using Crystallography**

Cristian determines that the spacing between the planes of a crystalline material is 2.46 x 10<sup>-10</sup> meters. When a beam of x-rays makes an angle of 15.20° with the planes of the crystal, first order constructive interference occurs. Determine the wavelength of the x-rays in nanometers with two decimal places please.

*Explanation:*

* Given:
- Spacing between planes (d): \( 2.46 \times 10^{-10} \) meters.
- Angle of incidence (\( \theta \)): 15.20°
- First order constructive interference: n = 1

* Formula:
\( n \lambda = 2d \sin(\theta) \)

Where:
- \( n \) is the order of constructive interference
- \( \lambda \) is the wavelength of the x-rays
- \( d \) is the spacing between planes
- \( \theta \) is the angle of incidence

* Steps to Solve:
- Convert the angle from degrees to radians if necessary.
- Substitute the given values into the formula and solve for \( \lambda \).
- Convert the wavelength from meters to nanometers.

* Additional Notes:
- Ensure precise calculations to obtain the wavelength accurate to two decimal places.
- Remember that 1 meter = \( 10^9 \) nanometers.

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