On a calcite crystal, the distance between atomic

To determine the grazing angle of X-rays necessary to observe a first-order diffraction maximum on a calcite crystal, with a distance between atomic planes of 0.3 nm and a wavelength of incident rays of 0.147 nm, you can use the Bragg-Wulf formula:

nλ = 2d sinth

where n is the order of the diffraction maximum, λ is the x-ray wavelength, d is the distance between the crystal lattice planes, and θ is the angle between the incident beam and the lattice plane.

For the first maximum n = 1, so:

λ = 2d sinth

From here we can express the angle θ:

θ = arcsin(λ/2d)

Substituting the values, we get:

θ = arcsin(0.147 nm / (2 * 0.3 nm)) = 14.1 degrees

Thus, X-rays must strike a calcite crystal at a grazing angle of 14.1 degrees for a first-order diffraction maximum to be observed.

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To determine the grazing angle of X-rays necessary to observe a first-order diffraction maximum on a calcite crystal, with a distance between atomic planes of 0.3 nm and a wavelength of incident rays of 0.147 nm, you can use the Bragg-Wulf formula:

nλ = 2d sinθ

where n is the order of the diffraction maximum, λ is the x-ray wavelength, d is the distance between the crystal lattice planes, and θ is the angle between the incident beam and the lattice plane. For the first maximum n = 1, so:

λ = 2d sinθ

From here we can express the angle θ:

θ = arcsin(λ/2d)

Substituting the values, we get:

θ = arcsin(0.147 nm / (2 * 0.3 nm)) = 14.1 degrees

Thus, X-rays must strike a calcite crystal at a grazing angle of 14.1 degrees for a first-order diffraction maximum to be observed.

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Product description:

A calcite crystal is sold that has a distance between atomic planes of 0.3 nm. This crystal can be used as an object for X-ray diffraction experiments. To obtain a first-order diffraction maximum, it is necessary for X-rays to be incident on the crystal at a grazing angle, which can be determined by the following formula:

sin(grazing angle) = λ / (2*d),

where λ is the wavelength of x-rays, d is the distance between the atomic planes of the crystal.

From the problem conditions it is known that λ = 0.147 nm and d = 0.3 nm. Substituting these values ​​into the formula, we get:

sin(grazing angle) = 0.147 nm / (2*0.3 nm) ≈ 0.245

Find the sliding angle using the inverse trigonometric sine function:

sliding angle ≈ sin^(-1)(0.245) ≈ 14.1 degrees.

Thus, for a first-order diffraction maximum to be observed on a calcite crystal, X-rays must strike the crystal at a grazing angle of approximately 14.1 degrees.

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