A certain crystal has a spacing of 0.442 nm between atoms.A beam of neutrons moving with a speed of 1640 m/s perpendicular to the surface is diffracted as it passes through the crystal.What is the angle from the central maximum to the next interference maximum? (m_neutr_on = 1.675 × 10^-27 kg,h = 6.626 × 10^-34 J ∙ s) A)17.0° B)21.0° C)33.1° D)60.0° E)90.0°

Question

Quizplus · Accepted Answer

We can use Bragg's law to solve this problem:

nλ = 2d sinθ

where n is the order of the interference maximum, λ is the wavelength of the neutron beam, d is the spacing between atoms in the crystal, and θ is the angle from the central maximum to the next interference maximum.

Since we don't know the wavelength of the neutron beam, let's rearrange the equation to solve for sinθ:

sinθ = nλ / 2d

We can use the de Broglie wavelength equation to find the wavelength of the neutron beam:

λ = h / mv

where h is Planck's constant, m is the mass of the neutron, and v is the speed of the neutron.

Substituting in the given values and solving for λ:

λ = (6.626 × 10^-34 J ∙ s) / (1.675 × 10^-27 kg)(1640 m/s) = 2.44 × 10^-10 m

Substituting in the values for λ, n, and d:

sinθ = (1)(2.44 × 10^-10 m) / (2)(0.442 × 10^-9 m) = 0.277

Taking the inverse sine to solve for θ:

θ = sin^-1(0.277) = 33.1°

Therefore, the answer is C, 33.1°.

A Certain Crystal Has a Spacing of 0