Neutron diffraction is used in determining the structures of...

Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at $1.00 \%$ of the speed of light. b. Calculate the velocity of a neutron with a wavelength of $75 \mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{~m}\right)$

Neutron diffraction is used in determining the structures of molecules.
a. Calculate the de Broglie wavelength of a neutron moving at $1.00 \%$ of the speed of light.
b. Calculate the velocity of a neutron with a wavelength of $75 \mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{~m}\right)$

Key Concepts

Neutron Diffraction

Neutron diffraction is an experimental technique used to determine the atomic or magnetic structure of a material by observing the scattering of neutrons. This method benefits from the wave-like behavior of neutrons as dictated by quantum mechanics, making it ideal for probing the structure of complex molecules and materials.

Momentum

Momentum in quantum mechanics is a fundamental property of particles that is directly related to their mass and velocity (p = mv). It plays a central role in determining the de Broglie wavelength of a particle, linking classical mechanics with wave mechanics and allowing for the prediction of diffraction effects.

Wave-Particle Duality

Wave-particle duality is the core quantum mechanical principle stating that every particle or quantum entity exhibits both wave-like and particle-like properties. This concept underlies the use of equations like the de Broglie relation, which connects a particle's momentum to its associated wavelength, thereby allowing the description of matter in terms of waves.

de Broglie Wavelength

The de Broglie wavelength is defined as the wavelength associated with any moving particle and is calculated using the relation ? = h/p, where h is Planck's constant and p is the momentum of the particle. This concept is crucial in understanding phenomena like diffraction in particles such as neutrons and electrons, highlighting the quantum nature of matter.

Transcript

00:01 A neutron scattering is very important when you're doing ah, characterization off the structure of a molecule.

00:07 But in order he did to get an accurate measurement of what you want to dio, you're gonna use the deplorably wavelength.

00:13 So here that abruptly wavelength formula is given wavelength represented by lambda is equal to plank's constant on a church divided by the product of the mass of the neutral and times its velocity.

00:29 So first thing, you need to know what units you're going to use, because if you mix up the units, especially on this particular magnitude, things going to come out very wrong.

00:40 So the wavelength is going to be given as meters plank's constant.

00:45 There's a lot of different versions you can use.

00:47 However, for this particular application, we're going to use jewels per hurts.

00:53 Where you remember that hurts is an inverse second, a mass just like the size of what we're using.

01:00 We're going to use kilograms, and the velocity will be in meters per second.

01:06 Now they were given a situation where neutron will be traveling at 1% the speed of light.

01:13 Now, for the speed of light, we use the speed of light in a vacuum, which is roughly three times 10 to the eighth meters per second.

01:24 Now multiply it by 0.1 or 1% and you're going to get three times 10 to the sixth meters per second.

01:38 No, we have to put in all the other values and just plug right through it.

01:43 So plank's constant is 6.626 times 10 to the negative 34 jules per hurts.

01:56 You get an idea of the magnitudes that we're talking about here very large and very, very small...

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