(a) In an X-ray diffraction experiment, what causes the...

(a) In an X-ray diffraction experiment, what causes the diffraction of the electromagnetic radiation? (b) Explain why X-ray diffraction results give a value of $103 \mathrm{pm}$ for the length of a localized 2 -centre 2-electron terminal B-H bond in the $\left[\mathrm{B}_{2} \mathrm{H}_{7}\right]^{-}$ ion (4.25) while the same bond is found to be $118 \mathrm{pm}$ in length from the results of a neutron diffraction experiment.

Key Concepts

Neutron Diffraction Mechanism

Neutron diffraction relies on the scattering of neutrons by atomic nuclei instead of electrons. Since neutrons interact with the nuclei rather than the electron clouds, the diffraction patterns provide information about the positions of the nuclei. This allows neutron diffraction to measure bond lengths based on actual nuclear positions with less influence from electron density distribution.

Influence of Scattering Mechanisms on Bond Length Measurements

The difference in bond length measurements between X-ray and neutron diffraction for a given bond, such as a localized two-center two-electron bond, stems from their different scattering mechanisms. X-ray diffraction, which measures electron density, can show a shorter, more concentrated region of electron density for a bond, while neutron diffraction, measuring the positions of the nuclei, may indicate a longer bond length that reflects the actual distance between the nuclear centers.

X-ray Diffraction Mechanism

X-ray diffraction arises when X-rays interact primarily with the electron clouds of atoms. As the coherent incident X-rays scatter off these electrons, interference patterns are produced. The resulting diffraction pattern directly reflects the electron density distribution within the sample, and through techniques like Bragg’s law, it is used to infer the crystal structure.

Transcript

00:01 Okay, so this question is asking if we can look at the differences in detection methods for a pretty simple physical property being bond length and see if we can explain why different detection methods might give us different answers.

00:17 And this is a very important question, the more detection methods and more properties you need to look into.

00:24 So it uses the example b2h7 anion.

00:31 And we're not going to worry about the lewis structure for this because it doesn't matter and it's kind of a nightmare.

00:37 So let's go ahead and just look at the fact that we have a boron hydrogen bond on a terminal end.

00:47 And so if we look at x -ray scattering, we get a bond length.

00:56 Of about 103 pica meters.

01:05 And if we look at neutron scattering, we get a length of 118 pica meters.

01:17 Okay, so both of these are incredibly accurate methods of measuring bond length to the point that x -ray diffraction is used as the way that we're we know how whole proteins look and many other molecules.

01:39 And neutron scattering is probably more accurate, but it's very expensive.

01:47 So we need to know, we can't say that one of them is just fundamentally less certain than the other.

01:56 They're both very, very good methods of detection.

01:59 So we need to examine why for this example, we see a different length for this bond.

02:10 So let's go ahead and look at that.

02:14 If we have an atom, here's the nucleus, here's the core electrons, and we're going to say there's another one here, here's its core electrons, and they're bound with their valence electrons, right? so nuclei, i'll do this for a neutron, or for a neutron, are going to, come in and be deflected by the nuclei, right? and so using this angle and this distance, which is not drawn proportionately, but this is going to be the same distance as this, and using this angle is going to be the same.

03:08 Using the difference in distance and angles and everything of different atoms, we can get the whole shape.

03:16 It's very, very accurate and very, very good.

03:18 And so nuclei will bounce off of the neutrons will bounce off of the nuclei.

03:28 But if they pass through the electron field, they'll basically just go right through because they're not charged or anything.

03:37 So if we do the same thing with x -rays, we do this for x -ray.

03:45 Right? so they're going to come in and bounce off of the core electrons.

03:54 Okay? because while x -rays are here, so this is nuclear notation, and x -rays are also zero...

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