Explain the difference between a plot showing the probability density for an orbital and one sho

Explain the difference between a plot showing the...

Key Concepts

Probability Density

Probability density describes the likelihood of finding an electron at an exact point in space, given by the square of the wavefunction |?(r,?,?)|². It contains both radial and angular information and represents a localized measure that can vary significantly with direction, especially in orbitals with complex shapes.

Radial Distribution Function

The radial distribution function is derived from the probability density by integrating out the angular variables, resulting in a function that depends only on the distance from the nucleus. It includes a factor of r² from the spherical volume element, which highlights the probability of finding an electron within a spherical shell at a given radius and often reveals peaks corresponding to the most probable electron distances.

Transcript

00:01 So how's it going people? for this question, we have to distinguish probability density plot or electron density plot and a radial probability plot.

00:10 So for both of those plots, they want to depict the probability of you finding an electron a certain distance away from the nucleus.

00:19 But one thing we have to note that for the electron density plot, this one, it sees the electron inside a cube.

00:28 So let's say we have the nucleus here, right, and there are some electrons away.

00:35 Basically, we're calculating what's the probability we can find an electron a certain distance away on a nucleus, and we want to imagine it as a cube, right? as for the radio probability distribution, let's say this is the nucleus, and we want to see, again, we have a radius r.

00:55 We want to see what's the probability you can find an electron, not in a cube, are distant away from the nucleus, but rather we're looking for a shell or an orbit.

01:11 So we want to see if there are any electrons inside the shell that's r distance away from the nucleus.

01:20 Right, so that's the key difference.

01:22 And now let's take a look at the probability plot.

01:27 The first thing i want you to note is that the electron density probability plot gets very, very, very, accurate one is getting very close to the nucleus.

01:37 So as you can see here, at a distance 0 p .m.

01:40 Away from the nucleus, we can see that the electrons have the highest probability to exist at a distance 0 p .m.

01:49 Away from the nucleus, and that's very counterintuitive, right, because the nucleus doesn't contain any electrons...

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