A chemistry instructor makes the following claim: "Consider that if the nucleus were the size of

A chemistry instructor makes the following claim: "Consider...

Key Concepts

Scaling and Proportional Reasoning

Scaling is the process of using a multiplication factor to convert the tiny dimensions of atomic structures to more relatable sizes. Using proportional reasoning, if the nucleus is imagined as a grape (a few centimeters in diameter), multiplying by the factor that relates nuclear to atomic dimensions (approximately 10^5) results in an atomic radius on the order of a mile. This calculation provides a tangible analogy for understanding the spatial distribution in an atom.

Mathematical Estimation in Chemistry

Mathematical estimation involves using approximate values and simple ratios to model physical phenomena. In the context of atomic structure, estimating the ratio between the atomic and nuclear dimensions helps in visualizing the distance between the nucleus and electrons, and supports claims by converting abstract numbers into concrete, real-world terms.

Atomic Structure

This concept refers to the organization of the atom, where the nucleus occupies a minuscule volume relative to the overall atom. The nucleus is extremely dense and small, while the electrons exist in a much larger region around it, highlighting that atoms are mostly empty space.

Orders of Magnitude

This concept involves understanding the enormous scale difference between the nucleus and the atom. Typically, the atomic radius is about 100,000 times larger than the nuclear radius. Such order-of-magnitude comparisons help justify the claim by showing that if the nucleus were scaled to a familiar size, the electrons would indeed be at a proportionally vast distance away.

Transcript

00:01 All right, so let's try out to claim that if, let's say, nucleus, let me draw a nucleus right here, that if a nucleus was the size of a grape, then the nearest electron, or on average, an electron would be one mile away.

00:19 So that's, whoops, almost brought it, one lime, one mile, one mile.

00:26 Okay, so what this is saying that, let's see, if we used a grape to model the nucleus, right, so we know, let's pretend this is a hydrogen atom just for simplicity.

00:40 So that's our simplest one, and it's also going to have our electrons be very near.

00:45 So let's pretend this grape.

00:47 First, let's come up with some ideas.

00:48 So let's say that this grape is just one inch.

00:51 All right, so this is a one inch grape.

00:54 Well, we know that the diameter of an atom compared to the nucleus is 6 ,000 times bigger.

01:02 So the diameter is going to be 6 ,000 times bigger.

01:05 So i'm going to write that down somewhere.

01:07 So a diameter of an atom is 6 ,000 times bigger than, let's see, than the diameter of the nucleus.

01:30 Of nucleus.

01:32 Okay.

01:33 So now we can just have some assumptions there.

01:35 First assumption is that the grape is 1 inch.

01:38 The second one is that the diameter, the atom is 6 ,000 times bigger in the diameter of the nucleus.

01:42 Now you can check that out mathematically, but it's going to be 6 ,000.

01:46 So now let's check out that claim that usually the electrons is going to be a mile away.

01:50 Well, there's some other information we need to know about the atoms.

01:53 So where are the electrons usually? well, the electrons can be at the outermost portion of the atom, but usually they actually hang out in this middle.

02:01 I'm going to put the middle a little bit darker so you can figure out that's right there.

02:05 So let's pretend that this portion here is just maybe half the diameter.

02:11 So they usually hang out near the nucleus.

02:14 They usually got the outside less off.

02:17 Okay, so now let's figure this out...

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