Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (a) How many

step 1 Hello, everybody. All right, so we're back with another question. This one states that too small

Two small aluminum spheres, each having mass 0.0250 kg, are...

Key Concepts

Mole Concept and Avogadro's Number

This concept involves converting a given mass of a substance into moles by using its molar mass and then multiplying by Avogadro's number (approximately 6.022×10^23 particles/mol) to find the total number of atoms. It is fundamental for determining the number of constituent particles, such as electrons, in a sample.

Atomic Structure and Electron Count

Understanding that the atomic number denotes the number of electrons in a neutral atom is key when counting electrons. For elements like aluminum, this concept enables one to calculate the total electron count per atom, which is then used to determine the overall number of electrons in an object made of that element.

Charge Quantization and the Elementary Charge

Electric charge comes in discrete units, with the elementary charge (approximately 1.602×10^?19 coulombs) being the charge of a single electron. This principle is essential in linking the number of transferred electrons to the net charge on an object and is crucial for precise charge calculations in physical systems.

Coulomb's Law

Coulomb's law expresses the force between two point charges as directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is applied in calculating the force arising from a specific charge distribution and is central to problems involving electrostatic interactions.

Proportional Reasoning in Charge Distribution

This involves using ratios to compare the number of electrons transferred relative to the total number of electrons present. It is important for assessing the significance of the change in electron count in relation to the overall system and for understanding the scale of charge redistribution in a given context.

Transcript

00:01 Hello, everybody.

00:02 All right, so we're back with another question.

00:05 This one states that too small aluminum spheres r separated by eighty centimeters and each have a massive point zero two five kilograms.

00:15 So what we're going to do right now is the label that information out point zero to five kilograms and it said a distance are eighty seven millimeters, so i'm just gonna call it point eight meters.

00:35 Cool.

00:35 So the first question asked, how many electrons does each sphere contain in the atomic mass of aluminum? an atomic number are given to the atomic mass for aluminum is twenty six point ninety two grams per mole.

00:54 So what i'm going to dio is put that immediately into kilograms just for the purposes of everything else.

01:06 That it's a mass is also in kilograms.

01:08 So this is easy.

01:11 You just times it by turn to the negative three.

01:15 Because going from graham's two kilograms, we'll have to divide my thousand.

01:27 There you go.

01:28 Kilograms permal.

01:30 And then what was it? the atomic number? i was thirteen.

01:36 Uh, e i think that z i think what would they call it? a z aluminum? mr.

01:45 T, i believe this is how they know atomic numbers and physics as well as chemistry.

01:53 Anyway, so i says, how many electrons are in each sphere? so that means we're gonna have to end up at the very end of this question.

02:04 Ah, in adam's, right, because we would know how many electrons are in each.

02:10 Adam.

02:11 So how do we get there? so what we're going to do first is find out how many aluminum how many moles of aluminum are within each year.

02:22 So how we do that is by making doing a ratio between the two.

02:28 The math of this fear over ah, no, the atomic mass of aluminum.

02:39 Okay, so by doing this, i want to write out.

02:45 Actually, the units roll quick so you can kind of see what's gonna happen here.

02:53 What's gonna happen here is we're going to end up with moles in the numerator when we do this little fraction, because if you notice here, this will cross out, and that will cross out.

03:06 And this will be in the denominator denominator, which is actually the numerator, right? so i'm not going to do the calculation for that at the moment because it's actually better to try toe khun, jumble everything into one big equation before you do.

03:25 Anyway, the calculator work.

03:27 All right, so we have this first converted.

03:31 This will give us moles from moles.

03:34 We're going to multiply by allah.

03:36 Guardo's number, which is a helpful tool that always knows how many atoms make up a mall of a substance.

03:46 That number is six point zero two times ten to the twenty third.

03:58 That's how many atoms per more there are.

04:03 Maybe you should write it on august testing to sink.

04:07 So that's how many atoms any type of adam are within.

04:12 And within that same amount of moles or whatever, you know, i don't think e think it makes sense.

04:19 I think you guys can intuitively get.

04:22 That would help me trying to explain.

04:23 But as you can see, that's a lot of atoms, which it should be.

04:29 It's completely fine that there is because adam's as we know, a very, very, very, very small all right, so from here, that mole and that more would cross out and we would end up with just a number of adam's right, and then from there we can use this guy right here.

04:48 I don't know.

04:49 I don't know this guy right here and say that since the atomic number is thirteen, that means there's thirteen protons within each atom of lim, um, as well as thirteen electrons within each atom of aluminum.

05:09 So that means whatever this number equates to, then we're going to times it my thirteen to get the number of electrons.

05:21 No hurry.

05:22 So we're going to do right now.

05:25 Is khun jumble all that into one equation? so then one equation is we're trying to find the number of electrons in one sphere.

05:35 They're both the same size.

05:36 So we're just focusing on one of this year's.

05:39 We know the math of this fear little m over the big um, which is the atomic math.

05:48 Now there is that.

05:49 Then we're going to times it by the avocados number to get into adams and then times it by how many electrons are found within each atom.

06:02 So thirteen doing all that math, we end up with seven point two five times ten to the twenty four, and oh, little elaborate a little bit before moving on to the next section.

06:27 But that is how many elektron end up being in each year.

06:33 So basically, i'm not really going.

06:37 Teo, plug in.

06:38 Chuck.

06:39 I think you guys can understand how to do that on your own, but especially with me listening them out right here.

06:47 But just for the sake of helping you guys, i'll at least write the little fraction part.

06:54 It's this.

06:55 Ah, remember, there's a thirteen in the front over twenty six point eight nine two.

07:10 Remember, we converted it to kilogram, so we have to add on that times ten to the negative three basically saying that this number is very small work and then times avocados number, which i am not going to write out.

07:28 That's too long over thinking it's right there.

07:32 But anyways, do that calculation and you should end up with this number.

07:38 Bingo.

07:39 Cruel, cruel.

07:41 All right, so let's see if i can i don't know if i can or not, but, um, all right, i can't make it a new ah slide.

07:54 So i'll just try teo race as much as i can as i do the next problem.

08:00 They're the next question.

08:01 No.

08:02 So part b says how many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude one times ten to the fourth nunes.

08:17 So we're going teo basically say one times ten to the fore.

08:25 Yeah, noone's right.

08:29 They're both right of let me think.

08:34 Let me make sure i know how to take away erase any i wanna try to erase some stuff.

08:44 But anyway, um, as i raised this stuff or tried tio, i will explain out like the concept.

08:53 I guess so.

08:54 In a previous problem, we talking about coup looms law, which is basically an equation.

08:59 That reference is how two charges ah, attract each other or repel each other.

09:07 And what the what the ah force would be that ah, associated with that action.

09:18 So in this problem, or this section of the problem, it gives you the value of the force for that situation.

09:28 So what we need to do and it also gives you how far away they are, i think, um, yeah, so the distance away is still the same.

09:42 So that means that what i'm not erasing the ah anyways, so that means that we're going to need to find how much charge is on one of the hey, one of the guys.

10:05 One of the spheres.

10:08 So what we do is not that refined.

10:13 How much charges on one of the spheres, but within the situation that would cause a force of that value.

10:21 What would be the charge on this fear? and then from what we got from party, we determine how much charge it has in the previous situation.

10:33 So then we can determine how much it needs to move over to the other.

10:38 Does that make sense? ah, go away.

10:46 Go on and sorry, guys.

10:53 No, go.

10:57 This's taken so long.

11:02 But anyways ah, try to think about it on your own long.

11:08 I do this, i guess, um, from what i explained, see if you khun, try to conceptualize it.

11:18 I'm going to keep this number of electrons up, though, because we're gonna kind of need it for the very last part of this, uh, part b.

11:32 I'm going to get rid of this other little part right here.

11:44 Todo this obnoxious thirteen.

11:52 I wrote it so big.

11:58 All right.

11:58 I think we're good now.

12:01 I'm gonna ad f equals one times ten to the fourteen tor little knowledge bar over here? no, for part b, they're saying that there's a situation where the two charges are repelling each other or no, they're attracting each other.

12:22 So they have this opposite.

12:25 Um, opposite.

12:28 Ah, charges more opposite signs.

12:35 There we go.

12:36 I didn't want to say charges that job that'll just confuse you.

12:40 But anyway, um, let me read it over one more time.

12:43 How many electrons would have to be removed from one sphere and added to the other to cause an attractive force between the spheres of magnitude blank.

12:54 And so what happens here is we know that this is how many electrons there are now.

13:03 We also know how much charge is found in one electron.

13:09 So what we're gonna do, we're gonna find out how much she charge is in.

13:14 Each is in each sphere...

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