(I) The distance between a carbon atom (m = 12 u) and an oxyge...

Question

(I) The distance between a carbon atom (m = 12 u) and an oxygen atom (m = 16 u) in the CO molecule is 1.13 x 10⁻¹⁰ m . How far from the carbon atom is the center of mass of the molecule?

Accepted Answer

Hey, everyone in this problem, we're asked to calculate the distance from the nitrogen atom to the center of mass of a nitrogen monoxide molecule. OK. So we have the nitrogen atom with a mass of 14 new and an oxygen atom with a mass of 16 U that are separated by 1.14 multiplied by 10 to the exponent negative 10 m. We have four answer choices all in meters. Option A 6.1 multiplied by 10 to the exponent negative 11. Option B 7.5 multiplied by 10 to the exponent negative 11. Option C 8.1 multiplied by 10 to the exponent negative 11. And option D 9.7 multiplied by 10 to the exponent negative 11 m. So let's start by drawing out what we have. And we're gonna consider that the nitrogen atom and the oxygen atom are point masses. OK. So on the left, we'll draw our nitrogen atom. And so this is nitrogen N and it has a mass which we'll call MN that is equal to 14 U and we have our oxygen atom. So we're gonna draw that on the right our oxygen atom O and it has a mass mo of 16 U. And we're told that these are separated by 1.14 multiplied by 10 to the exponent negative 10 m. And so these two atoms make up this nitrogen monoxide molecule. And what we wanna do is figure out the distance from the nitrogen atom to the center of mass. And so we have a center of mass somewhere along this line connecting N and O and we anticipate it's gonna be a little bit closer to the oxygen molecule because that oxygen molecule is more massive, it has more mass. We're just gonna mark the center of mass. It's gonna be somewhere around here. And the distance we're looking for is from that nitrogen atom to that center of mass. We're gonna call this XCM. Now, what we're gonna do here is we're just gonna calculate the center of mass relative to the nitrogen atom. And that's gonna give us that distance that we're looking for XCM. OK. So if we calculate XCM, right again, we're taking the center of mass relative to the nitrogen atom and recall that the center of mass is gonna be the mass of the first thing. So the mass of the nitrogen atom multiplied by its distance from a reference point XN plus the mass of the second thing. In this case, it's the oxygen atom multiplied by its distance from the reference point. So Moxo and we're dividing that by the sum of the masses MN plus mo. So we're really taking like a weighted average here. Now, these X values XN and XO, that's why we have to pick a reference point when we're finding our center of math. And because we're looking at the distance from those points, so our reference point we're taking from the nitrogen atta, OK. And so the X value is gonna be the distance from whatever atom we're interested in to that point. OK. So let's fill in the details. The mass of the nitrogen atom 14. You it's distance from this reference point. Well, it's just zero. OK. The nitrogen atom is our reference point. That's where we are, the distance between those two things is zero, which is 0 m. We're gonna add the mass of the oxygen 16 U and we're gonna multiply by its distance. OK. We're told in the problem that the distance between the nitrogen atom and the oxygen atom is 1.14 multiplied by 10 to the exponent negative 10 m. So that's gonna be the distance. OK? 1.14 multiplied by 10 to the exponent negative 10 m. And then we're gonna divide by the sum of the masses in this case 14 U plus 16 U. All right. So we're calculating our center of mass and we're doing it relative to the nitrogen atom. So that we're getting that distance from the nitrogen atom that we want. Let's go ahead and simplify our expression. So in the numerator, that first term is gonna go to zero, we're just left with 16 U multiplied by 1.14 multiplied by 10 to the exponent negative 10 m divided by 30. And the U will divide out. We didn't need to convert our unit of mass because it divides out anyway, so we can divide that out. And when we work this out, we are left with the center of mass being located 6.08 multiplied by 10 to the exponent negative 11 m away from the nitrogen atom. And so that is the answer we were looking for, that is the distance we were looking for. If we go back to our answer choices and we round to two significant digits, we can see that our answer corresponds with option a 6.1 multiplied by 10 to the exponent negative 11 m. Thanks everyone for watching. I hope this video helped see you in the next one.

Struggling with Physics?

(I) The distance between a carbon atom (m = 12 u) and an oxygen atom (m = 16 u) in the CO molecule is 1.13 x 10⁻¹⁰ m . How far from the carbon atom is the center of mass of the molecule?

Watch next

Intro to Center of Mass practice set