Copper has a density of 8.96 g/cm 3 . If a single copper atom as a mass of 1.055×10 -25 kg, what is the volume of a copper atom?

Hey, guys. Let's check out this practice problem. So for this copper, we have the density of copper, we've got the mass of a single atom, and we're trying to figure out what the volume is of a single atom. So we've got the density, that's rho, is 8.96, and the units for that are grams percent of meter cubed. Then for the mass, 1.055 times 10 to the minus 25, that's in kilograms, and we're looking for the volume. So that's the target variable. So we're gonna start with our density equation. Our density equation is rho equals mass over volume. So to solve for the volume, I can basically just flip these variables around. So So I've got volume is equal to mass over the density. So remember that I want everything to be in SI units. Right? Everything kilograms, meters cube, stuff like that. So let's look at the mass. The mass is equal to 1.055 times 10 to the minus 25, and it's in kilograms. That's the correct unit. So to plug this in, I've got 1.055 times 10 to the minus 25, that's in kilograms. Now for the density. Now what happens is the density is actually given to me in grams per centimeter cubed. So be very careful. Don't just plug this in and solve for the velocity be or sorry, solve for the volume because these aren't the same units. They don't speak the same language. So first, what we're gonna have to do is we're gonna have to convert this density to the correct units. So I'm gonna go over here and do that. So 8.96 grams per centimeter cubed, I'm gonna have to multiply by some conversion factors in order to get it to kilograms per meters cubed. And if you take a look, really these are just a couple of metric prefixes. So to go from grams to kilograms, I wanna go and I wanna, I wanna cancel out grams in the bottom. I wanna get kilograms on top, and I know the relationship is just 1 to a 1000. So I've got 1 divided by a 1000 over here. So that gets rid of grams and leaves me with kilograms, which is right. So now what I've got to do is I've got to convert the centimeters cubed to meters cube. That's also just another metric prefix, and I want to get meters, sorry. I want to cancel out centimeters on top and bottom and I want to get meters on the bottom. So I know the relationship there is a 100 centimeters to 1 meter. We have to be very careful when you do this volume conversion or this density conversion, because remember that we have centimeters cubed over here. So we're gonna have to multiply this conversion factor 3 times. And so that will cancel out centimeters cubed and leave me with just meters. So basically, what happens is I'm gonna do 8.96 times, and I'm gonna do a 100 cubed divided by 1,000. And if you plug this into your calculator, make sure that you're doing a 100 to the 3rd power, then you're gonna get 8,000 960 kilograms per meter cubed. So that's the density. And so now we can plug it back into this formula over here. So 8960 kilograms per meter cube. Now our new units are gonna work out and so our our volume, is gonna be 1.18 times 10 to the minus 29, and that's in meters cube. So if we look through our answer choices here, 1.18 times 10 to the minus 29 is equal to answer choice C. And that's it. So that's our answer choice. Let me know if you guys have any questions.

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Copper has a density of 8.96 g/cm3. If a single copper atom as a mass of 1.055×10-25 kg, what is the volume of a copper atom?

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Copper has a density of 8.96 g/cm³. If a single copper atom as a mass of 1.055×10^-25 kg, what is the volume of a copper atom?