An element in its solid phase has mass density 1750 kg/m^3 and number density 4.39×10^28 atoms/m^3. What is the element's atomic mass number?

Video transcript

Hey, everyone. So this problem is dealing with atomic mass numbers. Let's see what it's asking us. We have a spacecraft on a mission to explore a distant planet and that spacecraft discovers a solid mineral with a density of 2300 kg per meter cubed. The analysis reveals that the minerals number density is 6.25 times 10 to the 28 atoms per cubic meter. Find the atomic mass number of the element comprising this mineral. Our multiple choice answers here are a 28 B 26 C 24 and D 22. So the key here is to recall that the number of atoms N is equal to the equation M are mass divided by capital M or molar mass. And in turn that molar mass is equal to our atomic mass number or a multiplied by U. So we're going to use the information in the problem to first solve for our molar mass. And then we'll be able to solve for our atomic mass number. So if we rearrange this equation, this first equation to isolate molar mass, we have molar mass is equal to lowercase M mass divided by nr a number of atoms. In turn, we can recall that mass is equal to our density multiplied by our volume. So we can plug that in to our equation. So we'll have molar masses equal to row V divided by N. Now, looking at the values from the problem, we are told that this material has a mass density density of 2300 kg per cubic meters and the minerals number density. So number density is N divided by the. So that is our number over our volume and that is 6.25 times 10 to the 28 atoms per cubic meter. And so when we plug those in to our molar mass equation, sorry, let's get the right color there. So our Muller mass equation is going to be 2300 kg per meter cubed divided by 6.25 times 10 to the 28 Adams per meter cubed. And that leaves us with a molar mass of 3.68 times 10 to the negative 26 kg per atom. So now we can solve for our atomic mass number. That's a is equal to mass divided by you if we rearrange that second equation and we came up with our molar mass 3.68 times 10 to the negative 26 kg per atom. And then we can recall you is a constant 1.667 times 10 to the negative 27 kg. Which gives us an atomic mass number of 22. And so when we look at our multiple choice answers that aligns with answer choice D so D is the correct answer for this problem. That's all we have for this one, we'll see you in the next video.