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One mole of atoms consists of $6.02 \times 10^{23}$ individual atoms. If a mole of atoms were spread uniformly over the surface of the Earth, how many atoms would there be per square meter?
$1.18 \times 10^{9}$ atoms $/ m^{2}$
Physics 101 Mechanics
Chapter 1
Introduction, Measurement, Estimating
Physics Basics
University of Michigan - Ann Arbor
Simon Fraser University
Hope College
McMaster University
Lectures
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Our question says that one mole of atoms consist of 6.2 times 10 to the 23rd individual atoms. If a mole of Adams were spread uniformly over the surface of the Earth, how many atoms would there be per square meter? Okay, so I wrote down what we were given at the beginning of the problem, and that's that. One mole is equal to 6.2 times 10 to the 23rd Adams. That's one mole of atoms. And we also need to know because we want to know over the surface of the earth. We need to know the surface area of the earth, which is two pi times. The radius of the earth squared and the radius of the earth is equal to 6.38 times 10 to the six meters. Okay, and then again, the question is, how many atoms per square meter if you have this one mole spread across the surface of the earth. So to do that, we're going to start off with what we need, which is one mall divided by the surface area of the earth. Okay, and one more is 6.38 I'm sorry. No, it's a 6.2 times 10 to the 23rd Adams kill. And then we're going to divide that by the area of the earth, which is too times the surface area anyways, two times pi times 6.38 times 10 with the six nuts in meters and the radius is squared. So we're going to be squaring that value. And if you look at our units, we have Adam's on top and we're gonna end up with square meters on the bottom. And we're that's what we were asked to find was how many atoms we had per square meter. So we're gonna go ahead and carry out this calculation and we find that we have 1.18 three significant digits are going to be reporting, because that's Ah, the lowest number of significant digits we had in the values we used to calculate this. And it's 1.18 times 10 to the nine. And that is in Adams. Her square meter up and box it in as your solution
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