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Calculate the approximate (a) radius, (b) volume, and (c) density (in $\mathrm{kg} / \mathrm{m}^{3} )$ of a nucleus of gold, $_{79}^{197} \mathrm{Au}$ (You can ignore the binding energy of the nucleus for this calculation.)

$4.69 \times 10^{15} \mathrm{kg} / \mathrm{m}^{3}$

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Cornell University

Numerade Educator

University of Washington

University of Sheffield

So in this Christian you want to approximate a couple parameters a couple properties of the golden Adam. So there are a couple. There was one informal language to use. This is the only focus. Is 30 point to what I was only formed your spark even in section for section ofthe chapters. 30. So the formula we want to use is our equals are not times a concert. So here are is a radius. This is a constant and it's an empirical constant media is a constant. We drive by experiments instead of see me and hey, is samast number so part They asked us the Raiders of the goat and says is going to be fine ways this for murder because the question gives us ESA This question gives us that that's a foreman of a God. And for code is hey, you 79 y 97. And how do we interpret this number is at 1 97 Cece is C A. And this 79 is Suzie its atomic number. So we know is 1 97 and you can look up are not from the chapter. So we have the radius iss are not insane three equals are not because 1.2 times 10 to the negative 5th 15 meter times 1 97 to 1 cert just gives us a radius of 7.0 times 10 to the negative 15 year. So the second see me to find is some intensity as a failure of it. So the volume Okay, we know the formula of volume of a sphere. It's hi are cute. This's just like with the geometry of a sphere That's howyou finds volume on. We already know what arias So we just Oh, I need to do is to putting what we already have in, sir. Last question times 7.0 times 10 to collective of tin a meter cube. And this is 1.4 times 10 to Z inactive 42 a meter cube Last one asks us for so testy in kilograms per meter cube. So in order to do that, the first thing is we need to find it was a mass of the goat. So, you know, when you defend the mass, we have the mass number and mass number pretty much tells us how many particles, including both protons and mutual there are, and so book tells us the average mass for pro home or nutrients are similar is 1.67 times 10 Judy negative turns seven kilograms. So this is a mess hall when put on mutual. And if we have a a total of 197 protons and neutrons together, then we time it by their individual mass to get a hold on us. And once, because the tournaments we know the volume from her be, we can find the density. The row equals and overpay and them equals 1 97 times, 1.67 times tangent infected. And it's probably worse. Remember, is this number because we will be using it over and over, divided by massively find out his task and who's the negative According to thank you. This gives us two points three times 10 to Z at 17 kilograms per meter, which is actually insanely large because and it's understandable because all the protons and neutrons are tightly packed together, but even was a density of starch. We can see the volume is a response with nuclear is still very light

Princeton University