The proton has a radius of approximately 1.0×10⁻¹³ cm and a mass of 1.7×10⁻²⁴ g. Determine the density of a proton for a sphere V = (4/3)πr³.

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hey everyone for this problem, we're being asked to determine the density of a neutron in grams per cubic centimeter. If it has a radius of approximately 0.8 centimeters and a mass of 1.67 times 10 to the negative kg. So the formula for calculating density is density is equal to mass over volume, where r P represents the symbol row and this is density and we have mass over volume. And the question is asking us for the density and grams per cubic centimeter. So we know that is going to be our final unit. And so that means we need our mass in grams and our volume in cubic centimeters. So let's start off with what we're given. Our numerator for our equation is mass. So let's go ahead and calculate our mass They give us a mass of 1. times 10 to the negative kg. And we want this in grams. So we need to convert kilograms two g and we can do this using stoke eom a tree. So in one kg there is one 1000 grams and so are kilograms cancel. And when we do this math, we get 1.67 times 10 To the -24 g. Okay, so we have our mass. Now let's calculate our volume. We're told that we're calculating the volume of a neutron and a neutron is spherical in shape. And so for the volume of a sphere We get our volume is equal to 4/3 pie are cubed. So that's the volume of a sphere And our represents our radius and they tell us we have a radius of 0.8 cm and we need this in cm. So we need to convert 0. cm two cm. So let's go ahead and do that. And one centimeter we have one times 10 To the negative meters. And in one m there is 100 centimeters and so we'll make sure our units cancel our centimeters cancel, our meters cancel. And we're left with centimeters. And when we do this calculation we will get eight times 10 To the - centimeters. So now we can plug this in into our volume equation. So we get our volume is equal to four thirds pie. Our radius that we just converted into cm is eight times 10 to the negative 14 cm. Cute. And so when we do this calculation we'll get our volume and cubic centimeters, which is the unit that we need. So now when we do this calculation we get a volume of 2. times 10 To the negative cubic centimeters. So now we have our mass in kilograms and we have our volume and cubic centimeters and we can plug all of this in to calculate our density. So we get our density is equal to 1.6, 7 Times 10 to the negative g over our volume of 2.14 Times to the -39 cubic centimeters. Once we do this calculation, we will get a final answer of 7.79 times 10 to the 14th grams per cubic centimeter. This is 10 to the 14th, and that is the final answer for this problem. This is the density of a neutron in grams per cubic centimeter. That's the end of this problem. I hope this was helpful.

The proton has a radius of approximately 1.0×10⁻¹³ cm and a mass of 1.7×10⁻²⁴ g. Determine the density of a proton for a sphere V = (4/3)πr³.

Verified Solution

Key Concepts

Density

Volume of a Sphere

Proton Properties

The proton has a radius of approximately 1.0×10−13 cm and a mass of 1.7×10−24 g. Determine the density of a proton for a sphere V = (4/3)πr3.

Verified Solution

Key Concepts

Density

Volume of a Sphere

Proton Properties

The proton has a radius of approximately 1.0×10⁻¹³ cm and a mass of 1.7×10⁻²⁴ g. Determine the density of a proton for a sphere V = (4/3)πr³.