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Critical mass of neptunium. In the fall of $2002,$ a group of scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60.0 $\mathrm{kg}$ . (The critical mass of a fissionable material is the minimum amount that must be brought together to start a nuclear chain reaction.) Neptunium has a density of 19.5 $\mathrm{g} / \mathrm{cm}^{3} .$ What would be the radius of a sphere made of this material that has a critical mass? (Recall that density is mass divided by volume.)

4.19 centimeter

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Rutgers, The State University of New Jersey

University of Washington

University of Sheffield

Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

02:19

Neptunium. In the fall of …

02:28

03:05

In the fall of 2002, scien…

00:58

The radius of a uranium- 2…

01:39

Using $2.30 \times 10^{17}…

04:39

Consider the hydrogen atom…

Uranium $^{235}_{92}\mathr…

01:29

Calculate the mass of a so…

02:59

Calculate the mass density…

07:27

(II) $(a)$ Show that the d…

Neutron stars are composed…

08:51

07:35

(III) The americium nucleu…

04:55

Consider the fission react…

05:24

The critical density of th…

02:13

Using $2.3 \times 10^{17} …

04:08

01:21

The fissioning of plutoniu…

02:48

Neutron stars are believed…

01:52

(II) The americium nucleus…

Okay, You know what? Your instructor? Wrong problem. 21. So we know the density and mass so we can find the volume sphere of this Neptune Ian. So we can say the volume is the critical mass. Because it must be that we're talking about a critical part times the density which we'll call ro. So since we're giving the density and we know the critical mass, we just want to find critical Ray's assumed Mr Disappear. So if we can assume this is the sphere, we know that the volume can also be expressed as 4/3 pocket are cute. So now we can solve for this. And this will be the critical radius. So let's do some outer. Great. Here. So our critical kun, who's a soon's in critical over Raoh times three over for pie. Okay, so living coral recon is not it that you do this? He root of three, then over for pie. Throw. Cool. So now is plug ins and numbers can actually figure out what this is gonna be. So are are critical to his Queudrue ofthree times Our mass, which was 60 kilograms perfect 16 kilograms and divided by four pi And what is our density are density is 1945 graves for sin. You're cute. It's in 19 5 greens per centimeter. Cute. Now the top. Here we have kilograms and on the bottom we have Graham. So we're going to need to fix. So do that. Let's convert this screams two kilograms by multiplied by 1,000,000 creams for kilograms. Those will cancel out kilograms. Cancel O grams cancel fees. Perfect. So now we plug it all in our calculator and we see this simplifies down to just 9.7 meters Awesome.

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Neptunium. In the fall of $2002,$ a group of scientists at Los Alamos Nation…

In the fall of 2002, scientists at Los Alamos National Laboratory determined…

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Consider the fission reaction

$$\mathrm{n} + ^{235}_{92}\mathrm{U} …

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Neutron stars are believed to be composed of solid nuclear matter, primarily…

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