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Problem 10 Easy Difficulty

At the end of its life, a star with a mass of two times the Sun’s mass is expected to collapse, combining its protons and electrons to form a neutron star. Such a star could be thought of as a gigantic atomic nucleus. If a star of mass $2 \times 1.99 \times$ $10^{30} \mathrm{kg}$ collapsed into neutrons $\left(m_{n}=1.67 \times 10^{-27} \mathrm{kg}\right)$ what would its radius be? Assume $r=r_{0} A^{1 / 3}$.

Answer

1.6 \times 10^{4} m

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Meghan M.

McMaster University

Video Transcript

number 10. There is a star that has twice the mass of the sun. So here's the mass of the sun's. We have twice that, um, collapses and becomes a neutron store, and we wouldn't know what is the radius of it. We're supposed to treat it like an Adam. So the equation for the radius from Adam is this or not, which is a just a constant. So that's one port two times 10 negative 15 and a That's the mass number. Well, when a star becomes a neutron star, the protons electron combined make neutrons. So this is the mass of one neutron. So Mrs Conserved. So this whole mass of the star is now becoming neutrons. A mass number of it just be the number of neutrons there are. So that would be just this total mass. Oh, I'm just gonna be like that. The mass of this star divided by the massive one neutron up with those values in mess and start with this two times the mass of the sun 1.99 times 10 30 of divided by the massive one neutron. So this is basically telling me how many new transfer are raised to the 1/3 power and I get 15,958. That would be in meters. Um, well, you 236 figs called it like 16 point. Oh, cool, lumbers.

University of Virginia
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Meghan M.

McMaster University