Physics question 9 hw 22

Physics
Tutor: None Selected Time limit: 1 Day

Certain stars are thought to collapse at the end of their lives, combining their protons and electrons to form a neutron star. Such a star could be thought of as a giant atomic nucleus. If a star with a mass equal to that of the sun (of mass 1.99 × 1030 kg) were to collapse into neutrons, what would be the radius of the star? Answer in units of m.

Jul 17th, 2015

Thank you for the opportunity to help you with your question!

I assumed a Planck Length as that's the smallest space can be and that's apparently the space between nucleons on average.

 If we assume the inter neutron space is,

 s = 1E-35 m (a Planck Length) and all the 1.99E30 kg were somehow all neutrons,

 N = M/n = 1.99E30/1.67E-27 = 1.19162E+57 neutrons would be crammed into a volume 

Then,

V = 4/3 pi R^2  where R = sqrt(V/(4/3 pi)) = ? meters. 

n = 1.67E-27 kg is the rest mass of a neutron. 

As an approximation to the volume each neutron takes up, we assume that,

 v = s^3 = 1E-105 m^3, that is, the Plank Length cubed

So,

 V = Nv = 1.19E57 * 1E-105 = 1.19E-48 m^3. 

Now,

 R = sqrt(1.19E-48/((4/3)*pi())) = 5.33002E-25 m.  

Finally,

 the radius of the star would be 5.33002E-25 m.  


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

This seems correct and close to my work, but it is wrong according to the homework!

Jul 17th, 2015

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