A neutron star is a stellar object whose density is about that of nuclear matter,2×1017kg/m3 . Suppose that the Sun were to collapse and become such a star without losing any of its present mass. What would be its radius?

Short Answer

Expert verified

The value of the radius of the star is 13 km.

Step by step solution

01

Given data

The density of the nuclear matter,p=2×1017kg/m3

Mean density of Sun according to Appendix C,ps=1410×1017kg/m3

Mean radius of Sun according to Appendix C,Rs=6.96×108m

02

Understanding the concept of density  

As per the given concept, the Sun is to collapse to form into a star whose density is given. Thus, keeping the mass constant and relating this to the density, volume, and mass relation, we can get that the radius' cube value is inversely proportional to the density. Thus, using this proportionality relation, we can get the required value.

Formula:

The density of a spherical object, p=m43πR3.......(1)

03

Calculation of the radius of the star

From equation (1), we get that

pα1R3with all other terms as costant.

Rα1p1/3

Thus, using this above relation and the given data, we can get the radius of the star as follows:

R=Rspsp1/3=6.96×108m1410×1017kg/m32×1017kg/m31/3=1.3×104m=13km

Hence, the value of the radius is 13 km.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The nuclide244Pu(Z=94)is an alpha-emitter. Into which of the following nuclides does it decay:240Np(Z=93),240U(Z=92),248Cm(Z=96)or244Am(Z=95)?

A measurement of the energy Eof an intermediate nucleus must be made within the mean lifetime tof the nucleus and necessarily carries an uncertainty Eaccording to the uncertainty principle

E·t=h.

(a) What is the uncertainty Ein the energy for an intermediate nucleus if the nucleus has a mean lifetime of10-22s? (b) Is the nucleus a compound nucleus?

A7Linucleus with a kinetic energy of 3.00 MeV is sent toward a a232Thnucleus. What is the least center-to-center separation between the two nuclei, assuming that the(moremassive)232Thnucleus does not move?

After a brief neutron irradiation of silver, two isotopes are present: 108Ag(T1/2=2.42min)with an initial decay rate of 3.1×105/s,and role="math" localid="1661598035621" 110Ag(T1/2=24.6s)with an initial decay rate of. Make a semilog plot similar to Fig. 42-9 showing the total combined decay rate of the two isotopes as a function of time t = 0 from until t = 10min .We used Fig. 42-9 to illustrate the extraction of the half-life for simple (one isotope) decays. Given only your plot of total decay rate for the two-isotope system here, suggest a way to analyze it in order to find the half-lives of both isotopes.

A certain radionuclide is being manufactured in a cyclotron at a constant rate R. It is also decaying with disintegration constantλ. Assume that the production process has been going on for a time that is much longer than the half-life of the radionuclide. (a) Show that the numbers of radioactive nuclei present after such time remains constant and is given byN=Rλ. (b) Now show that this result holds no matter how many radioactive nuclei were present initially. The nuclide is said to be in secular equilibriumwith its source; in this state its decay rate is just equal to its production rate.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free