Question

When a star exhausts its nuclear fuel, the gravitational force causes it to col- lapse. As the density increases, the star enters the electron degeneracy limit and the electron degeneracy pressure may be able to support the star against gravitational col- lapse. The gravtiational pressure of N nucleons of mass MN is 1/3 P, - G(NM)?(45 V-4/3 Determine the radius of the star assuming that there are 2 nucleons per electron. Evaluate the radius for N - 1057, which is typical number of nucleons in a star with one solar mass and show that it is similar to the radius of the earth (RE6400km).

Answer 1

Solution The geapidation bressure of N mucelons of Mass MN IS 13 -413 So foe sdabi lidy, thic proscure musit opposed by the election degeneracy pressure As given, Sdar hos moss appror to Mass of son, and after exhausiting. it muclear fuel, it will twen into a whide dwarf. for cohide dwerf electhon dogeneracy pressuke is, 2. Pe = TL 15 me A ke balomcing the gravitational bress wee, ka dius of star is given by. 513 Ne 2/3 471 TL 3 Gme M mumber of electeons, Mw moss of mucloon of eleetron . 10oro for tohere Ne is mass N= 2Ne 1/3 13 2. 2. 512 G me M And for N = 10 1.05 X10-34)2 -31 /3 (10 )-46 6.67 X10"x 9.1 X10 x(1 67X16 512 0.0075 532X10 %3D 3. 7553, 2 XI0 7553.2 Km, twhich is mear abeut the radius of Earcth