Exam Questions: Physics of Compact Objects - Degenerate Fermion Gases, Exams of Physics

Download Exam Questions: Physics of Compact Objects - Degenerate Fermion Gases and more Exams Physics in PDF only on Docsity! The Handbook of Mathematics, Physics and Astronomy Data is provided KEELE UNIVERSITY EXAMINATIONS, 2009/10 Level III Wednesday 28th April 2010, 13.00-15.00 PHYSICS/ASTROPHYSICS PHY-30003 The Physics of Compact Objects Candidates should attempt to answer THREE questions. NOT TO BE REMOVED FROM THE EXAMINATION HALL /Cont’d 1 1. (a) Explain what is meant by the term “complete degeneracy” when applied to a gas of fermions. [10] (b) The density of particle momentum states in a gas can be written as g(p) = 8πp2/h3, where p is the particle momentum. Show that in a com- pletely degenerate gas of fermions, the Fermi momentum is given by pF = ( 3h3 8π )1/3 n1/3 , where n is the fermion number density. [20] (c) A white dwarf star, composed entirely of carbon, has a mass of 1 M¯, a radius of 4000 km and an interior temperature of 107 K. Assuming a constant density: i. Calculate the Fermi momentum of the electrons in the white dwarf. [15] ii. Show that the electrons in the white dwarf are close to complete degen- eracy. [15] iii. Using an appropriate criterion for their momenta, calculate what fraction of the electrons can be considered relativistic. [15] (d) In a real white dwarf, the density varies with radial distance from the stellar centre. Explain why this is and discuss how this changes the ideal equation of state in the star between its centre and its surface. [25] /Cont’d 2