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Neutron stars are remarkable objects, city-sized ( 10 km radius) but with masses

ID: 3280364 • Letter: N

Question

Neutron stars are remarkable objects, city-sized ( 10 km radius) but with masses in excess of the Sun ( 1.4 Mo). Neutron stars are thought to be formed from the collapse of the iron core of a massive ( 8-20 Mo) star at the end of it's nuclear burning phase. Most known examples are rotation-powered pulsars which are detected by their periodic bursts of radio emission The likely composition in the neutron star core is primarily neutrons, with a small fraction of electrons, protons, and possibly more exotic particles/phases.

Explanation / Answer

Because neutron’s mass is slightly greater than proton and electron combined electron should supply required K.E.

Using relativistic expression for K.E. of electron and equating it to rest energy difference we have following equation

This implies

To calculate ‘v’ in above equation we first find momentum ‘p’

From law of equipartition the total momentum


In degenerate electron gas is tightly packed and average distance is about ne-1/3. It follows that the estimate of pressure from uncertainty principle is px = (h/2.p). ne-1/3.

This implies

Where the term in the square braces is the expression for ne.

The velocity of electrons required in (1) is therefore given by v = p/me.

Solving for density r we have with A/Z = 1 for hydrogen,