Activity 5: Modelling Neutron Stars (WIP)
Neutron stars are astrophysical objects that we can think of as very large nuclei. Because neutron stars are (almost entirely) made of neutrons, we can set Z = 0 and therefore A = N. Therefore the liquid drop formula becomes:
As N ≫ 1, the symmetry (aS) and parity (aP) terms become negligible. However, gravitational attraction will play a role. Neglecting the symmetry (aS) and parity (aP) terms and including a term for the gravity, the liquid drop formula becomes:
Graph 4 (below) shows the theoretically calculated binding energy per nucleon (BE/A) using the modified liquid drop model (above). Because of the very large numbers of neutrons involved, a logarithmic scale is used.
| Symbol | Value |
|---|---|
| aV | |
| aA | |
We are again looking for the x-intercept, which will give the lowest number of neutrons for which the Binding Energy per nucleon is still positive. From the graph, a massive nucleus with gravitational interaction can exist as long as the number of neutrons is at least: 0 nucleons
5(a) :: If one neutron has a mass of 1.67x10-27 kg, what is the mass of the
neutron star above?
x10
kg
5(b) :: The mass of the Sun is 1.989x1030 kg. Use this to convert your
answer above into the mass of the neutron star in terms of solar masses.
solar masses
5(c) :: Based on the modified liquid drop model above, the radius of this neutron
star would be 0 km. What is its volume?
(Hint: the equation for the volume of a sphere is 
and don’t forget to check your units!)
m3
5(d) :: What would the density of this neutron star be?
kg/m3
How does this compare to the densities of materials here on Earth? Make a note of your answers and join the discussion on the FutureLearn course .