Question

Consider a neutron star of a mass equal to twice the mass of the sun. a) Evaluate the fermi energy and determine whether classical or relativistic kinematics should be used.

a) Classical kinematics
b) Relativistic kinematics
c) Both classical and relativistic kinematics
d) None of the above

Answer 1

To evaluate the Fermi energy and determine whether classical or relativistic kinematics should be used, we need to consider the mass and density of the neutron star.

The Fermi energy is given by the formula:

E_F = (h^2 / 2m)(3π^2n)^(2/3)

Where:

E_F is the Fermi energy

h is the Planck's constant

m is the mass of a neutron

n is the number density of neutrons

Given that the mass of the neutron star is twice the mass of the sun, we can assume a mass of approximately 2 * 1.989 × 10^30 kg.

However, without information about the density or number density of neutrons in the neutron star, we cannot calculate the Fermi energy accurately. The density of a neutron star is extremely high, and its number density is on the order of 10^17 to 10^18 particles per cubic centimeter.

Regarding the kinematics to be used, in the case of a neutron star, relativistic kinematics should be used. This is because the gravitational forces and densities involved are so high that the velocities of particles within the neutron star approach significant fractions of the speed of light. Therefore, classical kinematics is not applicable, and relativistic kinematics is necessary to accurately describe the behavior of particles within a neutron star.

So, the correct answer is:

b) Relativistic kinematics

Answer 2

The Fermi energy in a neutron star with mass twice that of the sun would be very high, and particle velocities would be close to the speed of light. Therefore, relativistic kinematics (b) is the correct approach to describe the motion of particles within a neutron star.

Step-by-step explanation:

For a neutron star with a mass equal to twice that of the sun, the Fermi energy would be extremely high due to the incredibly dense packing of neutrons. Neutron stars are compact objects that result from the gravitational collapse of a massive star after a supernova. In such extreme conditions, the velocities of the neutrons are a significant fraction of the speed of light, c, and thus, the kinematics of particles within a neutron star are best described by relativistic kinematics.

Classical kinematics fails to accurately describe motion at such high velocities, as it does not incorporate the effects of special relativity which become significant as you approach the speed of light. The correct answer to whether classical or relativistic kinematics should be used is (b) Relativistic kinematics.

If the speed of the neutron star is significantly less than the speed of light, classical kinematics can be used. However, if the speed of the neutron star is close to or approaching the speed of light, relativistic kinematics should be used.

Since the question does not provide any information about the speed of the neutron star, we cannot determine whether classical or relativistic kinematics should be used. Therefore, the correct answer is d) None of the above.