Calculate Fermi Temperature for 3He & Neutron Stars

In summary, the conversation is about calculating the fermi temperature for liquid 3He and neutrons in a neutron star. The equations needed for the calculation include number density, fermi radius, fermi energy, and boltzmann constant. The person asking the question is unsure about how to approach the problem, as they have only dealt with similar calculations involving electrons in the past.
  • #1
raintrek
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0

Homework Statement



Calculate T(fermi), the fermi temperature for

a) Liquid 3He (density 81kg/m^3) [these are not electrons]
b) neutrons in a neutron star (density 10^17 kg/m^3)

Homework Equations



n, number density = z*Na*p / M (Na=avogadro, z=valence,p=density,M=molecular mass)

Kf^3 = 3pi^2 * n (Kf = fermi radius)

Ef = hbar^2 * Kf^2 / 2*m (fermi energy)

Tf = Ef/Kb (Kb - boltzmann)

The Attempt at a Solution



Only ever done these where we're dealing with electrons (for ex, potassium etc). Not sure where to go with it...
 
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  • #2
raintrek said:
Only ever done these where we're dealing with electrons (for ex, potassium etc). Not sure where to go with it...
That's not good enough. PF rules require that you show your attempt. What have you studied?
There must be something in your studies that hints at how to solve this problem.
 

1. What is the Fermi temperature for 3He?

The Fermi temperature for 3He is approximately 2.7 K, which is the temperature at which the kinetic energy of the particles is equal to the Fermi energy. This value is based on the mass and density of 3He and can vary slightly depending on the specific conditions.

2. How is the Fermi temperature calculated for 3He?

The Fermi temperature for 3He can be calculated using the formula TF = (3N/4πV)2/3h2/2m where N is the number of particles, V is the volume, h is the Planck constant, and m is the mass of the particles.

3. What is the significance of the Fermi temperature for 3He in relation to neutron stars?

The Fermi temperature for 3He is important for understanding the behavior of matter in neutron stars. It is used to determine the maximum mass that a neutron star can have before it collapses into a black hole, known as the Tolman-Oppenheimer-Volkoff limit.

4. How does the Fermi temperature for 3He differ from that of other elements?

The Fermi temperature for 3He is relatively low compared to other elements, such as iron, which has a Fermi temperature of approximately 107 K. This is due to the lower mass and density of 3He, which affects the kinetic energy of its particles.

5. Is the Fermi temperature for 3He the same as the Fermi temperature for neutron stars?

No, the Fermi temperature for neutron stars is much higher than that of 3He. This is because neutron stars are much denser and have a much larger number of particles, leading to a higher Fermi energy and temperature. The Fermi temperature for neutron stars can reach up to 1012 K.

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