Calculating Fermi Energy for Neutrons Confined to a Nucleus

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SUMMARY

The discussion focuses on calculating the Fermi energy for neutrons confined within a nucleus containing 40 protons and 50 neutrons, approximated as a sphere with a radius of 4.6 x 10-15 m. The Fermi energy formula used is EF = ((ħ2(3π2n)2/3)/2m), where 'm' refers to the mass of the neutron, not the electron. The number density 'n' is determined using the relation n = N/V, where N is the total number of nucleons (protons plus neutrons) and V is the volume of the nucleus.

PREREQUISITES
  • Understanding of Fermi energy and its significance in nuclear physics
  • Familiarity with the formula for number density (n = N/V)
  • Knowledge of the mass of neutrons and protons
  • Basic concepts of nuclear structure and dimensions
NEXT STEPS
  • Study the derivation of the Fermi energy formula in quantum mechanics
  • Learn about the properties of neutrons and their role in nuclear stability
  • Explore the calculation of nuclear volume and its implications on number density
  • Investigate the effects of nuclear forces on neutron behavior within a nucleus
USEFUL FOR

This discussion is beneficial for physicists, nuclear engineers, and students studying nuclear physics, particularly those interested in the behavior of neutrons in atomic nuclei.

viviane363
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I am wondering about something:
Calculate the Fermi energy for the neutrons confined to a nucleus with 40 protons and 50 neutrons which roughly forms a sphere of radius 4.6 10^(-15) m.
the formula of the fermi Energy is EF= ((h-bar)^2*(3*pi^2*n)^(2/3))/2m
m:mass of electron, n = number density of electron
Then, in the problem we are given protons and neutrons. Where does influence the formula? and where do we use the radius there is one relation that is n = N/V ( N= protons+Neutrons)
is it right?
Also, do we use the mass of electron or the mass of proton = neutron this time?
 
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The number of protons is not directly relevant to the question (it will of course affect the volume of the nucleus). Indeed, ##n= N /V##. And you need to use the mass of the actual particle you are considering, namely the neutron.
 

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