Concentration of conduction electrons

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SUMMARY

The discussion focuses on calculating the concentration of conduction electrons in a substance using its mass density and molar mass, assuming the effective mass equals the free electron mass. The key formula involves determining the number of atoms per unit volume, which is derived from the mass density and molar mass, under the assumption that each atom contributes one free electron. The electrical resistivity is deemed unnecessary for this specific calculation, but it is relevant for subsequent calculations involving mean relaxation time, Fermi energy, Fermi velocity, and mean free path at the Fermi level.

PREREQUISITES
  • Understanding of mass density and molar mass calculations
  • Knowledge of conduction electrons and their role in electrical conductivity
  • Familiarity with the concept of effective mass in solid-state physics
  • Basic principles of Fermi energy and electron behavior in metals
NEXT STEPS
  • Calculate the concentration of conduction electrons using mass density and molar mass
  • Explore the relationship between electrical resistivity and conduction electrons
  • Learn about mean relaxation time and its significance in electron transport
  • Investigate Fermi energy and Fermi velocity in relation to conduction properties
USEFUL FOR

Students and professionals in physics, particularly those studying solid-state physics, electrical engineering, or materials science, will benefit from this discussion as it provides foundational knowledge for understanding electron conduction in materials.

steph_mil
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This is part of a longer problem, and probably obvious, but if I calculate this wrong, the rest of the calculations will be wrong too!...

Question: Given the mass density, molar mass, and electrical resistivity of a substance at room temperature, how do you calculate the concentration of the conduction electrons assuming the effective mass is equal to the free electron mass?

(Perhaps the electrical resistivity is not necessary to answer this part of the problem?)

The rest of the problem asks for mean relaxation time, fermi energy, fermi velocity, and mean free path at the fermi level. I know how to solve for these once I can calculate the concentration of conduction electrons, so I am not completely helpless, but I just can't get the problem started.

Thank you!
 
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Calculate no. of atoms electrons per unit volume using the given mass density and molar mass.
You probably need to assume that each atom contributes one free electron, since free electrons are the ones responsible for conduction.So you now have the free electron density n(=concentration of atoms).
 

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