Solid State Physics-II

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Chapter#1: Free Electron Fermi Gas

Team Quanta gladly presents all possible short questions of BS Physics book Solid State Physics – II’s Chapter#1: Free Electron Fermi Gas for the of students.

Q.1:- What do you understand by free electron gas?

The behavior of electron moving in a periodic potential by regular arranged positive ion cores is analyzed which is known free electron gas. The energy of free electron is given by;

  E_k=\frac{\hbar^2 k^2}{2m} where  k^2=k_x^2+k_y^2+k_z^2

Q.2:- Define Fermi energy for metals how does it depend on mass of sample?

The energy of top most level is called Fermi energy. The Fermi energy is given by;

    \[F_E=\frac{1}{1+e^{\left(\frac{E-EF}{KBT}\right)}}\]

The Fermi energy does not depend on mass it depends on temperature.

Q.3:- What is the significance of the Fermi distribution function.

The Fermi distribution function is given by;

    \[F\left(E\right)=\ \frac{1}{1+e^{\left(\frac{E-\mu}{KBT}\right)}}\]

EFo Fermi energy \mu Fermi function of temperature. The  Fermi distribution function gives the probability that an orbital at energy will be occupied in an ideal electron gas.

Q.4:- Can a metal be associated with two Fermi temperature.

Yes a metal can be associated with two Fermi temperature.

  • At  T = OK the Fermi function F(E) = 1
  • At all temperature the fermi function will be F(E) = 1/2

Q.5:- ON which factor hall coefficient depends.

The hall coefficient is given by

    \[R_H=\frac{E_H}{J_XB_Z}\]

The hall coefficient depends upon electric field strength, current density, magnetic field.

Q.6:- Can an electron possess negative mass? Justify

Yes an electron possess negative effective mass. Because the energy spectrum of electron is discrete. The concept of negative effective of electron is understood in terms of Bragg’s reflection when K close to \pm\frac{\pi}{a}. Due to Bragg’s reflection a force applied in one direction which results in the negative effective mass.

Q.7:- What is Fermi level and Fermi energy?

Fermi level: The top most filled energy level at absolute temperature is called Fermi level.

    \[n_F=\ \frac{N}{2}\]

Fermi energy: The energy of top most filled orbital at absolute zero is called Fermi energy.

Q.8:- Write down the Schrödinger equation for the electron in a one – dimensional potential box.

    \[-\frac{\hbar^2}{2m} \frac{d^2 \Psi }{dx^2}+V\left(x\right)\Psi =E\Psi\]

∵ For region V(x) = 0

    \[-\frac{\hbar^2}{2m} \frac{d^2 \Psi }{dx^2}+(0)\Psi =E\Psi\]

    \[-\frac{\hbar^2}{2m} \frac{d^2 \Psi }{dx^2} =E\Psi\]

    \[\frac{d^2 \Psi }{dx^2} =-\frac{2mE}{\hbar}\Psi\]

    \[\frac{d^2 \Psi }{dx^2} + \frac{2mE}{\hbar}\Psi =0\]

∵ k^2=\frac{2mE}{\hbar^2}

    \[\frac{d^2 \Psi }{dx^2} + K^2\Psi=0\]

Q.9:- Define thermal conductivity of metals.

The thermal conductivity of metals is define as the measure of  potentional to conduct heat. In materials of low thermal conductivity, heat transfer occure at lower rate than in materials of thermal conductivity.

    \[Q=K\ \frac{dT}{dx}\]

K is thermal conductivity of metals.

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