Team Quanta gladly presents all possible short questions of BS Physics book Solid State Physics – II’s Chapter#2: Band Theory of Solids.
Q.2.1:- :- 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 $k^2=k_x^2+k_y^2+k_z^2$
For three dimensions,
$$E_K\ =\frac{\hbar}{2m}(\ k_x^2+k_y^2+k_z^2)$$
Q.2.2:- Why a solid whose energy band is filled cannot a metal.
In molecules two atomic orbitals combine together to form a molecular orbit with two distinct energy level.In solid, 1023 stacked up lines confirmed in a tiny space would like a band. Therefore, a solid whose energy band is filled cannot be metal.
Q.2.3:- Give the order of band gap for a metal, a semiconductor and insulator.
Metal: In the metal, the band gap energy gap between valance band and conduction band is very or zero very small is of the order of Eg = 0ev.
Semiconductor: In the semiconductor the energy band gap between valance band and conduction band is small is of the order of 1ev.
Insulator: In the insulator the energy band gap between valance band and conduction band is very large is of the order of 6ev.
Q.2.4:- What is Bloch function?
The wave function is given by;
$$\mathrm{\Psi}x=\ {\mu k}{\left(x\right)}e^{\pm i k x}$$
Where ${\mu k}_{\left(x\right)}$ has periodicity of lattice given by;
$${\mu k}_{\left(x\right)}=\ \mu k(x+a)$$
“ The Eigen functions of the wave equation for a periodic potential are the product of plane wave $e^{ik.r}$ times a function $\mu k({r})$ with the periodicity of the crystal lattice”
Q.2.5:- Explain the concept of forbidden energy band.
The energy gap between valance band and conduction band is called forbidden energy band.
Example: The energy gap of insulator is very large is of the order of 6ev.
Q.2.6:- 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.2.7:- What is basic assumption given by Kronig and Penny in their theory.
This model explain the behavior of electrons in a periodic potential by a assuming a relatively simple one- dimensional model of periodic potential.
The potential energy of electron in a linear array of positive nuclei is assumed to have the form of periodic array of square wells with a period of (a + b).
At the bottom of well $0<x<a$ the electron is assumed to be in the vicinity of a nucleus and potential energy is assumed to be zero.
Q.2.8:- What are the shortcoming of free electron theory. What is main cause of its failure?
The treatment of a metal as containing a gas of electrons completely free to move within it.
Main cause of its failure: It fails to explain the electric specific heat and the specific heat capacity of metals.
- It fails to explain superconducting properties of metal.
- It fails to explain new phenomenon like photoelectric effect, Compton effect, black body radiation.
Q.2.9:- How does the band theory lead to the concept of negative effective mass?
The concept of negative effective mass may be 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. The concept of negative effective mass provides description of the charge carriers in crystal.
