What is the cause of failure of free electron theory?

What is the cause of failure of free electron theory?

The free electron model (as put forth by Drude, and modified by Sommerfeld and others) “failed” because for the most part, electrons aren’t completely free. They interact with (i) the lattice, (ii) each other, and (iii) impurities.

What are the drawbacks of free electron theory?

1) It fails to explain the electrical conductivity of semiconductors and insulators. temperature. 3) It fails to explain the concept of specific heat of metals. 4) It fails to explain the mean free path of the electrons.

What are the failures of Drude free electron theory?

The Drude model does have its limitations such as its failure to correctly account for the temperature dependence of resisitivity in metals, but it gives a good enough classical description of electrical conduction in metals which leads to Ohm’s law and shows that resistivity in a metal can be explained by the motion …

What is free electron theory of metal?

The free electron model considers that metals are composed of a quantum electron gas where ions play almost no role.

What are the salient features of Kronig Penney model?

The Kronig-Penney model [1] is a simplified model for an electron in a one-dimensional periodic potential. The possible states that the electron can occupy are determined by the Schrödinger equation, In the case of the Kroning-Penney model, the potential V(x) is a periodic square wave.

Which of the following phenomenon is failed to explain by classic free electron theory?

Explanation: Classical theory states that all free electrons will absorb energy. This theory cannot explain the photo electric effect.

What are failures of Drude model?

The Drude model cannot explain the conductivity of alloys. Even small impurities can drastically decrease the conductivity of metals in a way which is not predicted by the Drude model. From a classical mechanics perspective, the electrons should contribute greatly to the heat capacity of metals.

What are the assumptions of quantum free electron theory?

Assumptions : The energies of free electrons are quantized. The distribution of electrons is as per the Pauli’s exclusion principle. Electrons travel under constant potential and confine to the boundaries of metal.

What are the assumptions of free electrons theory of metals?

Assumptions of Classical free-electron theory: All metals contain large number of free electrons which move freely through the positive ionic core of the metals. Since these free electrons causes conduction in metal under the application of electrical field, they are called as conduction electrons.

Why non metals do not have free electrons?

Because they have no Free mobile electron. We all know that in solid electrons are carrier of electricity while ions are carrier in liquids. Otherwise, like other non-metals, the particles are held in the structure and able to move freely, resulting in non-metals being unable to conduct electricity.

What is the conclusion of Kronig-Penney model?

We have concluded in the Kronig-Penny model that the energy discontinuities in a monatomic one-dimensional lattice occur when k = (nπ/a), where n is any positive or negative integer.

How does the free electron theory of metals work?

Quantum free electron theory of metals: The distribution of electrons is as per the Pauli’s exclusion principle. Electrons travel under constant potential and confine to the boundaries of metal. All the attractive and repulsive forces are neglected.

Why was the free electron theory a failure?

Due to its limitations, the free electron model was unable to account for things like magnetoresistance, thermal dependence of conductivity, optical properties and the host of many body phenomena that result from electron-electron interactions being of importance. Aren’t the “free-electron theory” and the “free-electron model” the same thing?

What are the properties of a free electron?

Free Electron means unbound electron of the atom of any metal which can move freely. Many properties of metal-like electrical conductivity, magnetic susceptibility, Thermal conductivity, Mechanical strength, optoelectronic properties, etc. depend on the free electrons.

How are free electrons related to perfect gas?

The behaviour of free electrons moving inside the metals is considered to be similar to that of atoms or molecules in perfect gas. These free electrons are, therefore, also referred to as free electron gas and the theory is accordingly named as free electron gas model.