Question

STATEMENT-1: Band gap in germanium is small. because STATEMENT-2: The energy spread of each germanium atomic energy level is infinitesimally small. (A) Statement-1 is True, Statement- 2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement- 2 is False (D) Statement-1 is False, Statement-2 is True

Short answer

The correct answer is (C) Statement-1 is True, Statement-2 is False.

Step-by-step solution

Understanding the Band Gap in Germanium

The band gap of a material is the energy difference between the top of the valence band and the bottom of the conduction band. A small band gap in germanium means that less energy is required for an electron to move from the valence band to the conduction band.

Analyzing the Atomic Energy Level Spread

The energy spread of each atomic energy level in germanium is not 'infinitesimally small'. This refers to the width of the energy levels, which is finite and related to the material's quantum mechanical properties. If the spread were infinitesimally small, it would suggest a very sharp discrete energy level, which is not the case for bands in a semiconductor.

Comparing Statement-1 and Statement-2

Since the band gap in germanium is indeed small, Statement-1 is True. However, Statement-2 is False because the atomic energy levels in germanium have a finite energy spread, contributing to the formation of bands, rather than being 'infinitesimally small'. The correct explanation for the small band gap in germanium is due to the inherent properties of the material, such as its crystal structure and the nature of the bonds between its atoms.

Choosing the Correct Option

Based on the above analysis, Statement-1 is True, but Statement-2 is False. Hence, the correct answer is (C) Statement-1 is True, Statement-2 is False.

Key concepts

Semiconductor Physics

Semiconductor physics delves into the properties and behavior of semiconductor materials, which are a class of crystalline solids that exhibit electrical conductivity between that of insulators and conductors. This unique property arises from their band structure, which can be modified by introducing impurities, a process known as doping.

Germanium, as a classic example of a semiconductor, has a small band gap energy, meaning that it doesn't take much energy to excite an electron from the valence band to the conduction band. The implications of a small band gap mean that germanium can be used in various electronic devices that require the material to conduct current under certain conditions, such as diodes and transistors.

Understanding how band gap energy influences the behavior of semiconductors like germanium is essential for applications in electronics, impacting how they are synthesized and utilized in technology.

Atomic Energy Levels

The concept of atomic energy levels is fundamental to understand the electronic structure of atoms. These levels represent the fixed energies that electrons can have within an atom. In isolated atoms, electrons occupy distinct energy levels, or 'shells', which can be thought of as the rungs on a ladder: an electron can only be on a rung, not between them.

When atoms come together to form a solid, such as in a semiconductor like germanium, these discrete atomic levels broaden into energy bands due to interaction between the atoms. The degree to which these levels spread is crucial for determining the material properties, particularly its optical and electrical behaviors.

The broadening of atomic energy levels into bands is a critical phenomenon, challenging the notion of 'infinitesimally small' energy spreads suggested by Statement-2. This concept further elucidates why the band gap in germanium is not directly related to the spread of its atomic energy levels but to the physical properties and bonds within the lattice structure of the material.

Valence and Conduction Bands

In the context of semiconductor materials, the valence and conduction bands are crucial in understanding their electrical properties. The valence band is the highest range of electron energies where electrons are normally present at absolute zero temperature. Electrons in this band are bound to atoms and do not contribute to electrical conductivity.

On the other hand, the conduction band is the range of electron energies higher than the valence band, where electrons are free to move within the material, thus allowing it to conduct electric current. The gap between these two bands is known as the band gap. For semiconductors, including germanium, this band gap is relatively small, which means that thermal energy at room temperature can cause some electrons to leap from the valence band to the conduction band, enabling electrical conductivity.

Thus, the small band gap in germanium, as expressed in Statement-1, is related to the intrinsic properties that influence the energy difference between the valence and conduction bands, rather than the spread of the atomic energy levels, refuting the explanation given in Statement-2.