JEE Challenger
More from Semiconductor Electronics: Materials, Devices and Simple Circuits
ChemMedAdv 2007 • Paper 2

Band Gap in Germanium and Atomic Energy Levels

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

STATEMENT-1 :\textbf{STATEMENT-1 :} Band gap in germanium is small.

because\textbf{because}

STATEMENT-2 :\textbf{STATEMENT-2 :} The energy spread of each germanium atomic energy level is infinitesimally small.

Options

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

Correct
C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Topics & Concepts

Semiconductor Electronics: Materials, Devices and Simple CircuitsEnergy BandsSemiconductorsGermaniumBand Gap

Step-by-Step Solution

  1. Statement-1 is True: Germanium is an elemental semiconductor with a small energy band gap of approximately Eg≈0.67 eVE_g \approx 0.67\text{ eV} at room temperature.

  2. Statement-2 is True: In an isolated individual atom, quantum mechanical energy levels are discrete and have an infinitesimally small energy spread (governed only by natural lifetime broadening).

  3. Explanation Check: When atoms assemble to form a crystal lattice, Pauli exclusion causes the discrete atomic energy levels to split into continuous energy bands. The small band gap in germanium arises from the periodic potential and atomic spacing in the diamond cubic lattice, not simply because isolated atomic levels have small line width. Thus, Statement-2 is NOT the correct explanation for Statement-1.

Correct Answer: B

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