Q: In an insulator, the forbidden energy gap is typically:

Greater than about 3\text{ eV}. Diamond, for example, has a gap of about 6\text{ eV}, far beyond the reach of thermal energy at room temperature.

Q: In a semiconductor, the forbidden energy gap is typically:

Of the order of 1\text{ eV}. A gap of this size lets a useful number of electrons cross it by thermal excitation at ordinary temperatures.

Q: The energy gaps of silicon and germanium at room temperature are approximately:

1.1\text{ eV} and 0.7\text{ eV}. Germanium has the narrower gap, so it generates more thermal carriers and has the larger leakage current.

Q: A semiconductor has an energy gap of 1.1\text{ eV}. The longest wavelength that can excite an electron across it is approximately (hc = 1240\text{ eV}\cdot\text{nm}):

1127\text{ nm}. \lambda = \dfrac{hc}{E_g} = \dfrac{1240}{1.1} \approx 1127\text{ nm}, which lies in the infrared.

Q: Germanium has an energy gap of 0.7\text{ eV}. The corresponding threshold wavelength is approximately:

1771\text{ nm}. \lambda = \dfrac{1240}{0.7} \approx 1771\text{ nm}.

Question 1

The energy gap in a solid is the separation between the:

Accepted Answer

Top of the valence band and the bottom of the conduction band. No electron states exist within this forbidden gap, so an electron must acquire at least E_g to become free.

Question 2

In a conductor, the valence band and the conduction band:

Accepted Answer

Overlap each other. With overlapping bands, electrons can move to higher states under even the feeblest field.

Question 3

In an insulator, the forbidden energy gap is typically:

Accepted Answer

Greater than about 3	ext{ eV}. Diamond, for example, has a gap of about 6	ext{ eV}, far beyond the reach of thermal energy at room temperature.

Question 4

In a semiconductor, the forbidden energy gap is typically:

Accepted Answer

Of the order of 1	ext{ eV}. A gap of this size lets a useful number of electrons cross it by thermal excitation at ordinary temperatures.

Question 5

The energy gaps of silicon and germanium at room temperature are approximately:

Accepted Answer

1.1	ext{ eV} and 0.7	ext{ eV}. Germanium has the narrower gap, so it generates more thermal carriers and has the larger leakage current.

Question 6

The electrical resistivity of a semiconductor lies:

Accepted Answer

Between that of a conductor and that of an insulator. This intermediate behaviour, controllable by doping, is what makes semiconductors so useful.

Question 7

With rising temperature, the resistance of a semiconductor:

Accepted Answer

Decreases, because many more charge carriers are generated. The rapid growth in carrier number outweighs the increased scattering, giving a negative temperature coefficient.

Question 8

At absolute zero, a pure semiconductor behaves as:

Accepted Answer

A perfect insulator. Every valence electron is locked in a covalent bond, leaving the conduction band completely empty.

Question 9

A semiconductor has an energy gap of 1.1	ext{ eV}. The longest wavelength that can excite an electron across it is approximately (hc = 1240	ext{ eV}\cdot	ext{nm}):

Accepted Answer

1127	ext{ nm}. \lambda = \dfrac{hc}{E_g} = \dfrac{1240}{1.1} \approx 1127	ext{ nm}, which lies in the infrared.

Question 10

Germanium has an energy gap of 0.7	ext{ eV}. The corresponding threshold wavelength is approximately:

Accepted Answer

1771	ext{ nm}. \lambda = \dfrac{1240}{0.7} \approx 1771	ext{ nm}.

Question 11

A photon of wavelength 1240	ext{ nm} can just excite an electron across the gap of a semiconductor. The energy gap is:

Accepted Answer

1	ext{ eV}. E_g = \dfrac{1240}{1240} = 1	ext{ eV}.

Question 12

A material absorbs light of wavelength 620	ext{ nm} across its band gap. The energy gap is:

Accepted Answer

2	ext{ eV}. E_g = \dfrac{1240}{620} = 2	ext{ eV}.

Question 13

A semiconductor has an energy gap of 2.5	ext{ eV}. The maximum wavelength that can excite an electron across it is:

Accepted Answer

496	ext{ nm}. \lambda = \dfrac{1240}{2.5} = 496	ext{ nm}.

Question 14

An energy gap of 1.1	ext{ eV} expressed in joule is approximately:

Accepted Answer

1.76 	imes 10^{-19}	ext{ J}. 1.1 	imes 1.6 	imes 10^{-19} = 1.76 	imes 10^{-19}	ext{ J}.

Question 15

An insulator has an energy gap of 6	ext{ eV}. The wavelength needed to excite an electron across it is approximately:

Accepted Answer

207	ext{ nm}. \lambda = \dfrac{1240}{6} \approx 207	ext{ nm}, in the deep ultraviolet — which is why insulators are transparent to visible light.

Question 16

A semiconductor sample has resistivity 0.5\,\Omega\cdot	ext{m}. Its conductivity is:

Accepted Answer

2	ext{ S/m}. \sigma = \dfrac{1}{ho} = \dfrac{1}{0.5} = 2	ext{ S/m}.

Question 17

At room temperature, germanium has more thermally generated carriers than silicon because germanium has:

Accepted Answer

A smaller energy gap. With only 0.7	ext{ eV} to cross rather than 1.1	ext{ eV}, far more electrons make the jump at a given temperature.

Question 18

Gallium arsenide has an energy gap of 1.43	ext{ eV}. The corresponding wavelength is approximately:

Accepted Answer

867	ext{ nm}. \lambda = \dfrac{1240}{1.43} \approx 867	ext{ nm}.

Question 19

Two semiconductors have energy gaps of 1.1	ext{ eV} and 2.2	ext{ eV}. The ratio of their threshold wavelengths is:

Accepted Answer

2 : 1. \lambda \propto \dfrac{1}{E_g}, so the smaller gap corresponds to the longer wavelength.

Question 20

The energy needed to move an electron across a gap of 1.1	ext{ eV} is supplied by a photon of energy at least:

Accepted Answer

1.76 	imes 10^{-19}	ext{ J}. Converting: 1.1	ext{ eV} = 1.76 	imes 10^{-19}	ext{ J}.

Semiconductors & Energy Bands — MH-CET Physics MCQs with Solutions

Questions with solutions