Q.An intrinsic semiconductor has an electron (and hole) concentration of $n_i = 1.5\times10^{10}\ \text{cm}^{-3}$ at room temperature. If it is doped with a pentavalent impurity so that the free-electron concentration rises to $n_e = 5\times10^{15}\ \text{cm}^{-3}$, find the new hole concentration $n_h$, using the law of mass action $n_e n_h = n_i^2$.

Showing the 12 most recent of 16 on this concept.

1. CBSE 2025Set 55/6/11 markMCQ
   Q.Assertion (A): A hole is an apparent free particle with effective positive electronic charge. Reason (R): A hole is not necessarily a vacancy left behind by an electron in the valence band. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Both Assertion (A) and Reason (R) are false.

   ›Reveal solutionSolution

   The key idea is that a hole behaves as a positive charge carrier in a semiconductor, but the reason given misstates the definition of a hole — a hole is exactly a vacancy in the valence band. So Assertion is true, Reason is false.

   Concept first: What is a hole?

   In a semiconductor, the valence band is normally full of electrons. When an electron is excited to the conduction band, it leaves behind an empty state in the valence band. That empty state is called a hole. The hole is not a real particle — it’s a conceptual particle that makes it easier to describe the collective motion of the remaining valence electrons.

   Why does a hole behave like a positive charge? Because when an electric field is applied, the missing electron means the net current from the valence band is as if a positive charge were moving in the opposite direction. So the hole is treated as a free particle with effective mass (different from an electron’s) and an effective positive charge $+e$.

   Now let’s examine the statements.

   1. Assertion (A): “A hole is an apparent free particle with effective positive electronic charge.”

      This is correct. In semiconductor physics, a hole is a quasiparticle that carries a positive charge $+e$ and moves under an electric field just like a free particle, though its effective mass may differ. So (A) is true.

   2. Reason (R): “A hole is not necessarily a vacancy left behind by an electron in the valence band.” …

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2. CBSE 2025Set ANNUAL1 markMCQ
   Q.The conductivity of intrinsic semiconductors at absolute zero temperature is

   (a) zero

   (b) infinite

   (c) 1 mho/m

   (d) 100 mho/m

   ›Reveal solutionSolution

   Charge carriers in an intrinsic semiconductor are generated purely by thermal excitation of electrons across the energy gap; at T = 0 K there is no thermal energy available, so no free carriers exist.

   In an intrinsic semiconductor, at room temperature some valence electrons gain enough thermal energy to jump across the (relatively small) energy gap into the conduction band, leaving holes behind — these electron-hole pairs are the charge carriers. At absolute zero temperature, there is no thermal energy to excite any electron …

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3. CBSE 2025Set ANNUAL1 mark
   Q.What is the resistivity of pure semi-conductor at absolute zero ?

   ›Reveal solutionSolution

   At 0 K a pure semiconductor has no free charge carriers, so it cannot conduct — its resistivity is infinite.

   In a pure (intrinsic) semiconductor, conduction requires electrons to be thermally excited from the valence band across the (small) energy gap into the conduction band, leaving behind holes. At absolute zero temperature, there is no thermal energy available for this excitation — the valence band stays completely full and the conduction band stays completely empty. With no free electrons or holes available to carry current, the material behaves exactly like an …

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4. CBSE 2024Set ANNUAL1 mark
   Q.If in a semiconductor, the number of free electrons ($n_e$) is equal to the number of holes ($n_h$), then what type of semiconductor is this?

   ›Reveal solutionSolution

   Equal electron and hole concentrations is the defining property of a pure (undoped) semiconductor.

   In a pure (undoped) semiconductor, electron-hole pairs are created only by thermal excitation of valence electrons across the band gap, so free electrons and holes are always generated in equal numbers: $n_e = n_h = n_i$. This equality of electron and hole concentration …

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5. CBSE 2024Set A1 mark
   Q.Write True or False: Silicon and Germanium both are examples of compound semiconductor.

   ›Reveal solutionSolution

   Si and Ge are elemental semiconductors; compound semiconductors are made from two or more elements, e.g. GaAs.

   Semiconductors are classified as:

   • Elemental semiconductors: made of a single element from group 14 of the periodic table, such as silicon (Si) and germanium (Ge). …

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6. CBSE 2024Set ANNUAL1 mark
   Q.What are intrinsic semiconductors?

   ›Reveal solutionSolution

   An intrinsic semiconductor is a chemically pure semiconductor crystal, where conduction is entirely due to thermally-generated electron-hole pairs in equal numbers.

   An intrinsic semiconductor is a semiconductor material (such as pure Silicon or Germanium) in its pure form, without any impurity doping. At absolute zero it behaves like an insulator (the valence band is completely full, conduction band empty). At room temperature, thermal energy breaks a small fraction of covalent bonds, generating free electrons in the conduction band and leaving behind an equal number of holes in the valence band. Because electrons and holes are always created in pairs in this process, an intrinsic semiconductor always has

   $n_e = n_h = n_i$

   …

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7. CBSE 2024Set ANNUAL1 mark
   Q.What is an intrinsic semiconductor ?

   ›Reveal solutionSolution

   An intrinsic semiconductor is undoped, pure crystalline silicon or germanium in which conduction happens purely by thermally generated electron-hole pairs, always present in equal numbers.

   An intrinsic semiconductor is a semiconductor in its pure form, without any impurity atoms added. Common examples are pure silicon (Si) and pure germanium (Ge), which have four valence electrons and form covalent bonds with four neighbouring atoms in a crystal lattice.

   At absolute zero, all valence electrons are engaged in covalent bonds and there are no free charge carriers, so the material behaves like an insulator. At room temperature, thermal energy breaks a small number of covalent bonds, releasing free electrons into the conduction band and leaving behind vacancies called holes in the valence band (which behave like mobile positive charge carriers).

   Because every thermally freed electron leaves exactly one hole behind, an intrinsic semiconductor always has:

   $n_e = n_h = n_i$ …

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8. CBSE 2024Set ANNUAL1 markMCQ
   Q.When the conductivity of a semiconductor is only due to breaking of the co-valent bonds, the semi-conductor is called -

   (a) donor

   (b) acceptor

   (c) intrinsic

   (d) extrinsic

   ›Reveal solutionSolution

   Conductivity purely from broken covalent bonds (thermally generated electron-hole pairs), with no doping, defines an intrinsic semiconductor.

   A pure semiconductor crystal (like pure Si or Ge) has all its valence electrons in covalent bonds at 0 K, so it behaves as an insulator. At room temperature, thermal energy breaks some covalent bonds, freeing electrons and leaving holes — both electrons and holes contribute equally to conduction. This carrier generation purely from bond-breaking (no impurity …

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9. CBSE 2023Set MODEL1 markMCQ
   Q.Temperature coefficient of resistance for semiconductors is:

   (a) Zero

   (b) Positive

   (c) Negative

   (d) None of them

   ›Reveal solutionSolution

   Resistance of a semiconductor falls as temperature rises, so its temperature coefficient of resistance is negative.

   As temperature increases, more electron-hole pairs are thermally generated in a semiconductor, increasing the number of charge carriers and hence decreasing its resistance. Since resistance dec …

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10. CBSE 2023Set B1 mark
    Q.Write True or False: In an intrinsic semiconductor the number of free electron is equal to the number of holes.

    ›Reveal solutionSolution

    In an intrinsic (undoped) semiconductor, electrons and holes are created in pairs by thermal excitation, so their numbers are always equal.

    …

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11. CBSE 2023Set ANNUAL1 markMCQ
    Q.In intrinsic semi. conductor at room temperature, the numbers of electrons and holes are:

    (a) Equal

    (b) Zero

    (c) Unequal

    (d) Infinite

    ›Reveal solutionSolution

    In a pure (intrinsic) semiconductor, every electron that jumps to the conduction band leaves behind exactly one hole, so $n_e = n_h$.

    An intrinsic semiconductor has no added impurities. At room temperature, thermal energy breaks a small number of covalent bonds, and each broken bond releases one free electron into the conduction band while creating one hole in the valence b …

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12. CBSE 2023Set ANNUAL1 markMCQ
    Q.When a semiconductor is heated,

    (a) number of electrons increases while that of holes decreases

    (b) number of holes increases while that of electrons decreases

    (c) number of electrons and holes remains same

    (d) number of electrons and holes increases equally.

    ›Reveal solutionSolution

    Heating a semiconductor breaks more covalent bonds, generating electron-hole PAIRS, so electron and hole concentrations rise equally.

    In an intrinsic (pure) semiconductor, conduction electrons and holes are created by the thermal breaking of covalent bonds: when a valence electron gains enough thermal energy to jump into the conduction band, it leaves behind a hole in the valence band. Every such event creates exactly one free electron AND one hole simultaneously — they are generated in pairs.

    …

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