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NCERT Solutions · Class 12 Physics Semiconductor Electronics: Materials, Devices and Simple Circuits

6 exercises · 6 still being checked

Exercises 14.1–14.6

  1. Exercise 14.1

    In an n-type silicon, which of the following statement is true:
    (a)
    Electrons are majority carriers and trivalent atoms are the dopants.
    (b)
    Electrons are minority carriers and pentavalent atoms are the dopants.
    (c)
    Holes are minority carriers and pentavalent atoms are the dopants.
    (d)
    Holes are majority carriers and trivalent atoms are the dopants.

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    NCERT’s answer
    (c)
    In n-type silicon, tetravalent Si is doped with a pentavalent impurity (e.g., As, P, Sb). Each pentavalent dopant atom contributes one extra electron (beyond the four used in covalent bonding) that is loosely bound and easily goes into the conduction band, so electrons become the majority carriers and holes (from thermally broken bonds) are the minority carriers; the dopant atoms themselves are pentavalent.Correct statement: (c) Holes are minority carriers and pentavalent atoms are the dopants.

  2. Exercise 14.2

    Which of the statements given in Exercise $\displaystyle 14.1$ is true for p-type semiconductos.

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    NCERT’s answer
    (d)
    For p-type silicon, Si is doped with a trivalent impurity (e.g., B, Al, In). Each trivalent atom has one fewer valence electron than Si, creating a vacancy (hole) in the bonding structure. These holes vastly outnumber the thermally generated electrons, so holes are the majority carriers and electrons are the minority carriers, with trivalent atoms as dopants.Checking option (d) of $\displaystyle 14.1$'s list: "Holes are majority carriers and trivalent atoms are the dopants" — matches exactly.Correct statement: (d) Holes are majority carriers and trivalent atoms are the dopants.

  3. Exercise 14.3

    Carbon, silicon and germanium have four valence electrons each. These are characterised by valence and conduction bands separated by energy band gap respectively equal to (\(\displaystyle E_{g}\))C, (\(\displaystyle E_{g}\))Si and (\(\displaystyle E_{g}\))Ge. Which of the following statements is true?
    (a)
    (\(\displaystyle E_{g}\))Si < (\(\displaystyle E_{g}\))Ge < (\(\displaystyle E_{g}\))C
    (b)
    (\(\displaystyle E_{g}\))C < (\(\displaystyle E_{g}\))Ge > (\(\displaystyle E_{g}\))Si
    (c)
    (\(\displaystyle E_{g}\))C > (\(\displaystyle E_{g}\))Si > (\(\displaystyle E_{g}\))Ge
    (d)
    (\(\displaystyle E_{g}\))C = (\(\displaystyle E_{g}\))Si = (\(\displaystyle E_{g}\))Ge

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    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    NCERT’s answer
    (c)
    NCERT_Solution_Class12_Physics_Ch14_Q14-3The energy band gap \(\displaystyle E_g\) is the energy separation between the top of the valence band and the bottom of the conduction band. Among the Group-$\displaystyle 14$ elements, the band gap decreases as the atomic size increases (larger atoms hold their valence electrons less tightly, and the overlap/splitting of energy levels into bands is different), going down the column from carbon to silicon to germanium:\[(E_g)_C \approx 5.4\text{-}5.5\ \mathrm{eV}, \quad (E_g)_{Si} \approx 1.1\ \mathrm{eV}, \quad (E_g)_{Ge} \approx 0.66\ \mathrm{eV} \]So \(\displaystyle (E_g)_C > (E_g)_{Si} > (E_g)_{Ge}\). This is why diamond (carbon) is an insulator, silicon and germanium are semiconductors, with germanium being the more conductive of the two at room temperature.Correct statement: (c) \(\displaystyle (E_g)_C > (E_g)_{Si} > (E_g)_{Ge}\).

  4. Exercise 14.4

    In an unbiased p-n junction, holes diffuse from the p-region to n-region because
    (a)
    free electrons in the n-region attract them.
    (b)
    they move across the junction by the potential difference.
    (c)
    hole concentration in p-region is more as compared to n-region.
    (d)
    All the above.

    Not cross-checked

    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    NCERT’s answer
    (c)
    NCERT_Solution_Class12_Physics_Ch14_Q14-4Diffusion is the physical process by which particles move from a region of higher concentration to a region of lower concentration, driven purely by the concentration gradient — it does not require any attractive force or applied potential difference.In an unbiased p-n junction, before any depletion region/barrier field has formed by the diffusion itself, the p-region has a much higher concentration of holes than the n-region (and vice versa for electrons). This concentration gradient is what drives holes to diffuse from p to n (and electrons from n to p). The resulting exposed charges (immobile ions) build up the potential barrier at the junction, and it is this barrier field that subsequently opposes further diffusion (giving a small drift current), not something that causes it. So options (a) and (b) describe effects of the junction field, not the cause of hole diffusion, and (d) is therefore not correct either.Correct statement: (c) hole concentration in p-region is more as compared to n-region.

  5. Exercise 14.5

    When a forward bias is applied to a p-n junction, it
    (a)
    raises the potential barrier.
    (b)
    reduces the majority carrier current to zero.
    (c)
    lowers the potential barrier.
    (d)
    None of the above.

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    NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.

    NCERT’s answer
    (c)
    NCERT_Solution_Class12_Physics_Ch14_Q14-5In forward bias, the p-region is connected to the positive terminal and the n-region to the negative terminal of the external battery. The applied electric field is directed opposite to the built-in field of the depletion region, so it partially cancels the internal field.This narrows the depletion region and lowers the potential barrier at the junction (from its equilibrium value, typically by an amount close to the applied voltage for a significant forward bias). With a lowered barrier, majority carriers (holes from p, electrons from n) can cross the junction much more easily, giving a large forward current that increases rapidly with applied voltage — the opposite of raising the barrier or reducing the majority-carrier current to zero.Correct statement: (c) lowers the potential barrier.

  6. Exercise 14.6

    In half-wave rectification, what is the output frequency if the input frequency is $\displaystyle 50$ Hz. What is the output frequency of a full-wave rectifier for the same input frequency. Notes

    Disagrees with the book

    This working does not reach the answer printed in NCERT. One of the two is wrong and it has not yet been settled which — check it before you rely on it.

    NCERT’s answer
    $\displaystyle 50$ Hz for half-wave, $\displaystyle 100$ Hz for full-wave BIBLIOGRAPHY TEXTBOOKS For additional reading on the topics covered in this book, you may like to consult one or more of the following books. Some of these books however are more advanced and contain many more topics than this book. $\displaystyle 1$ Ordinary Level Physics, A.F. Abbott, Arnold-Heinemann ($\displaystyle 1984$). $\displaystyle 2$ Advanced Level Physics, M. Nelkon and P. Parker, \(\displaystyle 6^{th}\) Edition, Arnold-Heinemann ($\displaystyle 1987$). $\displaystyle 3$ Advanced Physics, Tom Duncan, John Murray ($\displaystyle 2000$). $\displaystyle 4$ Fundamentals of Physics, David Halliday, Robert Resnick and Jearl Walker, \(\displaystyle 7^{th}\) Edition John Wily ($\displaystyle 2004$). $\displaystyle 5$ University Physics (Sears and Zemansky’s), H.D. Young and R.A. Freedman, \(\displaystyle 11^{th}\) Edition, Addison—Wesley ($\displaystyle 2004$). $\displaystyle 6$ Problems in Elementary Physics, B. Bukhovtsa, V. Krivchenkov, G. Myakishev and V. Shalnov, MIR Publishers, ($\displaystyle 1971$). $\displaystyle 7$ Lectures on Physics ($\displaystyle 3$ volumes), R.P. Feynman, Addision - Wesley ($\displaystyle 1965$). $\displaystyle 8$ Berkeley Physics Course ($\displaystyle 5$ volumes) McGraw Hill ($\displaystyle 1965$). a. Vol. $\displaystyle 1$ - Mechanics: (Kittel, Knight and Ruderman) b. Vol. $\displaystyle 2$ - Electricity and Magnetism (E.M. Purcell) c. Vol. $\displaystyle 3$ - Waves and Oscillations (Frank S. Crawford) d. Vol. $\displaystyle 4$ - Quantum Physics (Wichmann) e. Vol. $\displaystyle 5$ - Statistical Physics (F. Reif ) $\displaystyle 9$ Fundamental University Physics, M. Alonso and E. J. Finn, Addison - Wesley ($\displaystyle 1967$). $\displaystyle 10$ College Physics, R.L. Weber, K.V. Manning, M.W. White and G.A. Weygand, Tata McGraw Hill ($\displaystyle 1977$). $\displaystyle 11$ Physics: Foundations and Frontiers, G. Gamow and J.M. Cleveland, Tata McGraw Hill ($\displaystyle 1978$). $\displaystyle 12$ Physics for the Inquiring Mind, E.M. Rogers, Princeton University Press ($\displaystyle 1960$). $\displaystyle 13$ PSSC Physics Course, DC Heath and Co. ($\displaystyle 1965$) Indian Edition, NCERT ($\displaystyle 1967$). $\displaystyle 14$ Physics Advanced Level, Jim Breithampt, Stanley Thornes Publishers ($\displaystyle 2000$). $\displaystyle 15$ Physics, Patrick Fullick, Heinemann ($\displaystyle 2000$). $\displaystyle 16$ Conceptual Physics, Paul G. Hewitt, Addision—Wesley ($\displaystyle 1998$). $\displaystyle 17$ College Physics, Raymond A. Serway and Jerry S. Faughn, Harcourt Brace and Co. ($\displaystyle 1999$). $\displaystyle 18$ University Physics, Harris Benson, John Wiley ($\displaystyle 1996$). $\displaystyle 19$ University Physics, William P. Crummet and Arthur B. Western, Wm.C. Brown ($\displaystyle 1994$). $\displaystyle 20$ General Physics, Morton M. Sternheim and Joseph W. Kane, John Wiley ($\displaystyle 1988$). $\displaystyle 21$ Physics, Hans C. Ohanian, W.W. Norton ($\displaystyle 1989$). Bibligraphy $\displaystyle 22$ Advanced Physics, Keith Gibbs, Cambridge University Press ($\displaystyle 1996$). $\displaystyle 23$ Understanding Basic Mechanics, F. Reif, John Wiley ($\displaystyle 1995$). $\displaystyle 24$ College Physics, Jerry D. Wilson and Anthony J. Buffa, Prentice Hall ($\displaystyle 1997$). $\displaystyle 25$ Senior Physics, Part - I, I.K. Kikoin and A.K. Kikoin, MIR Publishers ($\displaystyle 1987$). $\displaystyle 26$ Senior Physics, Part - II, B. Bekhovtsev, MIR Publishers ($\displaystyle 1988$). $\displaystyle 27$ Understanding Physics, K. Cummings, Patrick J. Cooney, Priscilla W. Laws and Edward F. Redish, John Wiley ($\displaystyle 2005$). $\displaystyle 28$ Essentials of Physics, John D. Cutnell and Kenneth W. Johnson, John Wiley ($\displaystyle 2005$). GENERAL BOOKS For instructive and entertaining general reading on science, you may like to read some of the following books. Remember however, that many of these books are written at a level far beyond the level of the present book. $\displaystyle 1$ Mr. Tompkins in paperback, G. Gamow, Cambridge University Press ($\displaystyle 1967$). $\displaystyle 2$ The Universe and Dr. Einstein, C. Barnett, Time Inc. New York ($\displaystyle 1962$). $\displaystyle 3$ Thirty years that Shook Physics, G. Gamow, Double Day, New York ($\displaystyle 1966$). $\displaystyle 4$ Surely You’re Joking, Mr. Feynman, R.P. Feynman, Bantam books ($\displaystyle 1986$). $\displaystyle 5$ One, Two, Three… Infinity, G. Gamow, Viking Inc. ($\displaystyle 1961$). $\displaystyle 6$ The Meaning of Relativity, A. Einstein, (Indian Edition) Oxford and IBH Pub. Co. ($\displaystyle 1965$). $\displaystyle 7$ Atomic Theory and the Description of Nature, Niels Bohr, Cambridge ($\displaystyle 1934$). $\displaystyle 8$ The Physical Principles of Quantum Theory, W. Heisenberg, University of Chicago Press ($\displaystyle 1930$). $\displaystyle 9$ The Physics—Astronomy Frontier, F. Hoyle and J.V. Narlikar, W.H. Freeman ($\displaystyle 1980$). $\displaystyle 10$ The Flying Circus of Physics with Answer, J. Walker, John Wiley and Sons ($\displaystyle 1977$). $\displaystyle 11$ Physics for Everyone (series), L.D. Landau and A.I. Kitaigorodski, MIR Publisher ($\displaystyle 1978$). Book $\displaystyle 1$: Physical Bodies Book $\displaystyle 2$: Molecules Book $\displaystyle 3$: Electrons Book $\displaystyle 4$: Photons and Nuclei. $\displaystyle 12$ Physics can be Fun, Y. Perelman, MIR Publishers ($\displaystyle 1986$). $\displaystyle 13$ Power of Ten, Philip Morrison and Eames, W.H. Freeman ($\displaystyle 1985$). $\displaystyle 14$ Physics in your Kitchen Lab., I.K. Kikoin, MIR Publishers ($\displaystyle 1985$). $\displaystyle 15$ How Things Work: The Physics of Everyday Life, Louis A. Bloomfield, John Wiley ($\displaystyle 2005$). $\displaystyle 16$ Physics Matters: An Introduction to Conceptual Physics, James Trefil and Robert M. Hazen, John Wiley ($\displaystyle 2004$). Physics $\displaystyle 354$
    NCERT_Solution_Class12_Physics_Ch14_Q14-6Half-wave rectifier: Only one half-cycle (say, positive) of each input AC cycle is passed to the output; the other half is blocked. So the rectifier produces exactly one output pulse for every one input cycle — the repetition rate of the output pulses equals the input frequency.\[f_{\text{half-wave}} = f_{\text{input}} = 50\ \mathrm{Hz} \]Full-wave rectifier: Both halves (positive and negative) of each input cycle are converted to output pulses of the same polarity (using a center-tapped transformer or bridge configuration), so two output pulses are produced for every one input cycle.\[f_{\text{full-wave}} = 2f_{\text{input}} = 2 \times 50\ \mathrm{Hz} \]Half-wave rectifier output frequency = $\displaystyle 50$ Hz; full-wave rectifier output frequency = $\displaystyle 100$ Hz.