A test on quantum Physics at the level of Plus-2 was given to a set of selected 40 Physics PGTs from Kendriya Vidyalaya Sangsthan. The test was to explore the kinds of misconception and lack of concepts prevailing among the Plus-2 teachers. It revealed that the topics based on quantum Physics are quite difficult for even the teachers from a very good organization such as KVS.

I. Introduction

The teaching at Plus-2 level is very important as it can create a deep interest for the subject or it can create a hatred for the subject. This has long lived effect on the career of the student. Thus it is important to identify the kinds of misconceptions prevailing among the teachers and then to develop modules to rectify those. National Anveshika Network of India (NANI) has undertaken a task to work on Physics PGTs of Kendriya Vidalayas (KV) and to do various exercises to improve upon the Physics teaching in KVS.

As a part of this project, NANI gave 10 workshops in the previous year, each of 3-days duration and selected the best 10% on the basis of their involvement, seriousness to learn and their current concept base. These selected 33 teachers were given a 10-days workshop at IIT Kanpur where a wide variety of sessions were given to them. In this sequence, a series of 7 tests were given on different areas of their Plus-2 syllabus. The answers were then analyzed to identify the misconceptions and these were thoroughly discussed in separate sessions.

In this article we give our analysis of one of these tests given on chapters based on quantum physics such as Photo-electric effect, Bohr’s model of hydrogen atom, Basic Nuclear Physics and Semiconductors. Questions and the analysis of their responses follows now.

2. Questions and Analysis

Q-1 : The electric field in a metal is zero in electrostatics. But in Rutherford gold foil experiment, alpha particles get deflected from the gold foil showing presence of electric field there. This is because,

  • (a) Gold is not a metal but is a semi metal

  • (b) When alpha particle moves in gold, this is not an electrostatic situation.

  • (c) The moving alpha particle creates a magnetic field which shifts the electron clouds to create the electric field.

  • (d) The electric field inside a metal is zero only in an average sense.

  • (e) The alpha particles are deflected from the surface of the gold foil and electric field may exist at the surface of a metal.


9 teachers wrote the right answer that E-field is zero in a metal only in an average sense, option (d). 19 teachers wrote (c) as the correct answer. It seems that in absence of any other plausible answer, they chose this option. Besides, 2 teachers wrote option (d) together with option (c).

It shows that about two third of the teachers have forgotten that particle is strongly deflected because of strong Coulomb repulsion. In other words, they only remember that particles are deflected strongly by the gold foil but could not connect why Rutherford concluded the nuclear model from this experiment. Also it shows that they deeply commit itself to the end statements such as there is no electric field inside a metal without thinking the origin of the statement.

Q-2 : A helium nucleus is stable because the nuclear attractive force dominates over Coulomb repulsion. Why 4 neutrons do not make a stable nucleus where there should be a strong nuclear attractive force but no Coulomb repulsion.


The teachers give a verity of answers but no one attributed it to Pauli exclusion Principle and neutrons being forced to occupy higher energy states.

This question was bit new to the teachers as they do not use the energy states of nucleons in a nucleus. However they very well know that for nuclear stability N/Z ratio has a range close to 1-1.4 and in case of 4 neutrons making up a nucleus that condition is not satisfied. Surprisingly only four out of 33 could use this argument to justify why this nucleus is not formed. 4 teachers talked of Yukawa theory having exchange of mesons converting neutrons to protons and vice versa, excluding the probability of a nucleus with neutrons only.

Some interesting answers bring in atoms into picture. It seems they have confusion that nucleus can only exist as a part of an atom and protons are necessary to hold the electrons in an atom. Hence any nucleus must have some protons so that an atom can exist at whose center this nucleus can sit.

Q-3 : A gamma decay is most often preceded by either alpha decay or beta decay. This is because

  • (a) gamma rays are produced by alpha or beta particles.

  • (b) a gamma decay alone does not conserve momentum conservation

  • (c) in alpha or beta decay, the daughter nucleus is prepared in an excited state

  • (d) in nuclear reactions, the energy released is so large that gamma ray alone cannot take up this energy.


This turned out to be the most straightforward question and 32 out of 33 have written the right answer (option c). Perhaps they have this statement explicitly stated in the textbooks and so no thinking was required.

Q-4 : A voltage is applied to a hydrogen discharge tube just enough to produce a faint orange light. Together with this,

  • (a) lots of ultraviolet radiation must be coming.

  • (b) lots of infrared radiation must be coming

  • (c) lots of visible light of different wavelengths must be coming.


This question was meant to test the ability to reason out from a known concept. They all know that visible light comes out (Balmer Series) when the electron makes a transition from n = 3 to n = 2 . First expectation was to realize that just faint orange line would mean the electrons are excited to a maximum of n = 3 level and not beyond. In that case only transitions possible are n = 3 → 1, n = 3 → 2,and n = 2 → 1.

Only one teacher could reason this out and wrote that lots of UV radiation will be emitted. Another teacher wrote this but also added that lots of infrared radiation will come out. 4 of them wrote that lots of visible light of different wavelengths will come together with the orange. But the vast majority (27 out of 33) have gone with option (c) saying that lots of infrared radiation must be coming together with this faint orange line. I would guess that they have connected low energy of infrared radiation to the minimum voltage supplied to emit visible light.

Q-5 : In Bohr’s model, the angular momentum of the electron in hydrogen atom for n = 1 orbit is Planck’s constant / (2π). But this electron is also called 1s electron having orbital angular momentum quantum number l = 0. Which of the two is more realistic?


As they teach Bohr’s model and extensively use l = nh / 2π, it was expected that they might go for l = h / 2π as the more realistic one. And it was like that. 22 out of 33 went with l = h / 2π and 8 preferred l = 0 in n = 0 state. Two teachers did not attempt and one said that both are realistic.

The response shows that most of the teachers see things in isolation. They know Bohr’s theory and they also know about quantum numbers n, l, ml, ms . They know that lis orbital angular quantum number and for ground state n = 1, l = 0. But they never thought there is some anomaly as they are talking of the same system.

Q-6 : A photo cell is exposed to light of frequency n1 in one experiment and of a higher frequency n2 in another experiment. The intensity of light is kept same in the two cases.

  • (a) In which case, the number of photons falling on the cathode is more? Or is it same in the two cases?

  • (b) Sketch the photocurrent I vs anode voltage V for the two cases.


This question once again shows that the teachers take things in isolation. Each one of the 33 teachers writes that the number of photons falling on the cathode will be the same. They very well know that

  • (i) Energy of a photon is E = h v

  • (ii) Intensity is energy falling per unit area (in proper orientation) per unit time..

But they could not connect the two, they have in mind that intensity is proportional to the number of photons and have used this for different frequencies too. This once again brings out that they cram a statement without caring for its origin.

During the discussion of cut off voltage they do use that higher the frequency, more is the energy of the photon. But still they argue that I ∝ n.

Part (b) is the climax of this. On the left side of the axis, they use E ∝ V and on the right side of the same graph, they forget to use E ∝ V.

No fault of teachers. They believe NCERT book from the core of their heart. And NCERT book for Class-12 has the same error from eternity.

Q-7 : A p-n junction is schematically shown in the figure. The depletion region extends for a width x1 on the p-side and for a width x2 on the n-side.

Sketch the graph of the following as a function of x.

  • (i) nh (number of holes per unit volume),   (ii) charge density ρ   (iii) electric field E, and   (iv) potential (taking V = 0 at x = 0).


None of the teachers could plot all 4 parts correctly. Few of them (7 out of 33) have understood variation of the hole density correctly but charge density and E-field was difficult task for them. Potential variation is also correctly displayed by few of them (11 out of 33). Most problem was in electric field where only 2 or 3 teachers plotted reasonably good variations.

3. Conclusion

Kendriya Vidyalay PGTs on the average are best among various groups as the process of recruitment is very rigorous. The present target group was even more elite as they were the top 10% of the total PGTs. The present analysis shows that even the best of the Plus-2 teachers need lot of mentoring to inculcate the qualities of being a good learner. Some of these qualities which are lacking may be listed as follows.

  • (a) Understanding the concepts deeply and applying them appropriately in a given situation.

  • (b) While using a theorem or a statement, remembering the conditions in which it was derived.

  • (c)Logically derive further results from the known results in a given situation.

  • (d) Not learning concepts in isolation. Ability to connect seemingly different situations which is governed by the same phenomena.

The list may be much longer.

It will be absolute injustice with the teachers, if I do not appreciate their sincerity and eagerness to learn. I can easily rank this group of teachers as one the best batches I have addressed in hundreds of the workshops that I have conducted. From early morning to late evening and perhaps till late night also, they were trying to learn as much as possible. The level of discussion was also very good. Each one of them worked with high level of interest in the lab sessions and enjoyed seeing Physics in action. It is our system that must rethink on their strategies to nurture such a nice group of teachers so that their potential is fully utilized in shaping our young students into vibrant scientists.

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