Preface
Atomic and molecular physics carries a steady eight to twelve marks in CSIR–NET / JRF, and a comparable weight in GATE (PH) and JEST. It is, on the face of it, an easy scoring area: the syllabus is small, the mathematics rarely goes beyond first-order perturbation theory, and the same dozen results are asked over and over. In practice candidates lose marks here more often than they should — not because the physics is hard, but because the standard formulae are memorised without the one or two conditions attached to each of them.
Almost every mark lost in this area can be traced to a handful of slips: using the Landé \(g\) factor when the field is strong enough for Paschen–Back; forgetting that a \(J=0\) level does not split at all; quoting \(\Delta J = \pm 1\) for a rotational Raman spectrum when it is \(\Delta J = \pm 2\); treating CO2 as microwave active because it is linear; writing a dissociation energy in meV when it must be a few eV. This book is built around those failure points. Each is stated explicitly, boxed, and then exercised on a question in which getting it wrong produces one of the printed distractors.
The organisation follows the sequence a candidate actually needs. Chapters 1–5 develop atomic structure, from the Bohr–Sommerfeld model through fine structure, angular-momentum coupling and hyperfine structure, to the Zeeman, Paschen–Back and Stark effects, X-ray spectra and line broadening. Chapters 6–10 cover molecular spectroscopy: a chapter of common fundamentals, then rotational, vibrational and Raman spectroscopy, and finally electronic spectroscopy together with NMR and ESR. Chapter 11 treats laser physics.
Every chapter opens with a statement of what it covers, develops the theory with numbered equations and figures drawn to scale, works graded examples in full, closes with a formula summary that can be revised in ten minutes, and then sets previous-year questions with complete solutions, grouped by paper.
Three principles have governed the writing.
Derive, then compress. A result that has been derived once is remembered; a result that has only been read is not. But an examination is not the place to re-derive anything, so each derivation is followed by the one-line form in which it should actually be used.
State the conditions. Every formula in the summary boxes carries its domain of validity. Most distractors in these papers are the right formula applied outside its range.
Correct the record. Standard coaching material carries a number of errors that propagate from book to book — a sign convention in a Boltzmann ratio, a factor of \(2\pi\) in natural linewidth, a dissociation energy out by three orders of magnitude. Where such an error has been found it has been corrected, and the correction stated openly in a note, so that the reasoning can be checked rather than taken on trust. Where the error lies in an official question paper, that too is said plainly.
I am grateful to the students of Pravegaa Education whose questions, and whose
mistakes, determined what needed to be said and at what length. Corrections and
suggestions for the next edition are welcome at
pravegaaeducation@gmail.com.
Jia Sarai, New Delhi
The recurring elements
Five kinds of box appear throughout, and each means something specific.
What this chapter covers — opens every chapter. Read it first, and again after finishing the chapter as a self-test: if any line is unfamiliar, that section has not landed.
Example — a worked problem, numbered by chapter. Attempt it before reading the solution. The examples are graded, the later ones in each chapter being at or slightly above examination standard.
Note — a condition, a caution, or a correction to a statement commonly made elsewhere.
Exam Tip — the specific form in which a point has actually been asked.
Formula Summary — the end-of-chapter revision sheet. In the last week before the paper, this and the previous-year sections are the book.
A three-pass method
First pass (understanding). Read the theory, and work every example with a pen before looking at its solution. Do not attempt the previous-year questions yet; at this stage they measure only what you have not yet read.
Second pass (technique). Work the previous-year section of each chapter under time — roughly two minutes per multiple-choice question, four for a numerical-answer question. Mark every question you got wrong, and identify which condition you missed. It is almost never the algebra.
Third pass (recall). Formula summaries only, plus the questions marked wrong on the second pass. A chapter's summary should take about ten minutes.
On the previous-year questions
The questions are grouped by paper — GATE, then CSIR–NET / JRF, then JEST — because the three differ in character. GATE rewards speed on a standard calculation. CSIR–NET rewards recognising which limit applies. JEST is the most conceptual of the three and least likely to be a substitution exercise.
Chapters 7–10 share a single combined question bank, printed at the end of Chapter 10, because the papers themselves mix rotational, vibrational, Raman and electronic spectroscopy freely within one question.
Solutions are given in full, not as answer keys. Where the official key appears to be wrong, or where a question admits no correct option among those printed, this is stated in the solution together with the reasoning — it is better to know that a paper contained an error than to conclude that one's own physics is broken.
Notation
SI units are used throughout, except that spectroscopic quantities are given in wavenumbers (\(\mathrm{cm^{-1}}\)), as they are in the literature and in the question papers. The symbol \(\bar\nu\) always denotes a wavenumber and \(\nu\) a frequency; the two are related by \(\bar\nu = \nu/c\), and confusing them is the single most common arithmetic error in this part of the syllabus. A bar over a term value (\(\varepsilon\), \(G\), \(F\)) likewise indicates \(\mathrm{cm^{-1}}\). Primed quantities refer to the upper state and double-primed to the lower, so that a band written \((v',v'')\) always reads upper-to-lower.
Values of the physical constants used are collected in Appendix 12, in the combinations that save the most time.