This chapter builds the quantitative core of atomic physics — Bohr's model, energy levels of hydrogenic systems, Rydberg relations and reduced‑mass corrections — which are repeatedly tested in CBSE board papers and form a basis for many JEE/NEET conceptual and calculation problems. Mastery here connects classical reasoning (orbital motion, momentum) with quantum ideas (quantization conditions, correspondence principle), so questions often combine algebraic manipulation with conceptual insight.
Competitive exams favour problems that mix numerical calculation, asymptotic reasoning and interpretation of spectral/data plots; hence focused practice on deriving relations, handling reduced‑mass and Z‑scaling, and translating graphs to formulas is essential to score well and to tackle multi‑step reasoning under time pressure.
15
Minutes
10
Questions
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Marking Scheme
Q1. (For the hydrogen‑like ion He () an electron makes a transition from to . Using the Rydberg formula
and , calculate the wavelength of the emitted photon.)
Q2. (A: For hydrogen the frequency of the photon emitted in the transition approaches the classical orbital frequency of the electron in the th orbit as .
R: Using one finds for large that , so , which tends to the classical orbital frequency according to the correspondence principle.)
Q3. (Using Bohr model with and the fact that kinetic energy in a Bohr orbit is , compute the kinetic energy (in eV) of the electron in the orbit of Li ().)
Q4. (An experimental plot of measured energy levels (in eV) of a single‑electron atom versus is a straight line through the origin with slope . Assuming Bohr's relation , determine the nuclear charge of this atom.)
Q5. (Using Bohr model the speed of the electron in the ground state () of hydrogen is , where is the fine‑structure constant. Take . Calculate .)
Q6. (Approximate nuclear masses by (protium) and (deuterium). With reduced mass the Rydberg constant scales as and hence for a given transition. Calculate the ratio for corresponding Lyman lines (give numerical value to four significant digits).)
Q7. (An experiment measures frequencies for transitions in hydrogen for large and finds that a plot of vs has slope approximately . Which of the following theoretical explanations accounts for this scaling?)
Q8. (A single‑electron ion produces a spectral line at corresponding to the transition . Using and the Rydberg relation , determine the atomic number of the ion.)
Q9. (A: The orbital magnetic moment of the electron in the th Bohr orbit is , where is the Bohr magneton.
R: Using and one obtains .)
Q10. (When a hydrogen atom emits the Lyman‑ photon () of energy , the proton recoils. Using and , estimate the recoil speed of the proton (use photon momentum and ).)