The chapter "Atoms" links classical scattering experiments, the Bohr model and spectral observations to quantitative formulas used directly in board and competitive problems. Mastery of this chapter builds facility with the Rydberg formula, reduced-mass corrections, scaling with nuclear charge , and energy-level algebra — all frequent sources of multi-step JEE/NEET/CBSE numerical and reasoning questions.
Beyond calculations, the chapter trains a student to interpret graphs and experimental data (e.g. slopes of vs plots), to spot common misconceptions (role of reduced mass, virial relations, origin of quantisation), and to answer assertion–reason type questions that probe conceptual depth required in board exams.
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Minutes
10
Questions
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Marking Scheme
Q1. The Balmer- line () for hydrogen and for deuterium differ slightly because the Rydberg constant depends on the reduced mass. Using and , estimate the fractional change . (Assume the Rydberg constant scales linearly with the reduced mass.)
Q2. A hydrogen atom () and a singly ionized helium ion He () both undergo the transition . If the wavelength for hydrogen is , what is the ratio ? (Neglect reduced-mass differences.)
Q3. Assertion (A): The energy levels of a hydrogen atom are independent of the nuclear mass.
Reason (R): Energy levels depend on the reduced mass of the electron–nucleus system.
Q4. In an experiment on a hydrogen-like ion, measured photon energies for various electronic transitions were plotted versus and the points lie on a straight line through the origin with slope . Using , the nuclear charge of this ion is
Q5. What is the minimum wavelength (in nm) of a photon required to ionize a He ion when its electron is in the level? Use and .
Q6. Assertion (A): In the Bohr model the allowed orbital angular momenta are given by .
Reason (R): This quantisation arises because the electron's mass increases relativistically with speed, and the relativistic mass increase enforces .
Q7. For the hydrogen atom in the Bohr model , kinetic energy and potential energy satisfy virial relations. Which statement is correct as increases?
Q8. Two hydrogen-like ions A and B have the same reduced mass. The wavelength of the photon emitted in the transition in ion A equals the wavelength emitted in the transition in ion B. The ratio equals
Q9. Assertion (A): The series limit of the Balmer series corresponds to ionisation from the level.
Reason (R): The series limit corresponds to the transition , which yields the maximum photon energy in the Balmer series.
Q10. A plot of energy levels (in eV) versus for an unknown hydrogen-like ion is a straight line with slope . Which of the following correctly identifies the ion and gives the wavelength (in nm) of the photon emitted in the transition ? (Use .)