Skip to main content
GIOPHYSICS
Menu
← University Quantum Mechanics I

University Quantum Mechanics I · Introduction to the Hydrogen Atom · 15.05

Hydrogen energy levels and the principal quantum number n

Eₙ = minus 13.6 eV over n-squared with a-nought = 0.0529 nm and l at most n minus one, giving the 13.6 eV ionisation energy and a continuum above it.

Course-map guide · not a complete lesson or simulation

Scope & orientation

What this subsection covers

Eₙ = minus 13.6 eV over n-squared with a-nought = 0.0529 nm and l at most n minus one, giving the 13.6 eV ionisation energy and a continuum above it.

A strong response uses effective-potential curves for each l and states where the model stops being reliable.

Reasoning checklist

Evidence, assumptions and limits

01

Assumptions to state

State the system, observable, approximation, and conditions held fixed before using a model.

02

Evidence to collect

Do measured Balmer wavelengths fit one over lambda equal to R times one-quarter minus one over n-squared for n of three and above, and does the fitted R match the value implied by 13.6 eV?

Read the complete note

Do measured Balmer wavelengths fit one over lambda equal to R times one-quarter minus one over n-squared for n of three and above, and does the fitted R match the value implied by 13.6 eV? Useful evidence includes calibrated wavelengths for at least four Balmer lines from a hydrogen lamp, a fitted Rydberg constant with residuals, propagated angular uncertainty, and the grating calibration that bounds the result..

03

Limits to state

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.

Read the complete note

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. It is a first dedicated quantum-mechanics course, distinct from University Physics V, which covers quantum mechanics alongside atomic, nuclear and particle physics in twenty units: this course is narrower, slower, and teaches the linear algebra it needs rather than assuming it. Hydrogen appears here as an introduction, with the full radial derivation belonging to a second course. A midterm examination is assumed around week 8. Follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.

Diagram & examples

Work the claim before choosing an equation

Interactive concept map

Follow the model from claim to evidence.

01 · Physical claimHydrogen energy levels and the principal quantum number n

Eₙ = minus 13.6 eV over n-squared with a-nought = 0.0529 nm and l at most n minus one, giving the 13.6 eV ionisation energy and a continuum above it.

Read the complete note

Eₙ = minus 13.6 eV over n-squared with a-nought = 0.0529 nm and l at most n minus one, giving the 13.6 eV ionisation energy and a continuum above it. Energy depends on n alone in this model; the same quoted solution for a one-electron ion of charge Z scales to minus 13.6 Z-squared eV over n-squared with radii a-nought over Z. The 13.6 eV is the fixed-nucleus, non-relativistic value.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

When should a model used for Hydrogen energy levels and the principal quantum number n be revised?

04 · Evidence & boundaryDecide, then qualify

Do measured Balmer wavelengths fit one over lambda equal to R times one-quarter minus one over n-squared for n of three and above, and does the fitted R match the value implied by 13.6 eV?

Read the complete note

Do measured Balmer wavelengths fit one over lambda equal to R times one-quarter minus one over n-squared for n of three and above, and does the fitted R match the value implied by 13.6 eV? Useful evidence includes calibrated wavelengths for at least four Balmer lines from a hydrogen lamp, a fitted Rydberg constant with residuals, propagated angular uncertainty, and the grating calibration that bounds the result..

Interactive diagram for Hydrogen energy levels and the principal quantum number n: follow the physical claim through its representation, proposed test, evidence, and model boundary.

modelModel, evidence, and boundary turns the stated idea into a representation that can make a prediction.

Example questions

Try the reasoning before revealing the structure.

Diagram check

When should a model used for Hydrogen energy levels and the principal quantum number n be revised?

Quick check

Test the reasoning, not recall

When should a model used for Hydrogen energy levels and the principal quantum number n be revised?

Choose an answer to test the model.