Chemistry IA · Structure 1 · Models of the particulate nature of matter · topic 2 of 25

Hydrogen's spectrum: pulling out the Rydberg constant · IB Chemistry IA idea: guide, sample graph and step-by-step plan

a clean model, so clean analysis is the test

Hydrogen's colours aren't decoration, they're data. Turn a handful of wavelengths into the energy it takes to pull an electron off an atom.

Difficulty●●○ Medium
KitComputer only: NIST Atomic Spectra Database, spreadsheet
TimeAbout 10 hours
FitsSL and HL (Rydberg formula: introduce it yourself)
  • ✓ you like clean physics-style chemistry
  • ✓ you enjoy fitting a straight line
  • ✓ you would rather skip the wet lab

The big idea

← this is your RQ hook!

Excited hydrogen atoms drop from a higher level n down to level 2 and emit light of a fixed wavelength. The lines crowd together as n rises, and they converge. Plot 1/λ against 1/n² and a model with one constant predicts a straight line: its gradient gives the Rydberg constant and its intercept gives the series limit. The physics is clean, so the marks come from how you handle a few data points: uncertainty, quality of fit, and what the numbers mean for the energy of the electron.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Add the Lyman series

Use the ultraviolet lines that end on n = 1.

→ Same idea with a different lower level; the series limit now relates to the ionisation energy of hydrogen. Vacuum wavelengths become essential.
Try a hydrogen-like ion

Use lines of He⁺ from the database.

→ Tests how the constant scales with nuclear charge. Harder: you must pick clean lines that belong to the same series.
Compare two ways to fit

Fit a straight line to the linearised data, and also fit the constant directly.

→ The evaluation compares fitting methods and the uncertainty each gives.
Study the residuals

Plot the difference between each measured 1/λ and the fitted line against n.

→ Shows whether the misfit is random or systematic (for example an air and vacuum mix).
Go to energy

Convert your series limit into kJ mol⁻¹.

→ Links spectra to ionisation energy; moles and unit conversions become part of the analysis.
Give it a purpose

Frame it around how astronomers identify hydrogen in stars.

→ A real context for the introduction. The data and analysis stay the same.

Your Chemistry IA research question: run the check

Write your own question first. Then make sure it ticks every box:

  • Names the lines used (which values of n, how many) and the database table, with air or vacuum wavelengths stated.
  • Says what you will plot and which quantity you will extract, with its units.
  • Says what you compare your fitted constant with, and where that value comes from.
  • Deals with having only a handful of lines: how will you judge the quality of the fit?
  • Is narrow enough: one series, one source, one fitting method.

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The set-up

No apparatus here: the 'set-up' is where the data come from and what you do with them. Sketch yours with the lines you actually choose.

76543400500600700wavelength / nm1/λ = R ( 1/2² − 1/n² )series limit: n → ∞upper level nn = 3, the red lineair or vacuum wavelengths?pick one, say which

How your Chemistry IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; why spectra matter for models of the atom; what you predict about the linearised graph.
Background chemistry~450
Energy levels, emission and convergence; where the formula comes from (cite it); what the gradient and intercept should mean; the link to ionisation energy.
Data source and selection~300
The database, the query you ran, which lines you took and why, observed or calculated wavelengths, and air or vacuum. Include the stated uncertainty.
Variablestable
Independent, dependent and controlled variables, each with how it is chosen or held constant.
Safety, ethics, environment~60
No lab hazards, so say so. Data ethics: cite the database and date, record the exact query, and say why you dropped any line.
Raw datatable
One clear table: n, wavelength with units and stated uncertainty, and the wavelength type (air or vacuum).
Processing~300
Wavelength to 1/λ in consistent units, uncertainty carried across, and one worked example.
Graphs and analysis~400
The linearised graph with error bars, the line of best fit and how you got its gradient and intercept with uncertainties; residuals.
Conclusion~400
Answer with numbers: your constant and series limit with uncertainties, compared with an accepted value (cite it, and say which one it is), and what the limit means for the energy of an electron.
Evaluation~600, the biggest part!
Quality and number of data points, air or vacuum issues, fit method, model limits; weaknesses ranked, with improvements linked.
Referencesnot counted
Every source for data, formula and accepted values.

What your Chemistry IA graph could look like

error bars on EVERY point ✓

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only

0.000.020.040.060.080.100.121.41.61.82.02.22.42.62.83.03.21/n² (n is exact, so no horizontal error bars)1/λ / µm⁻¹ (± 0.002)straight-line model 1/λ = R(1/2² − 1/n²)measured lines, with error barswhere the line meets x = 0is the series limitILLUSTRATIVE · MADE-UP DATA
  • Say what the gradient and intercept mean before you fit, not after.
  • Error bars on every point. Wavelengths have a stated uncertainty, so the bars may be tiny. Say so.
  • With five points, R² alone tells you little. Residuals tell you more.
  • The intercept is not forced to zero: it carries the series limit.
  • Another graph to consider: residuals of 1/λ against n. A pattern means something systematic is going on.

Your game plan

decide air or vacuum on day one

Tick steps off as you go. We'll remember on this device.

0 of 11 done

  1. Read and predictFind the formula for the Balmer lines and its source. Write down the graph you expect, and what the gradient and intercept should represent, before you open the database.
  2. Trial run (1 lesson)Query the database for hydrogen. Which columns are there? Observed or calculated wavelengths? Air or vacuum? Pick two lines and turn them into 1/λ in m⁻¹ by hand.
  3. Decide lines and conventionsChoose which values of n you will use, and why. Decide whether to use observed or calculated wavelengths, and air or vacuum. Use one type throughout.
  4. CollectRecord each wavelength with its uncertainty, the query, the date and the table version. Keep your raw sheet untouched.
  5. ProcessConvert to 1/λ with units you can justify. Decide how to carry the wavelength uncertainty into 1/λ.
  6. Graph and fitPlot with error bars. Fit a straight line, and decide how to get uncertainties on the gradient and intercept (max and min lines, or software statistics).
  7. Compare and interpretCompare your constant with an accepted value, and say which value and under what conditions. Then say what your intercept means in energy terms.
  8. Check the fitLook at residuals. Are the misfits random, or do they all lean one way? What could cause a lean?
  9. EvaluateRank the weaknesses: few lines, wavelength type, the model's limits. Make every improvement specific.
  10. Write, then cutWrite in the order of the layout above. Tables, calculations and graphs are not counted.
  11. Check before your teacher's draftRun the checklist, then get your RQ or draft checked. Your teacher reads one draft only.

Chemistry you'll need

Traps to avoid in this Chemistry IA

  • Mixing air and vacuum wavelengths. The database gives air values above about 200 nm and vacuum values below, so a silent shift creeps in.
  • Only three or four lines, then quoting a very precise constant. The fit has little statistical weight.
  • Using nanometres in 1/λ when the constant is quoted in inverse metres: units that do not match the accepted value.
  • Treating a rounded database value as exact. The table shows how many figures it has.
  • Comparing with the infinite-mass Rydberg constant without noting that hydrogen's own value differs slightly, because of the nuclear mass.
  • Forcing the fitted line through the origin with no physical reason. The intercept is your series limit.
  • Calling the Balmer series limit the ionisation energy of hydrogen. It is the energy to remove an electron from n = 2.

More Chemistry IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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