AP Chemistry 3.6: Spectroscopy and Beer–Lambert Law

• Electrons occupy specific, quantized energy levels .

  • "Quantized" means electrons cannot possess every possible energy value. Only certain allowed energies exist.

  • A useful analogy is a staircase: you can stand on one step or another, but not at every possible height between steps.

• An electron can absorb electromagnetic radiation and move from a lower-energy state to a higher-energy state.

  • This is an electronic excitation .

• For the transition to occur, the absorbed photon's energy must match the energy gap between allowed states:

  • ΔE = hν

Because:

• c = λν

  • we can also relate transition energy to wavelength:

  • ΔE = hc/λ

• A larger energy gap requires:

  • greater frequency,

  • shorter wavelength.

• A smaller energy gap corresponds to:

  • lower frequency,

  • longer wavelength.

• An excited electron can later return to a lower-energy state.

  • During this process, energy may be released as electromagnetic radiation.

  • The emitted photon's energy equals the difference between the two energy levels:

  • Ephoton = ΔE

• This explains why atoms can produce discrete line spectra rather than every possible wavelength.

  • Only particular transitions are allowed because the electron energies themselves are quantized.

  • Different elements have different energy-level structures, so their spectra can serve as identifying fingerprints .

  • Khan Academy's current electronic-transition section includes energy calculations and a worked example involving the maximum wavelength capable of causing ionization .

• Ionization occurs when enough energy is supplied to remove an electron entirely from an atom or species.

  • If a minimum energy is required to ionize a particle, the longest wavelength that can still cause ionization corresponds to exactly that threshold energy.

Use:

• E = hc/λ

  • Rearrange:

  • λ = hc/E

  • A photon with shorter wavelength than the threshold has greater energy and can also cause ionization, assuming the interaction occurs appropriately.

  • A photon with a longer wavelength has less energy and would not have sufficient energy.

  • This question often tests whether you understand the inverse relationship between energy and wavelength.

• Do not say that an electron can absorb "part" of a photon and make up the rest. In the simple model, photon energy must correspond to an allowed transition.

• Spectrophotometry measures how much electromagnetic radiation a sample absorbs or transmits at selected wavelengths.

  • A beam of light with initial intensity passes through a sample.

  • Some radiation may be absorbed by the species in solution.

  • The remaining radiation reaches a detector.

• Absorbance , A, measures how strongly the sample absorbs the selected radiation.

• The Beer–Lambert law is:

  • A = εbc

  • where:

  • A = absorbance,

  • ε = molar absorptivity,

  • b = path length through the sample,

  • c = concentration of the absorbing species.

• Absorbance is dimensionless in the usual presentation.

• Molar absorptivity depends on the identity of the absorbing species and wavelength being used.

• Path length is often determined by the cuvette width.

• If ε and b are constant:

  • A ∝ c

Therefore:

• higher concentration → higher absorbance

  • If concentration doubles under ideal Beer–Lambert behavior, absorbance also doubles.

• Similarly, with concentration and ε constant:

  • greater path length → greater absorbance

  • Khan Academy's Unit 3 includes spectrophotometry, the Beer–Lambert law, and concentration calculations.

• A calibration curve is often used experimentally.

  • Several solutions with known concentrations are prepared.

  • Their absorbances are measured at the same wavelength.

  • A graph is constructed with:

  • x-axis = concentration

  • y-axis = absorbance

  • Under conditions where Beer–Lambert behavior is valid, the data should be approximately linear.

  • The line can be represented:

  • A = mc + b

  • Ideally, the intercept may be close to zero after proper blanking, but real experimental data can contain a nonzero intercept.

• An unknown solution's absorbance can then be measured and its concentration determined from the calibration line.

Example:

• Calibration relationship:

  • A = 2.50c

  • Unknown absorbance:

  • A = 0.750

  • 0.750 = 2.50c

  • c = 0.300 M

• If an unknown solution is too concentrated for the calibration range, it may be diluted .

  • Determine the diluted sample concentration using the calibration curve.

  • Then use:

  • M₁V₁ = M₂V₂

  • to calculate the original concentration.

  • This connects Beer–Lambert law directly to the earlier solutions/dilution topic.

• Transmittance describes the fraction of incoming radiation that passes through a sample.

  • Greater absorbance means lower transmittance.

• A spectrophotometric experiment usually selects a wavelength strongly absorbed by the analyte so changes in concentration produce measurable changes in absorbance.

• Common AP mistakes include reversing axes on a calibration curve, assuming absorbance decreases with concentration, forgetting dilution, or extrapolating far outside the reliable calibration range.

• These are the ideas I would make sure a student can remember without looking at the notes before taking a Unit 3 test.

Unit 3 Questions Students Should Be Able to Answer

• By the end of this unit, a student should be able to look at two molecules and explain which has a higher boiling point using their actual intermolecular attractions , not merely guess based on molar mass. They should recognize London dispersion, dipole-dipole, hydrogen bonding, and ion-dipole attractions; explain vapor pressure and boiling; identify ionic, metallic, molecular, and network solids; interpret particle diagrams; solve PV=nRT and partial-pressure problems; explain gas behavior using KMT; predict when real gases deviate from ideal behavior; calculate molarity and dilution; interpret solution particle diagrams; explain distillation and chromatography; reason about solubility from particle interactions; connect wavelength, frequency, and energy; explain quantized electronic transitions; and calculate concentration using Beer–Lambert law.