AP Chemistry 1.6: Photoelectron spectroscopy

PES is the final content topic in Khan Academy's current Unit 1. It connects experimental evidence to shells, subshells, electron configurations, and nuclear attraction.

Photoelectron spectroscopy (PES) is an experimental method used to investigate electron energies.

A sample is exposed to high-energy radiation, commonly:

• ultraviolet radiation

• X-rays

• This radiation can eject electrons from atoms.

The emitted electrons are called:

• photoelectrons

Scientists measure their kinetic energy.

The incoming photon carries energy.

Some of that energy is needed to remove the electron.

Any remaining energy becomes kinetic energy of the emitted electron.

• So:

• photon energy = binding energy + kinetic energy

• Therefore:

• binding energy = photon energy − kinetic energy

Binding energy tells you how strongly the electron was held by the atom.

Khan Academy's PES material uses this relationship and describes PES spectra as photoelectron count versus binding energy.

High binding energy

• means:

• electron is strongly attracted to nucleus

• and requires lots of energy to remove.

Low binding energy

• means:

• electron is easier to remove.

Core electrons are closer to the nucleus.

• Therefore they generally have:

• high binding energies

Valence electrons are farther away and more shielded.

• Therefore they generally have:

• lower binding energies

A PES spectrum contains peaks.

Each peak generally represents electrons occupying a particular subshell .

• For example:

• 1s²2s²2p⁶3s²3p¹

• has five occupied subshells:

• 1s

• 2s

• 2p

• 3s

• 3p

• So an idealized PES spectrum would contain five major peaks .

Peak size tells you the relative number of electrons in that subshell.

• Example:

2s² contains:

• 2 electrons

2p⁶ contains:

• 6 electrons

• Therefore:

2p peak represents three times as many electrons as 2s.

• This relative intensity is extremely useful for identifying an unknown electron configuration.

Al:

• 1s²2s²2p⁶3s²3p¹

Occupied subshells:

• 1s²

• 2s²

• 2p⁶

• 3s²

• 3p¹

Expected peak relative electron counts:

• 2

• 2

• 6

• 2

• 1

The 2p peak should be much larger than a 2-electron peak.

The 3p peak should be smaller because it represents only one electron.

Khan Academy uses this kind of peak-count reasoning when interpreting PES.

1s electrons are extremely close to the nucleus.

• Therefore:

• they usually have the highest binding energy .

Outer-shell electrons have lower binding energies.

For something like aluminum:

• 1s → highest BE

• then 2s/2p

• then 3s/3p → lowest BE region

Some PES graphs show binding energy so that larger binding energies are toward the left .

Others may use a more conventional direction.

Never assume.

Read the axis labels.

Khan Academy specifically notes that PES plots may be arranged so binding energy decreases as you move right, and the energy scale can be logarithmic.

Suppose you compare Si and S.

Both are in period 3.

Si:

• [Ne]3s²3p²

S:

• [Ne]3s²3p⁴

Sulfur has:

• more protons

• the same occupied principal shells

• more electrons in 3p

• Therefore, compared with Si, sulfur's corresponding electrons generally experience stronger nuclear attraction.

You would expect:

• higher binding energies

• and the 3p signal should represent:

4 electrons instead of 2.

Khan Academy currently tests this type of comparison directly.

PES gives experimental evidence for ideas you learned earlier.

Across a period:

• nuclear charge increases.

Electrons in comparable subshells are generally held more strongly.

• Therefore their binding energies generally increase.

• So PES connects:

• nuclear charge

• ↓

• Coulombic attraction

• ↓

• binding energy

Do not confuse these.

• Mass spectrometry

Primarily helps identify:

• isotopes and their relative abundances

Think:

• mass of nuclei/atoms

• Photoelectron spectroscopy

Helps study:

• electron binding energies and electron configurations

Think:

• electrons

A good shortcut:

• Mass spectrum → isotopes

• PES spectrum → electrons

• UNIT 1 MASTER CONNECTIONS

• This is what separates memorizing Unit 1 from actually understanding it.

Connection 1: Periodic Table → Electron Configuration

An element's atomic number tells you:

• number of protons

• and, for a neutral atom:

• number of electrons.

• Those electrons determine the electron configuration.

Connection 2: Electron Configuration → Valence Electrons

• Example:

Mg:

• [Ne]3s²

• Therefore:

2 valence electrons.

Connection 3: Valence Electrons → Ionic Charge

Mg can lose those two electrons:

• Mg → Mg²⁺

Connection 4: Valence Electrons → Ionization-Energy Data

• Because Mg has two valence electrons:

IE₁ and IE₂ remove valence electrons.

IE₃ removes a core electron.

• Therefore:

• large jump after IE₂

Connection 5: Nuclear Charge → Atomic Radius

Across a period:

• more protons

• → stronger electron attraction

• → electrons pulled closer

• → smaller radius.

Connection 6: Nuclear Charge → Ionization Energy

Stronger attraction:

• → electron harder to remove

• → greater ionization energy.

Connection 7: Nuclear Charge → PES

Stronger attraction:

• → electrons more tightly bound

• → greater binding energy.

Connection 8: Isotopes → Atomic Mass

Different isotopes have different masses.

• Their natural abundances produce the:

• weighted average atomic mass

• shown on the periodic table.

Unit 1 Formulas You Should Know

Periodic Trends Table

Direction shortcut

• Atomic radius: ← ↓

• Ionization energy: → ↑

• Electronegativity: → ↑

Most Common Unit 1 Test Mistakes

Using grams instead of moles when finding an empirical formula.

Forgetting to turn a percentage into a decimal for weighted-average calculations.

Forgetting compound subscripts when calculating molar mass.

Thinking molecular and empirical formulas are always identical.

Rounding a ratio such as 1.5 instead of multiplying all ratios by 2.

Forgetting that 1 mol H₂O contains 2 mol H atoms .

Saying atomic radius decreases across a period "because there are more electrons" instead of explaining the stronger effective nuclear attraction .

Thinking cations are larger than their atoms. They are usually smaller .

Forgetting that more protons means a smaller radius within an isoelectronic series .

Removing 3d electrons before 4s when making transition-metal cations.

Confusing ionization energy, electron affinity, and electronegativity .

Confusing mass spectra with PES spectra .

Thinking PES peak position tells the number of electrons. Peak intensity/area represents relative electron count; position represents binding energy.

Missing the huge jump in successive-ionization-energy questions.

Giving an ionic formula whose total charge is not zero.