CourseCourseQ BankQuestion BankDocsDocuments

1.3.6 (HL)—Ionization energy (IE)

Syllabus
First assessment 2025
Objective
1.3.6
Level
HL

First Ionization Energy

HL only

First ionization energy is the energy required to remove one mole of electrons from one mole of gaseous atoms. The convergence limit in an emission spectrum corresponds to ionization.

Trend Explanation
Across a period Generally increases as effective nuclear charge increases
Down a group Generally decreases because the outer electron occupies a higher shell
Be → B dip The electron removed from B is in a higher-energy p subshell
N → O dip Pairing in a p orbital makes one electron easier to remove

E=hfandc=λfE = hf and c = λf

Worked example — hydrogen convergence limit

The local course book gives λ=9.12×10−8 m\lambda=9.12\times10^{-8}\,\mathrm{m}. First, f=c/λ=(3.00×108 m s−1)/(9.12×10−8 m)=3.29×1015 s−1f=c/\lambda=(3.00\times10^8\,\mathrm{m\,s^{-1}})/(9.12\times10^{-8}\,\mathrm{m})=3.29\times10^{15}\,\mathrm{s^{-1}}. Then Ephoton=hf=(6.63×10−34 J s)(3.29×1015 s−1)=2.18×10−18 JE_{\text{photon}}=hf=(6.63\times10^{-34}\,\mathrm{J\,s})(3.29\times10^{15}\,\mathrm{s^{-1}})=2.18\times10^{-18}\,\mathrm{J}. Convert one-photon energy to one mole and joules to kilojoules: IE=(2.18×10−18)(6.02×1023)/1000=1.31×103 kJ mol−1IE=(2.18\times10^{-18})(6.02\times10^{23})/1000=1.31\times10^3\,\mathrm{kJ\,mol^{-1}}. This is the molar energy for the first ionization process H(g)→H+(g)+e−\mathrm{H(g)\rightarrow H^+(g)+e^-}.

At the convergence limit, convert wavelength or frequency to energy per photon with E = hf, then multiply by the Avogadro constant and convert J mol⁻¹ to kJ mol⁻¹. Across-period trends are general patterns; subshell energy and electron pairing explain the named dips.

X(g)→X+(g)+e−firstionizationenergyinkJmol−1X(g) → X⁺(g) + e⁻ first ionization energy in kJ mol⁻¹

Explaining and Calculating Ionization Energy

HL only

Assessment in practice

2–4 marks in the two selected direct examples marks
How it is assessed

Questions combine spectral calculations using the convergence limit with explanations of periodic first-IE trends and their sublevel-related discontinuities.

Command terms

determine / explain

What earns marks

Convert molar ionization energy to energy per atom before using E=hf or E=hc/λ, and for trend explanations link nuclear charge, shielding, shell/sublevel energy and electron repulsion to the ease of removing the specified electron.

Watch for

Using molar energy directly in E=hf without dividing by Avogadro's constant

Representative question

Question 1

[Maximum number: 2]

Determine the frequency of electromagnetic radiation, in s−1\mathrm{s}^{-1}, equivalent to the first ionization energy of phosphorus. Use sections 1, 2 and 9 of the data booklet.

Electron Configurations Summary

Retrieve the chain: emission lines reveal discrete levels; capacities, sublevels, orbitals, and spin rules build configurations; first and successive ionization energies then reveal how electrons are held and arranged.

When checking an answer, ask: Did I link a line to a transition? Did I use 2n² and the filling rules? Did I explain an ionization trend or count electrons before a successive-IE jump?