DP IB Chemistry: HL

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First teaching 2014

Last exams 2024

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12.1.1 Emission Spectra & First Ionisation Energy

Convergence Limits on an Emission Spectrum

Emission Spectra

  • Electrons move rapidly around the nucleus in energy shells
  • Heat or electricity can be used to excite an electron to a higher main energy level
  • These range from n = 1 (ground state) to n = ∞
  • When the electrons 'fall' back down they must lose the energy difference between the two energy levels. This loss of energy is performed by releasing electromagnetic energy in the form of infrared, visible light or ultraviolet radiation.
  • When the electron falls back to n = 1 (ground state) the energy released is in the ultraviolet region of the spectrum
  • This corresponds to the Lyman series

 

Electron-Promoted-Photon-being-emitted, downloadable IB Chemistry revision notes

Promotion of an electron from the ground state (n=1) to n=2

7-1-3-electron-jumps-in-the-hydrogen-spectrum

Electron jumps in the hydrogen spectrum

  • This gives evidence for Bohr's model which is the idea that electrons exist in discrete energy levels so an exact amount of energy is required for an electron to 'jump' an energy level, a little like a ladder
  • There are however limitations to this model
    • Assumes positions of electrons are fixed
    • Assumes energy levels are spherical in nature
    • Bohr limited calculations to hydrogen only, so does not explain the line spectra of other elements containing more than one electron

The Limit of Convergence

  • As the line spectra is produced the lines will become closer together 
    • Where the lines appear to meet is called the limit of convergence
    • The convergence limit is the frequency at which the spectral lines converge
    • The energy required for an electron to escape the atom, or reach the upper limit of convergence, is the ionisation energy
    • The frequency of the radiation in the emission spectrum at the limit of convergence can be used to determine the first ionisation energy or IE1
    • In the Lyman series for the hydrogen atom (UV region), the frequency at the limit of convergence relates to the energy given out when an electron falls from n = ∞ to n = 1
    • For hydrogen, the lines converge to a limit with a wavelength of 91.16 nm or 91.16 × 109 m

Lyman Series Limit of Convergence, downloadable IB Chemistry revision notes

Lyman series (ultra-violet radiation) corresponds to transitions between higher shells and the ground state (n=1)

Calculating First Ionisation Energy

Calculating First Ionisation Energy

  • When dealing with the Lyman series the largest transitions represent the fall from the infinite level to n=1
  • In reverse, it can be considered to be equal to the ionisation energy (note that ionisation energy is given per mole of atoms)
  • Therefore, the first ionisation energy (IE1) of an atom can be calculated using the frequency (or wavelength) of the convergence limit
  • We can do this by using the following equations

ΔE = h ν

c = ν λ

  • In order to calculate first ionisation energy (IE1) we must first calculate the frequency using the given data and rearranging:

c = ν λ

as

ν = c ÷ λ

  • Once we know the frequency, we can use this to calculate the ionisation energy

Calculating First Ionisation Energy, downloadable IB Chemistry revision notes

Worked example

The convergence limit for the sodium atom has a frequency of 1.24 × 1015 s1. Calculate the first ionisation energy of sodium in kJ mol1.

Answer:

Step 1: Write out the equation to calculate the first ionisation energy (IE1)

ΔE = h ν

Step 2: Substitute in numbers from question and data booklet to give energy change per atom

          IE1 = 6.63 × 1034 × 1.24 × 1015

          IE1 = 8.22 × 1019 J atom1

Step 3: Calculate the first ionisation energy per mole by multiplying by Avogadro's constant

          IE1 = 8.22 × 1019  × 6.02 × 1023

          IE1 = 494 916 J mol1

Step 4: Convert J molto kJ mol1 by dividing by 1000

          IE1 = 495 kJ mol1

So the first ionisation energy (IE1) of sodium has been calculated as 495 kJ mol1

Worked example

The convergence limit for the hydrogen atom has a wavelength of 91.16 nm. Calculate the ionisation energy for hydrogen in kJ mol1.

Answer:

Step 1: Calculate the frequency of the convergence limit, converting wavelength into m (nm to m = × 109)

          c = ν λ

          ν = c ÷ λ

          ν = 3.00 × 108 ÷ 91.16 × 109

          ν = 3.29 × 1015 s1

Step 2: Substitute into the equation to calculate IE1 for one atom of hydrogen in J mol

ΔE = h ν

         IE1 = 6.63 × 1034 × 3.29 × 1015

         IE1 = 2.18 × 10-18 J atom1

Step 3: Calculate IE1 for 1 mole of hydrogen atoms

          IE1 = 2.18 × 1018  × 6.02 × 1023

          IE1 = 1 313 491 J mol1

Step 4: Convert J molto kJ mol1

          IE1 = 1313 kJ mol1

So the first ionisation energy (IE1) of hydrogen has been calculated as 1313 kJ mol1

Exam Tip

These equations are found in the data booklet so you don't need to learn them.Also, be careful to calculate the first ionisation energy (IE1) per mole by using Avogadro's constant (NA) 6.02 × 1023 and converting units to kJ mol−1.Finally, when working through calculations, keep the numbers in your calculator to avoid rounding up too early.

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