Atomic Structure and Spectra

Calculating emission spectra for hydrogen

The Rydberg formula allows us to calculate the wavelength of an electronic transition Where:

• \(R=\) Rydberg constant \(=3.29\times10^{15}\:Hz\)
• \(n=\) initial quantum number
• \(m=\)final quantum number
• Balmer series is \(m^2=2\)

\[ \frac{1}{\lambda}=R\bigg(\frac{1}{m^2}-\frac{1}{n^2}\bigg) \]

Calculating emission spectra for larger atoms

Utilise Z effective

• Zeff is the charge that is effectively felt by the valence electrons
• Since shielding occurs, this is an important factor to determining the activity of a valence electron
• Zeff is proportional to ionisation energy, since the amount of energy that is required to strip an electron off an atom will ultimately be the effect of how attracted it is to the nuclei
  • Increases going across a period
  • Decreases going down a group

Calculating Zeff

\(Z_{eff}=Z\)(nuclear charge)\(-\sigma\)(shielding electrons)

• Shielding electrons are all core electrons of that atom
  • E.g. \(Z_{eff}\) of F is \(+7\), since it has two core electrons (\(1s^2\))

Calculating emission spectra

Where:

• \(R_H=\) Rydberg constant \(=1.0974\times10^7\:m^{−1}\)
• \(Z_{eff}=Z-\sigma\)

\[ E=-\frac{R_H}{n^2}Z^2_{eff} \]

This gives the orbital energy, that can then be used to calculate the emission spectra