Development of Bohr's model of the atom


  • Niels Bohr (1885-1962) was a Danish scientist who also worked with Thomson.
    • FUN FACT: And like always with physicists, they didn't get along.
  • He later then went to work with Rutherford.
  • One of his major contributions to Physics was predicting that Hydrogen had only one electron, which was thought to be impossible.

Upgrading the Rutherford model

  • Bohr attempted to apply quantum physics to the Rutherford model of the atom to improve it.
    • Note that this was something new at the time, coming from Planck and Einstein
  • Bohr realised that the "atomic oscillators" mentioned in Planck's postulates were probably electrons
  • Bohr also observed that atoms produced radiation that formed a characteristic spectrum for each element.
    • This was observed in the Hydrogen discharge tube experiment
    • This is because when electrons become excited, they move to a higher energy state (explained later).
    • But in these states, they are unstable. So they lose the excess energy as photons or EM Radiation
  • At first, Bohr attempted to apply the quantum ideas of Planck to the atom, but failed.

The Balmer Series

  • In 1913, Bohr was introduced to Johann Balmer's work on Hydrogen spectra lines.
  • Angstrom, another scientist, was able to measure the wavelengths of the 4 most easily visible spectra lines of Hydrogen.
  • From that, Balmer formed a purely empirical and mathematical formula that could determine the wavelengths of the spectra lines:
\begin{align} \lambda = b \times \frac{n^2}{n^2 - 2^2} \end{align}
  • Where:
    • $\lambda$ is the wavelength of the spectra line (m)
    • $b$ is the Balmer constant, which was found to be $3.6456\times 10^{-7}m$
    • $n$ is an integer, which was found to be 3, 4, 5 or 6.
  • It should be noted that, Balmer did not know the meaning behind it and it was merely a formula which resulted from trying random numbers until they worked.
  • Jannes Rydberg, a scientist trying to find his own equation for spectral lines, altered Balmer's equation to fit Hydrogen-like atoms.
\begin{align} \frac{1}{\lambda} = R_h [Z^2] \bigg(\frac{1}{{n_f}^2} - \frac{1}{{n_i}^2}\bigg) \end{align}
  • Where
    • $\lambda$ is the wavelength of the spectra line (m)
    • $R_h$ is Rydberg's constant ($1.097 \times 10^7$)
    • $n_f$ and $n_i$ are integers.
    • ($Z$ is the atomic number of the element. This is not required by the HSC)
  • After Bohr saw these equations, he realised how electrons were arranged in the hydrogen atom and how quantum ideas could be introduced to the atom.
  • ANALYSIS: Thus, the Hydrogen spectrum was pivotal in the development of Bohr's model of the atom, allowing him to incorporate his quantum ideas (covered later) into his model of the atom.