Development of Bohr's model of the atom

#### Introduction

• 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.

• 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:
(1)
\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.
(2)
\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.
page revision: 1, last edited: 04 Jul 2011 10:33