The Balmer Series – Learn

Rutherford’s Model of the Atom

Ernest Rutherford had described a new model of the atom, building upon the plum pudding model which had earlier been suggested by JJ Thomson. Thomson had been successful in isolating the electron, however, the positive pudding from his model was rejected following Rutherford’s interpretation of the Gieger-Marsden experiment, as discussed previously. 

Consequently, Rutherford suggested a nuclear model of the atom that obeyed the following principles:

  • The vast majority of the mass of an atom occupied an extremely small and dense area in the middle of the atom. He coined this the nucleus.
  • The nucleus contained all of the positive charge of the atom. 
  • Electrons occupied the large amounts of empty space that surrounded the nucleus of the atom.

However, Rutherford’s model was limited by two important factors:

  • The behaviour of electrons was largely unexplained. 
  • The unknown composition of the nucleus (It is interesting to note that Rutherford did successfully isolate the proton years later, and suggested the existence of the neutron).

Bohr’s contribution to Rutheford’s model of the atom-

Bohr extended upon the work of Rutherford, suggesting modification to his model which attempted to explain the behavior of electrons. Initially, Bohr examined the emission spectra produced by excited hydrogen gas. The wavelengths of light emitted by these atoms could be associated with a specific amount of energy, in accordance with E=hf. Bohr reasoned that this was the energy being emitted by electrons changing energy levels surrounding the nucleus. 

Bohr concluded that electrons could occupy a range of quantised orbits around a nucleus, and could transition between these orbits. The electron could absorb energy to move up orbitals, or emit energy, as electromagnetic radiation, to move down orbital. These orbits can be considered like a staircase, electrons are able to exist on different steps, but never half way between the steps. The lowest energy state that an electron can occupy is known as the ground state (n = 1). The hydrogen emission spectra which stimulated Bohr’s proposal, represented the transition of the electrons from higher energy states to the first excited state (n = 2). While a range of transitions are possible, these transitions are the only ones that emit light in the visible spectrum, and are called the Balmer series. Transitions to the ground state emit shorter wavelength UV radiation, while transitions to the n = 3 and above, emit longer wavelength infrared radiation. The wavelength of light emitted by each specific transition can be determined using the Rydberg equation, which is present below. 

\frac { 1 }{ \lambda } =R\left[ \frac { 1 }{ n_{ f }^{ 2 } } -\frac { 1 }{ n_{ i }^{ 2 } } \right]


R – Rydberg constant (1.097 × 107 m-1) – found on the data sheet

nf – Final energy state of electron

ni – Initial energy state of electron

λ – Wavelength of light emit (m)

In summary, Bohr’s planetary model of the atom is sometimes referred to in terms of three key principles (often called postulates), they are as follows:

  • Electrons move around the nucleus in a circular orbit.
  • Electron orbits are quantised.
  • Electrons can change energy levels from one orbit to another and this is always accompanied by the emission or absorption of a photon. 

The limitations of Bohr’s model 

Classical physics disagreed with the quantised model of electron orbits proposed by Bohr. The idea that electrons could exist in stationary orbits, did not align with the behaviour charged particles previously explained by Maxwell. It was known that charged particles, like electrons, emitted electromagnetic radiation when accelerated. The circular nature of the electron orbits proposed by both Rutherford and Bohr suggested that they were experiencing centripetal acceleration. If the electrons were to emit energy as a result of this, as electromagnetic radiation, this must lead to decreases in the total energy of the electron, in accordance with the Law of Conservation of Energy. The decrease in energy would mean that the electron should spiral in towards the nucleus, eventually colliding.

Furthermore, the model struggled to explain the complicated emissions spectra of larger elements. Lastly, it was unable to explain the differing intensities of emission lines and other known phenomena like the Zeeman effect (the splitting of spectral lines by magnetic fields).

While the Bohr model contributed immensely to the understanding of the atom, it still represented an incomplete model of the atom. Continued investigation and analysis, used Bohr’s proposals to help build the current accepted model. 

Example 1:

Determine the wavelength of light emitted when an electron falls from the fourth energy level to the second energy level.

\frac { 1 }{ \lambda } =R\left[ \frac { 1 }{ n_{ f }^{ 2 } } -\frac { 1 }{ n_{ i }^{ 2 } } \right]

\frac { 1 }{ \lambda } =1.097\times 10^{ 7 }\left[ \frac { 1 }{ 2^{ 2 } } -\frac { 1 }{ 4^{ 2 } } \right]

\frac{1}{\lambda } \ =\ 2056875

\lambda \ =\ 4.86\times 10^{-7} m

The example shows that light with a wavelength of 486 nm will be emitted. This corresponds with the blue line in hydrogen emission spectra, confirming it as part of the Balmer series: