M8-S7: Bohr's and Rutherford's Atomic Models and their Limitations

  • assess the limitations of the Rutherford and Bohr atomic models

  • investigate the line emission spectra to examine the Balmer series in hydrogen (ACSPH138)

Limitations of Rutherford’ Atomic Model

There are three main limitations:

  • Rutherford's model failed to address how and why the electrons were stable in their orbits. In other words, electrons did not decay to collide with the nucleus. 
In classical physics, accelerating particles emit energy including ones undergoing circular motion. In this case, why do electrons not emit energy despite experiencing electrostatic attraction towards the positive nucleus? 
  • The model could not give a description of where the electrons were.
  • The constituents of the nucleus could not be explained clearly, that is, the constituents were unknown. Rutherford and the results from the Geiger-Marsden experiment only demonstrated its positive nature.

 

Bohr’s Atomic Model 

Niels' Bohr's atomic model overcame the limitations of Rutherford's model.

Niels Bohr proposed three postulates in his atomic model:

  • Electrons exist and orbit in stable and circular orbits about the nucleus under the influence of electrostatic attraction. In these orbits, electrons do not emit energy.

 

 Bohr’s model of the atom describes electrons orbiting in stable energy levels as opposed to Rutherford's model in which electrons' motion was not described.

  • Energy is absorbed or emitted is specific packets called quanta when electrons move from one stable energy level to another. The photon emitted has energy given by E = Ef - Ei
  • Electrons orbited the nucleus such that their angular momentum is an integral multiple o. In other words, the angular momentum of electrons is quantised.

 

Bohr’s postulates were based off the hydrogen spectrum.  

Spectral lines observed in the Balmer Series or hydrogen spectrum (part of) are a result of electronic transition from higher energy levels to n = 2. Knowledge of Lyman and Paschen Series are not required in detail but students are recommended to be aware of what they represent.

  • The discrete energy levels of electrons provide an explanation for hydrogen’s emission spectrum when it is excited by a source of energy. Bohr proposed that the emission bands represent electrons’ transition in between these discrete orbits.
    • The absorption of energy will allow an electron to reach a higher energy level
    • When an electron returns to its ground state (usual energy level), the energy that was absorbed is now emitted in the form of visible light.
  • Bohr’s model of the atom allowed scientists to predict the energy levels in a hydrogen atom from spectroscopy data.

 

The Balmer Series

The emission spectrum of hydrogen produced when an electron returns to the second electron orbit (n = 9) is formally as the Balmer series as shown below.

 

  • The energy levels become closer, the further away they are from the nucleus. This causes the emission lines to be closer towards the higher energy (shorter wavelength) region of the spectrum.

 

Table shows the energy difference, wavelength and colour associated with each electron transition of the Balmer Series

Transition of n

3→2

4→2

5→2

6→2

7→2

8→2

9→2

∞→2

Wavelength (nm)

656

486

434

410

397

389

384

365

Energy difference (eV)

1.89

2.55

2.86

3.03

3.13

3.19

3.23

3.40

Colour

Red

Aqua

Blue

Violet

Ultraviolet

 

Limitations of Bohr's Atomic Model

There are several limitations of Bohr's model.

  • Firstly, the model is a combination of both classical and quantum physics. The circular motion of electrons stems from classical physics while the quantisation of its momentum is an application of quantum physics.
  • There is also a lack of evidence supporting his postulates and model, thus having no theoretical justification. There was also no explanation as to why no energy is emitted from the orbiting electrons
  • Relative Intensity of the spectral lines could not be explained when observing the spectrum. Some lines appeared brighter than others and Bohr's model could not explain this.
  • Larger atoms could not be explained by the Bohr model. Predictions made by Bohr’s model is only accurate for unielectron species (atoms or ions with only one electron in its outermost orbit) e.g. He+. However, the accuracy of these predictions decreases as the effective nuclear charge of an atom or ion increases (due to greater number of protons).
  • Hyperfine Splitting, which is the appearance of lines very close together on a close examination. Each line actually consisted of a number of smaller lines, something which Bohr's model did not predict (it predicted only one line for each transition).
  • The Zeeman Effect, occurring when a strong magnetic field was passed through the discharge tube (containing hydrogen) increasing the hyperfine splitting, also could not be explained by the model.
    • Electrons possess magnetic moment which contributes to their stable energy levels. When a strong magnetic field is present, this magnetic property of electrons is inevitably influenced which leads to changes to the energy states. However, the changes are relatively insignificant which gives rise to hyperfine lines.

 

 

    Practice Question 1

    What are Bohr's postulates in his atomic model? (2 marks)

    Practice Question 2

    Explain why Bohr's atomic model is a mixture between classical and quantum physics. (2 marks)

    Practice Question 3

    Outline THREE limitations of Bohr's model. (3 marks)

     

    Previous section: Rutherford's Atomic Model and The Geiger-Marsden Experiment

    Next section: Energy Calculation Using Rydberg's Equation