The breakdown of the Bohr atomic model

Author: Chihiro Fukushima

 

The evidence that Bohr used to support his model of the atom

Successive ionization energies provide evidence for the existence of quantum shells. The Bohr atomic model was proposed by Niels Bohr in 1915. He came to the conclusion that electrons orbit in shells around the nucleus of an atom, the shells having discrete energy levels. The presence of only certain lines in atomic spectra meant that an electron can only adopt certain discrete energy levels (the energy is quantized); hence the idea of quantum shells. The photon frequencies absorbed or emitted by an atom are fixed by the differences between energy levels of the orbits. In order to back up his model of the atom, he used quantum theory which was proposed by Max Planck in 1900. Planck suggested that energy was not continuous but came in tiny particles called quanta. By using quantum theory, he explained the electromagnetic radiation produced when elements are excited, such as when they are heated to high temperatures or placed in discharge tubes. When hydrogen is energised in a discharge tube, spectra lines of different frequencies are emitted.

Bohr assumed that the electron moved around the proton in a circle due to the Coulomb force between the electron and proton. From this he determined that the total mechanical energy of the electron in orbit depends only on its distance from the proton. First, Bohr assumed that the angular momentum of the electron was quantized, so that only certain orbits are allowed for the electron. When this relationship is combined with the energy relationship it was found that the electron orbits can only correspond to certain energies.

Bohr’s second quantum assumption described the nature of electron transitions between allowed energy levels. Bohr assumed that an electron could make the transition to a lower energy level if it emitted a photon in the process. The photon must carry away an amount of energy equal to the energy difference between the two levels involved in the transition. E = hf, where E is the energy of the photon and f is the frequency of the wave. h is Planck’s constant = 6.63×10-34 m2 kg / s.

The electron could also make a transition to a higher energy level which would require the absorption of a photon carrying an amount of energy equal to the energy difference between the two levels involved in the transition. This was appropriate for describing hydrogen absorption spectra or emission spectra.
Bohr’s complete model for hydrogen predicts that emission lines correspond to the emission of a photon that occurs when an electron makes the transition from a higher energy state to a lower energy state. The photon carries off an amount of energy equal to the difference between the two states involved in the transition. The Balmer series can be understood as corresponding to the photons that are emitted when the electron makes a transition to the higher energy states causing the electron to drop back to the second series.

Different colours of light are produced depending on which orbit the electron starts from and to which orbit it drops.

Ionisation energy is the energy required to remove one mole of electrons from the outermost shells of one mole of atoms in the gaseous state to form a positively charged ion.

M(g) M+(g) + e-

This process can be repeated again to give the second ionisation energy. This is the removal of one mole of electrons from one mole of monopositive ions in the gaseous state.

M+(g) M2+(g) + e-

This can be continued until all of the electrons within an atom have been removed.

The successive ionisation energies of an element can tell us what group the element is in and also how many electron shells the atom has. A graph of the successive ionisation energies of sodium are shown below:

The electronic configuration of sodium shows that it has electrons in three different energy levels. The electrons closest to the nucleus (first shell) are the 1s2 electrons. The next eight electrons are the 2s2 and 2p6 electrons and the last electron in the outer shell is the 3s2 electron.

There is a big jump between the first and second ionisation energies because the second electron is removed from a shell closer to the nucleus and so more energy is required to overcome the electrostatic force of attraction exerted by the nucleus on the electrons. The same goes for the huge leap between the 9th and 10th ionisation energies for the same reason. Successive ionisation energies generally increase because the nuclear attraction of the protons is increasing as more and more electrons are removed.

There are two rules which need to be applied to explain the trend. It takes more energy to remove an electron from a full or half full sub-shell because it is more stable and as the number of protons in the nucleus increase, the nuclear attraction increases, therefore making it more difficult to remove an electron. This supports the Bohr model.

 

The evidence that convinced scientists that Bohr’s atomic model needed refining

First ionisation energies of successive elements provide evidence for the existence of characteristics energy levels of s, p and d orbitals. Bohr’s model of the atom proved difficult to apply to all but the simplest atoms for example hydrogen, helium and lithium. Heisenberg discovered the uncertainty principle in 1927. This principle was true because even the best methods used to measure the position and momentum of a moving particle disturbs the particle. For example physicists might scatter photons off a moving electron to ‘see’ its position but in a collision a photon transfers momentum to the electron. Therefore physicists cannot verify precisely both the position and momentum of the electron at the same time. Hence circular orbits were a problem.

Werner Heisenberg’s theory was based only on what can be observed which was the radiation emitted by the atom. He said that we are not always able to assign an electron a position in space at a given time nor follow it in its orbit so we cannot assume that the planetary orbits postulated by Niels Bohr actually exist. Mechanical quantities such as position, velocity, etc. should be represented not by ordinary numbers but by abstract mathematical structures called “matrices” and he formulated his new theory in terms of matrix equations.

The following graph shows how ionisation energy varies in period two and why the Bohr model needed refining.


The lowest ionisation energy is for lithium because it has only 3 protons in the nucleus and it can lose its outer 2s1 electron easily because it will then have a full 1s2 sub-shell which is very stable.

The highest ionisation energy is for Argon because it has a full 2p6 sub-shell and it has 10 protons in its nucleus.

Boron has a lower ionisation energy than Beryllium even though there is a greater nuclear attraction in Boron because Boron loses it’s 2p1 electron from the sub-shell easily to gain a full 2s2 sub-shell and Beryllium has a full 2s2 sub-shell giving it extra stability and therefore making it more difficult to remove an electron

Oxygen has a lower ionisation energy than Nitrogen because Oxygen loses it’s 2p4electron in its sub-shell easily to gain a half full 2p3 sub-shell which is more stable and Nitrogen has it’s outer electron in a half full 2p3 sub-shell giving it extra stability and therefore making it more difficult to remove an electron.

The outer electrons are held in their shells by the attractive force of the positive protons in the nucleus, the nuclear attraction. As more and more electron shells are added this force gets weaker because the distance between the outer electrons and the nucleus is increasing and the inner electrons shield the nuclear electrons from the outer electrons, electronic shielding. The lower the ionisation energy the easier it is to remove electrons from the outermost shell of the atom. As you go down a group the ionisation energy decreases which also explains why metals get more reactive as you go down a group. It gets easier for them to give up electrons to form bonds.

The sodium emission spectrum has a prominent yellow line called the sodium D line. This can be observed in the yellow cast of low-energy sodium streetlights. This line arises from the transition of an electron from the excited electronic state in which the valence electron is in a 3p orbital to the ground electronic state in which the valence electron is in a 3s orbital. By measuring the sodium spectrum you will be able to determine the energy difference between these two electronic states and therefore work out the energy difference between the 3p and 3s orbitals. The existence of this emission line shows that electrons in the 3s and 3p orbitals are of different energy and that their energy depends on the orbital angular momentum quantum number as well as the quantum number. This explains that the Bohr model of the atom was not detailed enough, nor was his model able to be applied to every atom in the periodic table therefore it needed refining with sub-divided quantum shells.

 

Sites and book used during research and for images

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodium.html#c1 http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodium.html
http://www.teachmetuition.co.uk/Chemistry/Atomic_Structure/atomic2.htm
http://www.colorado.edu/physics/2000/quantumzone/bohr.html
http://teachers.web.cern.ch/teachers/archiv/HST2003/publish/standard%20model/History/layer1.htm
http://www.chemguide.co.uk/atoms/properties/atomorbs.html#top http://www.chemguide.co.uk/atoms/properties/atomorbs.html
http://astro.u-strasbg.fr/~koppen/discharge/

6 thoughts on “The breakdown of the Bohr atomic model

  1. Thanks for this great summary,

    I like how the spdf sub-level orbitals give a better explanation for the differing ionisation energies we observe for elements. How the orbitals fill in the spdf model makes sense of understanding atomic stability in terms of ‘full orbitals/ shells’.

    Your summary and example of sodium at the end of this paper is great. The valence electron in the 3s orbital ‘jumps’ to the 3p orbital as it is excited by energy, the fact that we can use the emission spectra of sodium to determine energy difference between the 3s and 3p orbital is great scientific finding! It would be interesting to look into how these calculations are made and the unit used. The unexpected number of emission lines in sodium’s atomic spectra is another aspect worth looking into.

  2. Thank you for your insightful paper on Bohr’s atomic model,

    Throughout the paper, I gained a deeper understanding of the evidence behind ionisation energy ‘increasing as electrons are removed’. A clear explanation of how each element has a unique quantum shell was integrated throughout paragraph two. For an electron to leap to the next shell, the electron must be excited. The electron transitions from a high-energy state to a lower energy state. I found this information comprehendible. Electrons held in the outer shell are held in orbits by an attractive nuclear force. The inner elections shield the outer electrons from the nucleus as the distance increases between outer electron and its nucleus. low ionisation energy allows from electrons to be removed from the outermost shell.
    The emission spectrum was explained clearly new the end of the paper, where examples were provided to enhance my understanding. The comparison between sodium and hydrogen painted a clear picture as to why the transition of an electron from the excited state back down to ground state differentiates down and across the periods and groups.
    However, clarity could be made on the differences; how electrons emit different energy levels and what makes each element unique.
    Isabella Buman

  3. Thank you for your paper as it has given me a deeper understanding in the evidence of quantum shells as a result of successive ionization energies. I found it interesting regarding ‘the lines in an atomic spectra meant that an electron can only adopt certain discrete energy levels’ and therefore where the idea of quantum shells originated from. The theory then extends to explain an elements’ ‘excited state’ (when heated to high temperatures or placed in discharge tubes) explaining how electromagnetic radiation is produced.
    Following on in the paper, I found the diagrams extremely useful to understand more the content of the paper. For example the image/graph of ‘Successive Ionisation Energies of Sodium’, allowed me to better grasp the ideas of the different shells of an atom and the different energy levels present in each. Actually graphically seeing the jump between the first and second ionisation energies was due to the second electron being removed was a result of it situated closer to the nucleus was helpful. I was also able to see why more energy ‘is required to overcome the electrostatic force of attraction exerted by the nucleus on the electrons’.
    However, I found confusing the two rules supporting the Bohr model in relation to stability of the shells as I don’t have a complete understanding of the stability of the electrons present in an atom. Also, further research is needed to totally understand an atom as the ‘Bohr model of an atom was not detailed enough… to be applied to every atom’.

  4. Thank you for your informative paper,
    Your explanation on the stability of outer electrons and how they are held in their shells by the attractive force of the positive protons was very helpful. As more electrons shells are added, the attractive force becomes weaker because the distance between the outer electrons and the nucleus is increasing and the inner electrons shield the nuclear electrons from the outer electrons, known as electronic shielding. Your paper then goes on to explain that the lower the ionisation energy is, the easier it is to remove the electrons from the outer shell. This corresponds with heightened levels of reactivity as you move down groups on the periodic table.
    I found that the relation between shells having discrete energy levels and the emission of photons stood out to me. These discrete energy levels are called quanta and as electrons are excited either by photons or heat, they can jump up to the next energy level before falling back down to their ground state. The difference in energy between levels is exactly that of the frequency of photons being emitted.
    Further research could be put into techniques and methods of measuring the frequencies and quantities of energy being given off by atoms.

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