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Atomic models

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There has been a variety of atomic models throughout history of atomic physics, that refers mainly to a period from the beginning of 19th century to the first half of 20th century, when a final model of atom which is being used nowadays (or accepted as the most accurate one) was invented. Although the awareness of atom existence goes way back to the antique period of the world history (Greek conception of atom), this article will be mainly about five basic atomic models, from which each one has somehow contributed to how we percept the structure of atom itself – Dalton´s Billiard Ball Model, J.J Thomson’s “plum pudding” model, Rutherford’s Planetary model, Bohr’s Atomic model, Electron Cloud Model/Quantum Mechanics Model.

John Dalton’s atomic model

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Ilustration of Dalton’s perception of atom

John Dalton was an English scientist, who came up with an idea that all matter is composed of very small things. It was the first complete attempt to describe all matter in terms of particles. He called these particles atoms and formed an atomic theory. In this theory he claims that:

• All matter is made of atoms. Atoms are indivisible and indestructible
• All atoms of a given element are identical in mass and properties
• Compounds are formed by a combination of two or more different kinds of atoms
• A chemical reaction is a rearrangement of atoms

Parts of his theory had to be modified based on the discovery of subatomic particles and isotopes. We now also know that atoms are not indivisible, because they are made up of neutrons, electrons and protons.

Ilustration of Thomson’s perception of atom

Plum pudding model

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After discovery of an electron in 1897, people realised that atoms are made up of even smaller particles. Shortly after in 1904 J. J. Thomson proposed his famous “plum pudding model“. In this model, atoms were known to consist of negatively charged electrons, however the atomic nucleus had not been discovered yet.
Thomson knew that atom had an overall neutral charge. He thought that there must be something to counterbalance the negative charge of an electron. He came up with an idea that negative particles are floating within a soup of diffuse positive charge. His model is often called the plum pudding model, because of his similarity to a popular English dessert.

Rutherford’s model of the atom

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Rutherford was first, who suggested that Thomson’s plum pudding model was incorrect. His new model introduces nucleus to the atom theory. Nucleus contains relatively high central charge concentrated into very small volume. This small volume also contains the bulk of the atomic mass of the atom. Nucleus is surrounded by lighter and negatively charged electrons. His model is sometimes known as the planetary model of the atom.
However, there were still some major problems with this model. For example Rutherford could not explain why atoms only emit light at certain frequencies. This problem was solved later by a Danish physicist Niels Henrik David Bohr.

Bohr’s model of the atom

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Bohr model describes the atom as a positively charged nucleus, which is surrounded by electrons. Electrons travel in circular orbits, attraction is provided by electrostatic forces. Normally occupied energy level of the electron is called the ground state. The electron can move to the less – stable level by absorbing energy. This higher – energy level is called excited state. The electron can return to its original level by releasing the energy. All in all, when electron jumps between orbits, it is accompanied by an emitted or absorbed amount of energy (hv).

Electron Cloud Model/Quantum Mechanics Model of Atom

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Quantum Mechanics Model of Atom is nowadays being taught as the most “realistic” atomic model that describes atomic mechanisms as how present science presumes they work. It came to exist as a result of combination of number of scientific assumptions:

1. All particles could be percieved as matter waves with a wavelength. (Louis de Broglie)
2. Resulting from the previous assumption, atomic model which treats electrons also as matter waves was proposed. (Erwin Schrödinger, quantum mechanical atomic model emerged from the solution of Schrödinger’s equation for electron in central electrical field of nucleus.)
3. Principle of uncertainty states that we can’t know both the energy and position of an electron. Therefore, as we learn more about the electron’s position, we know less about its energy, and vice versa. (Werner Heisenberg)
4. There exists more than one energy level of electron in the atom. Electrons are assigned certain atomic orbitals, that can differ from one another in energy. (Niels Bohr)
5. Electrons have an intrinsic property called spin, and an electron can have one of two possible spin values: spin-up or spin-down. Any two electrons occupying the same orbital must have opposite spins. (the Stern-Gerlach Experiment)

Basic description of the quantum mechanical atomic model:

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Quantum mechanics physics propose that electrons are moving around the nucleus not on specifically defined electron paths (as we have seen eg. in Rutherford’s planetary atomic model), but in a certain three dimensional space (atomic orbital), in which their own occurrence has a certain probability, meaning their position cannot be calculated with 100% accuracy.

Four numbers, called quantum numbers, were introduced to describe the characteristics of electrons and their orbitals.

Quantum numbers

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Principal quantum number: n

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• describes the energy level of the electron in an atom (it also describes the average distance of the orbital from nucleus)
• It has positive whole number values: 1, 2, 3, 4,… (theoretically speaking the numbers could go to infinite, practically there are 7 known energy levels), it can be seen sometimes described in capital letters instead of numbers, beginning with K (K, L, M, N…)
• the n value describes the size of the orbital

Angular momentum quantum number: l

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• describes basically the shape of the orbital
• This number is limited by the principal quantum number. Its value goes from 0 to n-1. For example, for orbitals with principal quantum number n=2 there can by 2 different shapes of orbitals (2 different values l=0 and l=1)
• for every number exists a letter describing the shape of the orbital as shown in the table below
• Value of l (subshell) Letter

Value of l (subshell)
Letter

0
s

1
p

2
d

3
f

4
g

Orbital shapes and their orientation for different angular momentum and magnetic numbers

Magnetic quantum number: ml

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• describes how different shapes of orbitals are oriented in space. Its value can be from -l to 0 to +l. For example, for value l=1 there exists 3 values m= -1, 0, +1, meaning that the shape of that orbital can be oriented in 3 different ways in space.

Value of l
Values of ml

0
0

1
-1,0,+1

3
-3,-2,-1,0,+1,+2,+3

Spin quantum number: ms

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• describes in which direction is an electron spinning in a magnetic field . That can be either clockwise or counterclockwise and as a result, there are only 2 values allowed: -1/2 and +1/2.
• One consequence of electron spin is that a maximum of two electrons can occupy any given orbital, and the two electrons occupying the same orbital must have opposite spin. This is also called the Pauli exclusion principle.

Principles of atom structure

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Based on knowledge of quantum numbers, we are now able to build an electron configuration of an atom that describes electron arrangement in an atom. Apart from Pauli exclusion principle, there are 2 other rules that we must follow:

• Aufbau principle: Each electron occupies the lowest energy orbital available.

Basic ilustration of the Aufbau principle

• Hund’s rule: a single electron with the same spin must occupy each orbital in a sublevel before they pair up with an electron with an opposite spin.

Hund’s Rule of Maximum Spin Multiplicity

Examples of atoms described by quantum numbers

The importance of quantum mechanical atomic model has 2 main aspects. First, being able to build an electron structure of atoms of specific substances helps us to understand how the atoms interact in molecules, therefore we are one step closer to a more detailed description of attributes of those substances. Second, it leaves an open door to more potential theories which could expand our knowledge and perception of the world and universe surrounding us.

• What are the 6 models of the atom? | Socratic. (2015, May 23). Retrieved October 29, 2017, from https://socratic.org/questions/what-are-the-6-models-of-the-atom
• Kvantově mechanický model atomu. (n.d.). Retrieved October 29, 2017, from http://www.dobreznamky.cz/kvantove-mechanicky-model-atomu/
• Stavba atomového obalu. (2008, October 4). Retrieved October 29, 2017, from https://www.odmaturuj.cz/fyzika/stavba-atomoveho-obalu/
• The quantum mechanical model of the atom. (n.d.). Retrieved October 29, 2017, from https://www.khanacademy.org/science/physics/quantum-physics/quantum-numbers-and-orbitals/a/the-quantum-mechanical-model-of-the-atom
• Benešová, M., & Satrapová, H. (2002). Odmaturuj z chemie. Didaktis.
• Plum pudding model. (2017, October 12). Retrieved October 29, 2017, from https://en.wikipedia.org/wiki/Plum_pudding_model
• Bohr model. (2017, October 19). Retrieved October 29, 2017, from https://en.wikipedia.org/wiki/Bohr_model
• The Editors of Encyclopædia Britannica. (2014, June 05). Bohr atomic model. Retrieved October 29, 2017, from https://www.britannica.com/science/Bohr-atomic-model
• Orbital shapes and their orientation for different angular momentum and magnetic numbers – MEFANET, síť lékařských fakult ČR a SR. (n.d.). Orbital. Retrieved October 29, 2017, from http://www.wikiskripta.eu/w/Orbital#/media/File:Single_electron_orbitals.jpg
• Ilustration of Thomson’s perception of atom – W. (n.d.). Retrieved October 29, 2017, from https://www.meritnation.com/ask-answer/question/why-is-thomsons-model-also-known-as-plum-pudding-model/structure-of-the-atom/1299876
• Basic ilustration of the Aufbau principle – Electronic configuration. (n.d.). Retrieved October 29, 2017, from http://www.chemie.utb.cz/rvicha/Sac/vystprincip.html
• Hund’s Rule of Maximum Spin Multiplicity. (n.d.). Retrieved October 29, 2017, from http://www.eurekasparks.org/2015/07/hunds-rule-of-maximum-spin-multiplicity.html
• Examples of atoms described by quantum numbers – (n.d.). Retrieved October 29, 2017, from http://chemie-obecna.blogspot.cz/2011/08/radioaktivita.html

What is a PhD proposal?

A PhD proposal is a an outline of your proposed project that is designed to:

• Define a clear question and approach to answering it
• Highlight its originality and/or significance
• Explain how it adds to, develops (or challenges) existing literature in the field
• Persuade potential supervisors and/or funders of the importance of the work, and why you are the right person to undertake it

Research proposals may vary in length, so it is important to check with the department(s) to which you are applying to check word limits and guidelines. Generally speaking, a proposal should be around 3,000 words which you write as part of the application process.

What is the research proposal for?

Potential supervisors, admissions tutors and/or funders use research proposals to assess the quality and originality of your ideas, your skills in critical thinking and the feasibility of the research project. Please bear in mind that PhD programmes in the UK are designed to be completed in three years (full time) or six years (part time). Think very carefully about the scope of your research and be prepared to explain how you will complete it within this timeframe.

Research proposals are also used to assess your expertise in the area in which you want to conduct research, you knowledge of the existing literature (and how your project will enhance it). Moreover, they are used to assess and assign appropriate supervision teams. If you are interested in the work of a particular potential supervisor – and especially if you have discussed your work with this person – be sure to mention this in your proposal. We encourage you strongly to identify a prospective supervisor and get in touch with them to discuss your proposal informally BEFORE making a formal application, to ensure it is of mutual interest and to gain input on the design, scope and feasibility of your project. Remember, however, that it may not be possible to guarantee that you are supervised by a specific academic.

Crucially, it is also an opportunity for you to communicate your passion in the subject area and to make a persuasive argument about what your project can accomplish. Although the proposal should include an outline, it should also be approached as a persuasive essay – that is, as an opportunity to establish the attention of readers and convince them of the importance of your project.

Is the research proposal ‘set in stone’?

No. Good PhD proposals evolve as the work progresses. It is normal for students to refine their original proposal in light of detailed literature reviews, further consideration of research approaches and comments received from the supervisors (and other academic staff). It is useful to view your proposal as an initial outline rather than a summary of the ‘final product’.

Structuring a Research Proposal

Please check carefully with each department to find out whether a specific template is provided or required. In general, however, the following elements are crucial in a good research proposal:

Title

This can change, but make sure to include important ‘key words’ that will relate your proposal to relevant potential supervisors, funding schemes and so on. Make sure that your title goes beyond simply describing the subject matter – it should give an indication of your approach or key questions.

Overview of the research

In this section you should provide a short overview of your research and where it fits within the existing academic discourses, debates or literature. Be as specific as possible in identifying influences or debates you wish to engage with, but try not to get lead astray into a long exegesis of specific sources. Rather, the point is to sketch out the context into which your work will fit.

You should also use this section to make links between your research and the existing strengths of the department to which you are applying. Visit appropriate websites to find out about existing research taking place in the department and how your project can complement this.

If applying to multiple departments, be sure to tailor a unique proposal to each department – readers can tell if a proposal has been produced for ‘mass consumption’!

Be sure to establish a solid and convincing framework for your research in this section. This should include:

• research questions (usually, 1-3 should suffice) and the reason for asking them
• the major approach(es) you will take (conceptual, theoretical, empirical and normative, as appropriate) and rationale
• significance of the research (in academic and, if appropriate, other fields)

Positioning of the research (approx. 900 words)

This section should discuss the texts which you believe are most important to the project, demonstrate your understanding of the research issues, and identify existing gaps (both theoretical and practical) that the research is intended to address. This section is intended to ‘sign-post’ and contextualize your research questions, not to provide a detailed analysis of existing debates.

Research design & methodology (approx. 900 words)

This section should lay out, in clear terms, the way in which you will structure your research and the specific methods you will use. Research design should include (but is not limited to):

• The parameters of the research (ie the definition of the subject matter)
• A discussion of the overall approach (e.g. is it solely theoretical, or does it involve primary/empirical research) and your rationale for adopting this approach
• Specific aims and objectives (e.g. ‘complete 20 interviews with members of group x’)
• A brief discussion of the timeline for achieving this

A well developed methodology section is crucial, particularly if you intend to conduct significant empirical research. Be sure to include specific techniques, not just your general approach. This should include: kinds of resources consulted; methods for collecting and analyzing data; specific techniques (ie statistical analysis; semi-structured interviewing; participant observation); and (brief) rationale for adopting these methods.

References

Your references should provide the reader with a good sense of your grasp on the literature and how you can contribute to it. Be sure to reference texts and resources that you think will play a large role in your analysis. Remember that this is not simply a bibliography listing ‘everything written on the subject’. Rather, it should show critical reflection in the selection of appropriate texts.

Possible pitfalls

Quite often, students who fit the minimum entrance criteria fail to be accepted as PhD candidates as a result of weaknesses in the research proposal. To avoid this, keep the following advice in mind:

• Make sure that your research idea, question or problem is very clearly stated, persuasive and addresses a demonstrable gap in the existing literature. Put time into formulating the questions- in the early stages of a project, they can be as important as the projected results.
• Make sure that you have researched the departments to which you are applying to ensure that there are staff interested in your subject area and available to supervise your project. As mentioned above it is strongly advised that you contact potential supervisors in advance, and provide them with a polished version of your proposal for comment.
• Make sure that your proposal is well structured. Poorly formed or rambling proposals indicate that the proposed project may suffer the same fate.
• Ensure that the scope of your project is reasonable, and remember that there are significant limits to the size and complexity of a project that can be completed and written up in three years. We will be assessing proposals not only for their intellectual ambition and significance, but also for the likelihood that the candidate can complete this project.
• Make sure that your passion for the subject matter shines through in the structure and arguments presented within your proposal. Remember that we may not be experts in your field – it is up to you to make your project and subject matter engaging to your readers!

The following books are widely available from bookshops and libraries and may help in preparing your research proposal (as well as in doing your research degree):

Bell, J. (1999): Doing Your Research Project: A Guide for First-time Researchers in Education & Social Science, (Oxford University Press, Oxford).
Baxter, L, Hughes, C. and Tight, M. (2001): How to Research, (Open University Press, Milton Keynes).
Cryer, P. (2000): The Research Student’s Guide to Success, (Open University, Milton Keynes).
Delamont, S., Atkinson, P. and Parry, O. (1997): Supervising the PhD, (Open University Press, Milton Keynes).
Philips, E. and Pugh, D. (2005): How to get a PhD: A Handbook for Students and their Supervisors, (Open University Press, Milton Keynes).