Models of the Atom
Key Questions
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As far as I know, Rutherford's atomic model says that atoms have a center (the nucleus) of concentrated positive charge and this center is very very small compared to the actual size of the atom.
The electrons on the other hand, orbit this nucleus thus, completing the model of the atom.
This may seem obvious (we see that in most elementary textbooks). Before this, J.J Thomson proposed his own atomic model: The atom is made out of a positive sphere with electrons in it. Admirable but it is still a flawed model.
Rutherford's one is an improvement.
The problem is, atoms emit and absorb certain wavelengths of light which shows that the atom has different energy levels. Rutherford's model cannot explain this phenomenon.
Next, the electron as proposed by Rutherford moves in circular orbit. According to Maxwell, charges in circular motion must emit radiation. In Rutherford's model, the atom would eventually cease to exist because the electron would collapse into the nucleus (something which we never observe).
Hope this would suffice.
*Update
This is an article about an electron moving in circular motion. Physicists manage to detect electromagnetic radiation from an electron. This is not coming from an electron in an atom mind you.
Cheers.
http://news.sciencemag.org/physics/2015/04/physicists-detect-radio-waves-single-electron
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A model in which electrons orbit the nucleus with quantised angular momentum.
Bohr used Balmer's work on the line spectrum of Hydrogen to prove the quantisation of electron energy levels in the atom. This complemented Planck's work which had given rise to quantum theory. So it was very significant.
There is a flaw in the model, that is, Bohr believed that electrons orbited the nucleus in much the same way as planets orbit the Sun. That is incorrect. Schrödinger proposed a model nearer to how we understand atomic structure which is based on wave behaviour. In the model electrons exist as a type of standing wave within the confinement of the nucleus' influence. I don't have a very strong grasp of this model so that's as far as I can explain it.
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The first model of the atom was developed by JJ Thomson in 1904, who thought that atoms were composed purely of negatively charged electrons. This model was known as the 'plum pudding' model.
This theory was then disproved by Ernest Rutherford and the gold foil experiment in 1911, where Rutherford shot alpha particles at gold foil, and noticed that some went through and some bounced back, implying the existence of a positive nucleus.
In 1913, Niels Bohr proposed a model of the atom where the electrons were contained within quantized shells that orbited the nucleus. This was because it was impossible for the cloud of negative electrons proposed by Rutherford to exist, as the negative electrons would be drawn to the positive nucleus, and the atom would collapse in on itself.
In 1926, the Austrian physicist Erwin Schrödinger created a quantum mechanical model of the atom by combining the equations for the behavior of waves with the de Broglie equation to generate a mathematical model for the distribution of electrons in an atom.
However the model used today is closest to the Bohr model of the atom, using the quantized shells to contain the electrons.
De Broglie equation: http://chemistry.about.com/od/chemistryglossary/a/debroglieeqdef.htm