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Atoms,orbits and my problem

  1. Apr 27, 2009 #1
    I am a student of the 9th standard...My main question is that-we know the nucleus has positive charge and the electrons have negative charge.Moreover opposite charges attract, but in that case then the electrons should be merged with the nucleus itself and not be revolving in the imaginary orbits.So why does this happen?I would be really glad if someone helpso.
     
  2. jcsd
  3. Apr 27, 2009 #2

    alxm

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    Well, that's a problem that occupied some of the world's leading physicists between 1910-1930, essentially as soon as they'd figured out that atoms were made out of negatively-charged electrons and a positively-charged nucleus that was small compared to the size of the atom.

    Now, the opposite charges attract. But this is not a problem if the electrons are moving - in which case they could form stable 'orbits', like a planet revolving around a sun. (if the Earth stopped it would fall in).

    The real problem with this picture, is that the laws of electromagnetism (Maxwell's laws) predict that a charging particle that moves like that, would emit radiation (heat/light), losing kinetic energy and slowing down. So the electron would end up spiraling into the nucleus, which obviously doesn't happen.

    Then Bohr (in 1913 IIRC) made his model of the hydrogen atom, where he postulated (assumed) that the electrons were only 'allowed' to move in certain orbits, corresponding to energy (angular momentum) levels proportional to 1/(n^2) (where n is an integer, 1,2,3..etc). From this, he was able to correctly predict the approximate radius of the hydrogen atom (now known as the 'Bohr radius'), and also (approximately) explain the hydrogen atom spectrum - the spectral lines corresponded to photons who's energy difference was equal to the difference between such levels. (So the spectrum is understood as coming about from moving between these 'allowed' levels)

    There are several problems with Bohr's model - to begin with, it didn't really explain all the experimental results exactly. Nor could he explain why only certain energy levels were 'allowed'.

    At the same time, people were investigating the 'wave-particle duality' - that microscopic particles could act like waves, in some ways. Every particle has a wavelength known as the de Broglie wavelength. Using the de Broglie wavelength for electrons, it turned out that the 'allowed' orbits of hydrogen in the Bohr model had circumference that was equal to a whole number of electron wavelengths. The electrons orbiting the atom were acting like standing waves!

    The explanation for why the electron simply couldn't fall into the nucleus came about in 1925, with the Heisenberg Uncertainty Principle. Which states that a particle cannot simultaneously have a well-defined momentum and a well defined position. So, an electron cannot be stationary (a well-defined momentum - it's zero!) and located exactly at the nucleus (a well-defined position). Or to put it another way: Nothing in the universe is 'allowed' to be perfectly stationary.

    The 'final' solution to the problem of atoms came with the Schrödinger equation in 1927, when quantum physics was 'invented'. Using the Schrödinger equation, an equation similar to the wave equation, to describe the electron moving around the nucleus, you only get certain 'allowed' solutions. But the 'why' in this case is now purely mathematical - the equation only has a certain set of allowed solutions, analagous to the situation with the wave equation and standing waves.

    The Heisenberg uncertainty principle is 'built in' to the Schrödinger equation, so it too predicted that the electron would not fall into the nucleus. But unlike Bohr's model, the electron did not have a definite 'orbit'. It could be close or far from the nucleus. (thanks to uncertainty) But: If one calculated the average distance from the nucleus (or rather the 'expectation value'), then you got the same value as the Bohr model!

    The Schrödinger equation description of the hydrogen atom also explained quite a number of experimental results the Bohr model had not - and more importantly, it worked for every atom, and molecules! Not just Hydrogen. And it was much more accurate, but not 100% accurate, because it didn't take relativity into account. (This was done a few years later with the so-called Dirac equation.) The only problem is that it's very difficult to solve these equations - most of the time they cannot be solved exactly or analytically ("using paper and pen"), but must be calculated approximately, using computers. But in principle, it's all clear now. Paul Dirac said in 1929:

    So we still need chemists and experiments. But as computers get faster, and the methods of approximating the solutions to the Schrödinger and Dirac equations for atoms and molecules get better, 'quantum chemistry' as its called, is playing an increasingly important role.
     
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