Thread: please explain me quantum mechanical model of electron

hi i didn't understand this concept from the book ,could you please make it clear for me. I'm also searching for material on solid state to understand the basic concepts( especially point groups and symmetry),could you please help me....

Oh, dang. So that is a really good question in your thread title. Unfortunately, it would be almost impossible answer you on this site (you could legitimately write a book on the topic and still not fully explain it). I am going to let someone else attempt to answer this concisely, because I'm afraid that if I begin to answer it, I will be sitting here at my computer for weeks. But just to start, an electron is a subatomic particle that can be described as a wave (in quantum theory, you could technically describe anything as a wave (anything that is moving) because everything has a wavelength... check out the de Broglie wavelength equation). Oh man, I can feel myself beginning to dig up everything I know about quantum theory (actually not that much! But it is kind of complicated and difficult to write in words). So I will let someone else take over from here.

Originally Posted by Darling

hi i didn't understand this concept from the book ,could you please make it clear for me. I'm also searching for material on solid state to understand the basic concepts( especially point groups and symmetry),could you please help me....

This is quite a challenge. Here is an attempt I made once, in another context, but it may help a bit.

In Quantum Mechanics, which is needed to explain how matter at the atomic scale behaves, the concept of a "particle" becomes problematic. Instead, one deals with "wave-particles", which behave in some respects like a particle and in others like a wave. The concept of the "orbital" was developed to replace the old Rutherford-Bohr idea of the "orbit" of an electron moving round the nucleus like a planet around the sun, with something that recognised the wave-like aspect. The orbital is like a "probability wave", the probability being the likelihood of finding the electron at various points in space. The electron in an orbital has kinetic and potential energy, so is a bit like an orbiting planet. It also has a "spin", a bit (though not wholly) like a planet spinning on its axis. However, unlike an orbiting planet it may or may not have any angular momentum! Electrons in s orbitals have no angular momentum, while those in p, d, f etc orbitals do.

It is impossible to track a trajectory for an electron in any of these orbitals: all one can say is there is a probability of finding them at a certain point, given by the mod square of the amplitude of the "wavefunction" (a.k.a. state function or eigenfunction) at that point. One knows less about the motion of a "particle" in QM than one would in classical mechanics. This is most famously encapsulated in Heisenberg's Uncertainty Principle, which sets limits on what information one can have simultaneously about a QM wave-particle.

The various types of orbital can be compared with a standing wave, e.g. in the fundamental and harmonics of a resonating vibrating string. The 1s orbital has only +ve phase (fundamental) while the 2 s (1st "radial" harmonic) has 2 concentric spherical shells, one of +ve phase and one of -ve phase. The 2p has one lobe of +ve phase and one of -ve phase, so this too is an "harmonic" but angular rather than radial this time, so "vibrating" differently in space. (Incidentally a vibrating rubber ball will have rather similar resonant modes of vibration.) Each orbital can contain 2 electrons, with opposed spin orientations (the Pauli Exclusion Principle limits it to 2). Each electron occupies the full orbital however.

Some of this is very counterintuitive, which is why I found (and still find) it so fascinating. If any of this is unclear I'll do my best to try to find alternative ways to describe it to make it clearer.

Symmetry groups are used in chemistry to exploit the fact that orbitals have a wave-like character and thus can interfere constructively or destructively with one another, according to their phase. This enables conclusions about chemical bonding and relative energy levels to be drawn, in many cases, on the basis of qualitative reasoning. This saves the huge arse-ache of trying to do multi-centre QM calculations in each case. But group theory of symmetry groups is another big subject in its own right. I found F Albert Cotton's book on it excellent, but that was 40 years ago - I don't know if it is still used today.