How did they derive the modern model for the atom?

[gib65]

What I really wanted to ask about was how they derived those funny looking shapes for orbitals. I understand it has something to do with quantum physics (hence the reason I posted this in QM). The funny looking shapes I'm refering to are the regions of highest probability where you'll find an electron around a nucleus. It used to be described as a spherical cloud of negative charge surrounding a nucleus, but now you've got some that look like donuts, others that look like light bulbs stemming off one side of the nucleus. Some have several such light bulbs stemming 90 degrees from each other, and so on. How did they derive these shapes?

[mezarashi]

The quantum model of the atom is based on electron's probability distribution. Why the distribution curves look like so is a mathematical task that I must admit has eluded me. It is derived by that horrendous looking time and space variant Schroedinger's equation.

 

Back to the topic however, the funny looking shapes you refer to are known as the orbitals in the subshell. For each principle quantum number, there exists a number of available orbitals. The higher the principle quantum number, a higher a Azimuthal quantum number it will have. The Azimuthal quantum number basically describes something like its orbital momentum. In addition, there is a concept known as "spin" or magnetic spin. Hund's Rule and the Pauli Exclusion principle both indicate that for each orbital there can be only 2 electrons in orbit.

 

I found this link that shows the relationship between the probability distribution and the "funny shapes" they take on in 3D space.

 

http://www.chem.ufl.edu/~chm2040/Notes/Chapter_9/quantum.html

 

There is also an interesting phenomenon that happens to these orbitals when atoms get close together, called hybridization. The orbitals will actually combine to form a new hybrid orbital. This is usually studied in chemistry for chemical bonding. Interestingly, if you understand how these wave functions interact, it will better your understanding of the quantum atomic model. The interaction of atoms through quantum orbits is also used in semiconductor and nano-engineering, take for example carbon nano-tubes ^^

[Johnny5]

What I really wanted to ask about was how they derived those funny looking shapes for orbitals.

 

Answer: Mathematical theory of probability. Treatment of electron's position as a random variable, in the center of mass reference frame of a single hydrogen atom.

 

Born Interpretation of

[math] \psi^* \psi [/math]

 

I can actually run through it for you, its really complicated though.

 

The quickest way to answer your own question, depending on how much you already know, is to find a site that discusses QM, and ask about some of the formulas you see there.

 

You will get different answers from different people, i assure you.

[Ophiolite]

You will get different answers from different people, i assure you.

I guess that's the uncertainty principle at work.

[Annemarie]

Another key point here is that electrons weigh 10^-31 KG, and are TINY, it's not possible for us to ever "see" an electron, in the tradition sense of a photograph (this is because the wavelength of light that is visible to us has too long a wavelength to be diffracted opr affected in anyway by the presense of an electron in it's path, and when a photon is incident on an electron the interaction that occurs, (bound free absorbtion or scattering, in any number of processes), we still won't be able to "see" it. Therefore it has no "shape". The pictures that you have seen are visual representation which try to help us recall the information more clearly, visual aids always help, but they're not true to the quantumness of the atom.

[gib65]

http://www.chem.ufl.edu/~chm2040/Notes/Chapter_9/quantum.html

 

Thanks for the website. It looks like an easy read and I'll take a look at it later.