Most of us are not used to thinking of electrons as waves, and we still refer to the density as the probability of finding the electron (a particle). The electron density diagrams given in many text books can be plotted using the appropriate wave functions. They are not the results of artists' imagination. In this demonstration, the computer will plot the densities according to an algorithm, which is based on the wavefunctions of various atomic orbitals.
The representation of atomic orbitals and their visualization has fascinated young and old scientists for ages. This link gives interesting pictures and molves. Copngratulation to Dean Dauger - dauger@physics.ucla.edu, who has been a student winner twice in a row in Computer In Physics's Software Contest. His real-time visualization of the quantum mechanical atomic orbitals is a real treat.
Some more links regarding atomic orbitals:
The probabilities of finding electrons anywhere in a three dimensional space around the hydrogen nucleus are proportional to the squares of the values of the wavefunction in the volume element corresponding to that space. Thus, the plot of probability should be done in a 3-dimensional space. However, such a plot not only requires a high degree of programming and viewing skills, it also takes a lot of computer time and a better monitor to do the job right. The next best way to represent them are looking at cross sections. This is the way we treat this subject here.
Lately, many diagrams to represent atomic orbitals have been made available via the web. The picture shown here is a 3p_{z} atomic orbital. The learning matter of chemistry is linked to a few useful places that provide various forms.
probability | |. | | . | | . | | . | . | . | . | . |________________________________________._______ rYou may feel the probability of finding the electron is the highest in the nucleus, yet you have learned that the electron is most likely at a distance r = 53 pm from the center of the atom.
The radial density plot of 1s orbital has a shape as shown below:
probability | | | | | | . ' . | . . | . . | . . |________________________________________._______ rAt the center of the atom, the value of the wavefunction is large, but when r = 0, the volume element (4*pi*r^{2}) is almost zero when r -> 0. Thus, the radial distribution rises as r increases, reaching a maximum at some value of r. For the H atom, the maximum of the radial distribution is at r = 53 pm.
The simulation of electron density and showing orbitals is very well done in
The following program is no longer available, but the description is left here to you to used when you look at the above simulation
The computer plots of cross section of electron clouds for 1s, 2s, 2p, 3s, 3p, and one 3d orbital are available. When the orbital is plotted the radial density is plotted versus r in the right lower corner of the screen. The function used for the plot is shown on the bottom of the screen. You do not need to copy the wave function, as you will get that later in a chemistry course.
The purposes of the computer simulation are given below:
The Orbitron is a link that gives wonderful views of the atomic orbitals.
If your answer is...I'm lost!
Consider...
An ns orbital has (n-1) nodal shell(s). When n = 2, there is 1 nodal shell.
If your answer is...2s
Excellent...
How does a electron get through a nodal shell?
If your answer is...I'm lost!
Consider...
The 2s orbital has a nodal shell, whereas the 2p_{z}.qn
orbital or 2p orbitals have a nodal plane.
If your answer is...p_{z} or 2p_{z}
Excellent...
A nodal plane is a plane in which the probability of finding a
electron is zero. The 2s orbital has a nodal shell, whereas the 2p_{z}
orbital or 2p orbitals have a nodal plane.
If your answer is...I'm lost!
Consider...
Not all d orbitals have the same shape.
If your answer is...a
Excellent...
All p orbitals have a dumbbell shape, but from the plot, you should
recognize the difference between 2p and 3p orbitals.
If your answer is...I'm lost!
Consider...
Only a is accepted as the correct answer, although reasons given
in other items sound all right.
If your answer is...a
Excellent...
Electron density means finding the electron per unit volume.
Radial electron density means finding the electron at r.
If your answer is...I'm lost!
Consider...
The Bhor's radius is 53 pm.
If your answer is...53 pm
Excellent...
The results is the same as Bohr's prediction.