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shivamdabas
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I know that the shape of s orbital is sphere, p orbital is dumbbell shaped and d orbital is like a doughnut but why do these orbitals have these shapes why not some other shape.
Think of the total wavefunction as the product of an angular wavefunction and a radial wavefunction.shivamdabas said:how can we know about the shape of these orbitals.
shivamdabas said:Thanks for you reply
Now, I know that the shapes of the orbitals are governed by nodes which are the places where probability of finding an electron is zero but how can we know about the shape of these orbitals.
DrDu said:The node count mentioned only works for real orbitals. As the OP mentioned doughnut shaped d-orbitals, I think he talks about complex orbitals with definite z-component of angular momentum.
In these toroidal shaped orbitals the phase of the wavefunction changes, at least in the simplest cases, like exp(imf) where f is the angle in the x-y axis. The real orbitals are combinations of complex orbitals with +m and -m, hence they change like cos(mf) or sin(mf).
ZapperZ said:3. If you plot the wavefunction, you get those shapes!
PhaseShifter said:Well, that's great if you can visualize four dimensions to plot it in, or visualize the probability density as the turbidity of a fog...
shivamdabas said:I know that the shape of s orbital is sphere, p orbital is dumbbell shaped and d orbital is like a doughnut but why do these orbitals have these shapes why not some other shape.
shivamdabas said:Thanks for you reply
Now, I know that the shapes of the orbitals are governed by nodes which are the places where probability of finding an electron is zero but how can we know about the shape of these orbitals.
ZapperZ said:Who said anything about plotting?
ZapperZ said:Er... let's get the obvious out of the way here because I think there's some miscommunications going on.
1. You solve the Schrodinger equation for, say, the hydrogen atom. You get the wavefunction.
2. In doing #1, you end up with two parts: the radial solution R(n,l), and the orbital solution P(l,theta).
3. If you plot the wavefunction, you get those shapes!
So to know where those shapes came from, you have to solve for the wavefunction. Check out this link:
http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html
PhaseShifter said:Since you asked:
I was just pointing out that the way you plot orbitals isn't the normal way you plot a function.
I'm not just being pedantic or trying to get the last word in...from my experience teaching, it's a non-trivial step for some people to follow.
ZapperZ said:So to know where those shapes came from, you have to solve for the wavefunction. Check out this link:
http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html
shivamdabas said:Thanks everyone especially ZapperZ and PhaseShifter, if you can then please explain me what is radial wave function and angular wave function.
Anti-Crackpot said:Great link and I want to understand this better, ZapperZ, so notationally speaking...
n, m, l are Principal, Magnetic and Azimuthal Quantum Numbers
a_0, I am assuming is the Bohr Radius.
e, in these equations, I am also assuming is Euler's number. (As opposed, for instance, to the elementary charge)
R_ml, Y_lm and r are what exactly?
TIA,
AC
Atomic orbitals are regions around the nucleus of an atom where electrons are most likely to be found. They are represented by mathematical equations that describe the probability of finding an electron in a specific location.
There are four types of atomic orbitals: s, p, d, and f. These types differ in shape, size, and orientation in space.
The s orbital is spherical in shape, the p orbital is dumbbell-shaped, the d orbital is cloverleaf-shaped, and the f orbital is more complex and has multiple lobes.
Electrons fill atomic orbitals from the lowest energy level to the highest, following the Aufbau principle. Each orbital can hold a maximum of two electrons, and they must have opposite spins.
The shapes of atomic orbitals are determined by the quantum numbers that describe them. These numbers represent the energy, size, and orientation of the orbital, and they dictate the shape of the orbital based on the solutions to the Schrödinger equation.