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### Topic: Quantom mechanical Model  (Read 9217 times)

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#### ssssss

• Guest ##### Quantom mechanical Model
« on: August 28, 2004, 11:39:46 AM »
Ok i got real problem in chemistry,toughest approach i have ever dealt with.Please explain your answer/approach in detail .I will be grateful to the replier.

I am studying quantom mechanical model of an Atom.
This is what i have understood:
1.It is observed by Schroninger Equation which is based upon the wave nature of matter.
2.Solving Schrodinger equation we get a value,in common called as psi.This value tells about the probability of finding an electron in an atom.[Correct position could never be determined as concluded by Heisenberg].
3.This psi has no significane.The square of this has a significane which is proprtional to the probability density.Also this psi has two factors called Radial wave function and Angular wave function.Now i am clear with the radial wave function,it tells about the orbital,electron probability with increasing Distance from the nucleus.

My 1st point is that what is this angular wave function?

4.Now taking both the functions into account we overall makes the probability Density curves.
This gives a sherical shape called the S Orbital,A two lobed shape called p orbital and further more.Now i am clear with the probability distribution of s orbital.My 2nd Doubt arises with p orbitals.

Now as you know it contains of 2 lobes,in common a dumbell shape seperated by a nodel Plane.We have probability of electrons in any of the two lobes.Now my question is that if at an instant an electron is in one of the lobe than how could at any other instant the electron can exist in the other lobe as we got a nodel plane in between.This approach is just hurting my intuition.

Lastly can you tell me what is the correct order in which electrons fill in the orbital.I know it is according to aufbau rule but please give correct order as i am having contradiction somewhere.Also when we write an orbital configuration of ion we remove or add electrons in the parent configuration of atom.Can you tell in which way we remove or add electrons.

« Last Edit: August 28, 2004, 11:41:09 AM by ssssss »

#### Demotivator

• Guest ##### Re:Quantom mechanical Model
« Reply #1 on: August 30, 2004, 09:35:23 AM »
1) The angular wave function includes the information on how the orbilal is oriented. One of the angular components,the Phi component, is:
[1/sqroot(2(pi))]exp(iml(phi))
where ml is the magnetic quantum number which defines the possible directional orientations of an orbital of value l. For a P orbital m has values of 0, 1, -1 for pz, px, py.

2)It is an irksome aspect of quantum physics that matter is to be viewed in a dual particle/wave fashion. The wave equation is based on a standing wave model. So The electron can be viewed as completely occupying the orbital as a "cloud" of varying densities within the orbital, just as a standing wave is complete with varying amplitudes above and below the node. This is unlike the Bohr model where the assumption was that an electron is a particle revolving in an orbit.
No one really knows what these things look like. Both Particle laws and wave laws are applied depending on whichever explains a phenomenon.

3) Order of orbital filling:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p etc
Contradiction? like why the 4s is filled before the 3d?
It's because higher level s electrons actually have some presence (check out their radial probability graphs) near the nucleus which lower their energy relative to the d orbitals.

Also there are some anomalies that occur during afbau filling. Like special cases:
Cr:  [Ar] 4s1 3d5
Cu: [Ar] 4s1 3d10
That's because the electrons like to either half fill or completely fill an orbital set if possible. The 4s and 3d orbitals are close enough in energy to allow for such a jump.
« Last Edit: August 30, 2004, 11:06:56 AM by Demotivator »

#### ssssss

• Guest ##### Re:Quantom mechanical Model
« Reply #2 on: August 31, 2004, 04:26:36 AM »
Thanks friend.You really did much for me.I was really messed up with these points but now its clear.

But why this odd name-Demotivator.
« Last Edit: August 31, 2004, 04:37:58 AM by ssssss »

#### Demotivator

• Guest ##### Re:Quantom mechanical Model
« Reply #3 on: August 31, 2004, 05:02:40 PM »
You're welcome, sssssssssssssssssssss Hey, I like odd names #### Juan R. ##### Re:Quantom mechanical Model
« Reply #4 on: September 03, 2004, 12:43:02 PM »
Hi chemists

I read that those nodal planes of p and d orbitals vanish when one introduce relativistic effects. That is, the relativistic p orbital has not orbital planes. I did not the calculations for verifying this!

However, there is a typical error of interpretation of wave functions in usual textbooks. The interpretation of wavefunction phy is probabilistic, i.e. P = (phy)2 is the probability of finding the particle at a point.

The usual interpretation of p-orbitals, particles in a box (note that there are nodes inside the box for the corresponding wavefuntions) or tunnel effects is not correct one. A previous proffesor mine said that the problem of the p-lobes was a “paradox” of quantum mechanics. There is no paradox. I discuss next only p orbitals by brevity but the discussion could be adapted to the other cases.

The electron is not a part of time in a lobe and after of a time it is in the other lobe. First, that is not the interpretation of the stationary Schrödinger equation H*phy = E*phy. Second, in quantum mechanics there is not trajectories, then the electron cannot be here and after there, passing by this point or plane. There are not trajectories!

Really the P says us that the electron is “distributed” over a region or volume. Forget the physicist point of view and take a more chemical view. This is easy to see from the density charge, density = e*P, with e the electron charge in your favorite units. Then one can see half one electron in a lobe (density = e/2) and other half one in the other lobe, with a total charge of e in all the space, because the total probability is 1.

According to Schrödinger, this interpretation is not correct because one cannot measure fractions of charge, i.e. the electron is an indivisible particle. One cannot detect 0.5 electrons here and 0.5 electrons in that other region. But one would remember that p orbitals say that succeed before the measure process. When one measures electron position the wavefunction collapses to a Dirac delta function; that is, all the charge (e) is concentrated in an only point. We then detect a punctual particle with charge e.

It is somewhat as a water cloud, disperses in the sky. When some tiny part of it collapses, then makes a little sphere of water. The analogy is water cloud <=> Orbital and water sphere <=> electron as a particle.

I believe that this interpretation of electron as a diffuse cloud that collapse is more close to reality.

With regards to order filling of 4s and 3d, some textbooks are mistaken as it is claimed that 3d level has a lower energy than 4s for elements as scandium, but the real configuration is 4s2 3d1. The details of this are computational (quantum chemistry). The configuration of first transitions elements is

Sc 4s2 3d1
Ti 4s2 3d2
V 4s2 3d3
Cr 4s1 3d5
Mn 4s2 3d5
Fe 4s2 3d6
Co 4s2 3d7
Ni   ?
Cu 4s2 3d9
Zn 4s1 3d10

The case of nickel turns out to be very interesting. According to many chemistry and physics textbooks the configuration of this element is given as 4s2 3d8. However the research literature on atomic calculations (see below) always quotes the configuration of nickel as 4s1 3d9.

Note: a Dirac function, D, can be see as the limit of an exponential

D(x) = limit  [exp(-(x2)/a]
a --> 0

Literature:

C.W. Bauschlicher, P. Siegbahn, and G.M. Petterson. The Atomic States of Nickel. Theoretica Chimica Acta 74: 479–491, 1988.

:red_bandana:
The first canonical scientist.

#### ssssss

• Guest ##### Re:Quantom mechanical Model
« Reply #5 on: September 06, 2004, 03:40:52 AM »
Hi chemists

I read that those nodal planes of p and d orbitals vanish when one introduce relativistic effects. That is, the relativistic p orbital has not orbital planes. I did not the calculations for verifying this!

However, there is a typical error of interpretation of wave functions in usual textbooks. The interpretation of wavefunction phy is probabilistic, i.e. P = (phy)2 is the probability of finding the particle at a point.

The usual interpretation of p-orbitals, particles in a box (note that there are nodes inside the box for the corresponding wavefuntions) or tunnel effects is not correct one. A previous proffesor mine said that the problem of the p-lobes was a “paradox” of quantum mechanics. There is no paradox. I discuss next only p orbitals by brevity but the discussion could be adapted to the other cases.

The electron is not a part of time in a lobe and after of a time it is in the other lobe. First, that is not the interpretation of the stationary Schrödinger equation H*phy = E*phy. Second, in quantum mechanics there is not trajectories, then the electron cannot be here and after there, passing by this point or plane. There are not trajectories!

Really the P says us that the electron is “distributed” over a region or volume. Forget the physicist point of view and take a more chemical view. This is easy to see from the density charge, density = e*P, with e the electron charge in your favorite units. Then one can see half one electron in a lobe (density = e/2) and other half one in the other lobe, with a total charge of e in all the space, because the total probability is 1.

According to Schrödinger, this interpretation is not correct because one cannot measure fractions of charge, i.e. the electron is an indivisible particle. One cannot detect 0.5 electrons here and 0.5 electrons in that other region. But one would remember that p orbitals say that succeed before the measure process. When one measures electron position the wavefunction collapses to a Dirac delta function; that is, all the charge (e) is concentrated in an only point. We then detect a punctual particle with charge e.

It is somewhat as a water cloud, disperses in the sky. When some tiny part of it collapses, then makes a little sphere of water. The analogy is water cloud <=> Orbital and water sphere <=> electron as a particle.

I believe that this interpretation of electron as a diffuse cloud that collapse is more close to reality.

With regards to order filling of 4s and 3d, some textbooks are mistaken as it is claimed that 3d level has a lower energy than 4s for elements as scandium, but the real configuration is 4s2 3d1. The details of this are computational (quantum chemistry). The configuration of first transitions elements is

Sc 4s2 3d1
Ti 4s2 3d2
V 4s2 3d3
Cr 4s1 3d5
Mn 4s2 3d5
Fe 4s2 3d6
Co 4s2 3d7
Ni   ?
Cu 4s2 3d9
Zn 4s1 3d10

The case of nickel turns out to be very interesting. According to many chemistry and physics textbooks the configuration of this element is given as 4s2 3d8. However the research literature on atomic calculations (see below) always quotes the configuration of nickel as 4s1 3d9.

Note: a Dirac function, D, can be see as the limit of an exponential

D(x) = limit  [exp(-(x2)/a]
a --> 0

Literature:

C.W. Bauschlicher, P. Siegbahn, and G.M. Petterson. The Atomic States of Nickel. Theoretica Chimica Acta 74: 479–491, 1988.

:red_bandana:

Ohhh good that p orbital is a diffused cloud of electron.Gee i wonder how will these things look like in reality.

Anyway thanks for that knowledge about Ni configuration.

#### Juan R. ##### Re:Quantom mechanical Model
« Reply #6 on: September 07, 2004, 08:02:19 AM »
Hi