orbital doubt

by Petrichor Wed Oct 09, 2013 12:11 pm

If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?

by FluteHolder Wed Oct 09, 2013 12:13 pm

So you also want to try for Nobel Prize like our Rahul? Smile

by Petrichor Wed Oct 09, 2013 12:16 pm

Yes, I would like my name to be pronounced with a halting Swedish accent. Smile

Nobel is optional.

by Rishi Wed Oct 09, 2013 12:21 pm

Petrichor wrote:If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?

>>> One MIT educated physics major told me that this model of electrons going around a nucleus is not correct. He said there is something called electron cloud.

The guy works with me. He has a degree in mechanical engineering also. He told me that he did not know what he could do with his undergraduate degree in Physics. So he got an engineering degree. He said even mechanical engineering is nothing but physics.

by Petrichor Wed Oct 09, 2013 12:24 pm

Yes, it is cloud alright...and the s-orbital is spherical, supposedly. I was thrown off by sal khan that electron is likely found near the center of the sphere...which confused me.

by Seva Lamberdar Wed Oct 09, 2013 1:30 pm

Petrichor wrote:If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?

yes, with the hundred percent probability (such as during the beta decay).

by Petrichor Wed Oct 09, 2013 1:56 pm

Seva Lamberdar wrote:
Petrichor wrote:If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?
yes, with the hundred percent probability (such as during the beta decay).

I am talking about a non-excited state. Just the basic electron configuration...

by MaxEntropy_Man Wed Oct 09, 2013 2:17 pm

all physical measurements in quantum mechanics should be considered as expectation values which can be computed from knowledge of the wave function of the system. in that sense the deterministic bohr model is incorrect though convenient.

by Rishi Wed Oct 09, 2013 2:26 pm

Seva Lamberdar wrote:
Petrichor wrote:If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?
yes, with the hundred percent probability (such as during the beta decay).

Seva,

Did you already know this stuff or did you google it?

I thought this is far away from agricultural engineering and aerospace engineering.

by MaxEntropy_Man Wed Oct 09, 2013 2:33 pm

Rishi wrote:
Seva Lamberdar wrote:
Petrichor wrote:If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?
yes, with the hundred percent probability (such as during the beta decay).
Seva,

Did you already know this stuff or did you google it?

I thought this is far away from agricultural engineering and aerospace engineering.

don't all engineers do a basic chem course? and most also do what used to be called mod phy-- quantum + solid state.

by Rishi Wed Oct 09, 2013 2:52 pm

MaxEntropy_Man wrote:
Rishi wrote:
Seva Lamberdar wrote:
Petrichor wrote:If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?
yes, with the hundred percent probability (such as during the beta decay).
Seva,

Did you already know this stuff or did you google it?

I thought this is far away from agricultural engineering and aerospace engineering.
don't all engineers do a basic chem course? and most also do what used to be called mod phy-- quantum + solid state.

>>>> That may be. But how many remember that stuff if they have gone ahead and received advanced degrees in fields like civil engineering? In fact, I have met some guys (IIT alumni included) who have flunked the first part of the P.E exam i.e the EIT exam which tests your knowledge on the fundamentals in various branches of engineering.

by MaxEntropy_Man Wed Oct 09, 2013 10:42 pm

MaxEntropy_Man wrote:all physical measurements in quantum mechanics should be considered as expectation values which can be computed from knowledge of the wave function of the system. in that sense the deterministic bohr model is incorrect though convenient.

in QM, the wave function of a system contains in principle all the information about the system. it is in general a complex valued function. its absolute value squared (after suitable normalization), i.e. product with its complex conjugate, gives the probability density function. you can use this to calculate the expectation value of any quantity including distance from the nucleus. so the bohr radius that you hear about is the most probable distance, and not an exact specification. it turns out that for the ground state of the hydrogen atom, the probability density function has a spherical symmetry.

in fact you can see that the bohr theory is absurd if you consider the following contradiction. in basic chemistry you learn that the orbital angular momentum of the electrons is quantized and that it is equal to sqrt[(l(l+1)](hcross), where hcross is planck's constant over 2*pi, and l =0,1,2,....n-1 (where n is the principal quantum number). in the ground state of the H-atom, l=0 and thus the orbital angular momentum is zero. however, the bohr picture with its definite orbit at a fixed distance will give you a non-zero orbital angular momentum given by the vector cross product of its position with its linear momentum. that contradiction alone tells you that the bohr model can't be correct. in fact the QM result (zero orbital angular momentum) is the correct result and the bohr picture is wrong. the resolution lies in the principle of superposition which is fundamental to QM. if you really want to know how to resolve the contradiction, i can write more.

by Seva Lamberdar Thu Oct 10, 2013 9:31 am

Rishi wrote:
Seva Lamberdar wrote:
Petrichor wrote:If an electron could be found in 1s^1 position, it is stated that it could really be anywhere within the sphere and that it is all probabilistic anyways. I had an outdated classical understanding that 90% of the time the electron will be on the circumference surface of the sphere give or take a few gazillionths of a mm. Is it really true that electrons could possibly be found a few gazillionths of a mm from the nucleus itself, in a slim probabilistic kinda way?
yes, with the hundred percent probability (such as during the beta decay).
Seva,

Did you already know this stuff or did you google it?

I thought this is far away from agricultural engineering and aerospace engineering.

I knew it as a farmer.

Honestly speaking, if you read my profile on the Internet, I have worked on the design / analysis of equipment used in the nuclear reactors, which included taking into consideration in the design the short term and long term effects of alpha and beta particles and gamma radiation on humans and materials (metals and plastics etc.) in reactor vicinity.

by Petrichor Thu Oct 10, 2013 4:34 pm

Thanks Max - did not entirely follow the Bohr-repudiation argument but it suffices that it involves higher math, angular momentum etc. Just refreshing the electron configurations, periodic trends, exceptions and the four quantum numbers for now. For now, let me bask in the 92% on the most recent test. Time to step up the game - more quizzes and tests round the corner.

For a discussion on superposition principle, general QM topics including wave function, we will defer it for some wisdom when there is a future 'guested-in' brunch at a local college.

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