Empty space in atoms vs orbits

[skepticwulf]

We often read that atoms are mostly empty space. A common example is given as, if the atom was a big as a football stadium the nucleus would be as big as a tennis ball on the center and nearest electrons circling around at far side of seats or something like that.
How does this reconcile with the fact that first orbit of electron is "s" and it has a shape of sphere; the electron occupying a "s" orbit can be anywhere in this orbit determined by quantum mechanics? The orbit is actually an probability function of where you might find an electron if you want to calculate it.
If nucleus is so small surrounded by "s" orbit, how can we say that nearest electrons are far far away?
Doe it mean electrons mostly occupy outer shell of this sphere? rarely traveling close to nucleus?

 

[aman patel]

no..electron do come closer to nucleas but its quatam physics don't allow us to put permennant place that we can find it...we can find them on sphere as you said..there are diffrent types of spheres according to their shap S is circular...further you can study by do some google my friend...

 

[bhobba]

Doe it mean electrons mostly occupy outer shell of this sphere? rarely traveling close to nucleus?

Particles in QM don't actually have a position until its observed to have a position. Those orbital diagrams give the probability of finding it in that position if you were to observe it.

Thanks
Bill

 

[skepticwulf]

Can we then safely assume the picture is false? there's no huge space between nucleus and first orbit of electrons but electrons can be anywhere in that particular s orbit filling the sphere?
The reason I'm focusing on s orbits is s being the closest to the nucleus and is most relevant with stadium analogy.

 

[jtbell]

We often read that atoms are mostly empty space. A common example is given as, if the atom was a big as a football stadium the nucleus would be as big as a tennis ball on the center and nearest electrons circling around at far side of seats or something like that.

This kind of image is used in connection with the Bohr model with its circular orbits, which has been obsolete for ninety years or more. Banish it from your mind.

 

[skepticwulf]

This kind of image is used in connection with the Bohr model with its circular orbits, which has been obsolete for ninety years or more. Banish it from your mind.

:) ok

 

[PWiz]

The thing is that in the standard model all elementary particles (including electrons) are assumed to be point like, and as such have no spatial dimension. So it doesn't really make much sense to ask how much of space in an atom is not occupied by electrons, because electrons do not themselves have any volume.

 

[skepticwulf]

one thing can travel at certain distance, at "d", from nucleus regardless of its volume. it can not?
my question is, inside a s orbit, do electron prefer designated areas more to the other like closer to shell rather than center OR do they distribute themlseves equally all the volume of sphere "s"? If latter is correct, than stadium analogy should be totally false as there's no such thing as empty space between nucleus and first 1s or 2s electrons. They can be anywhere in "s"

 

[PWiz]

one thing can travel at certain distance, at "d", from nucleus regardless of its volume. it can not?

Motion is not so easy to understand on the quantum level. You have to make an observation (an interaction) on the electron to determine to its position, but this inevitably affects its momentum, and hence its motion. Besides, in an atom electrons are just standing waves in bound states, so the idea of motion doesn't seem all that useful. AFAIK, the expectation value for momentum is always 0 in a stationary state.

I'm not aware of the details, but for n=1 (the H atom), Schrödinger's wave equation solution gives us a probability density function that only depends on the radial distance from the nucleus. So yes, the probability of finding an electron will vary within the s orbital (of an H atom).

 

[jtbell]

do electron prefer designated areas more to the other like closer to shell rather than center OR do they distribute themlseves equally all the volume of sphere "s"?

Neither, in general. See Figure 3-4 on the following page, for the ground state of hydrogen:

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

Warning: You often see plots of the "radial probability density" which goes to zero as the distance from the center goes to zero, like this:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html

This is something different from the first link. The quantity plotted in the first link is the probability per unit volume, whereas the second link shows the probability per unit distance from the center (nucleus). They're different because, crudely speaking, (probability per radial distance) = (probability per volume at that distance) * (number of points at that distance). As the distance from the center increases/decreases, so does the number of points at that distance. Think of the area of a sphere, 4πr². There are fewer points with small r than with large r, and only one point with r = 0.

[Added] Another way to think of the difference: the first graph is (loosely speaking) the probability of the electron being located at a single point with the specified distance from the center, whereas the second graph is the probability of the electron being located anywhere on a spherical shell with the specified radius.

 

[bhobba]

one thing can travel at certain distance, at "d", from nucleus regardless of its volume. it can not?

The picture of a quantum particle traveling at a certain distance is false. QM is a theory about the results of observations. When not observed you can't say it has any property like traveling at a certain distance.

Thanks
Bill

 

[skepticwulf]

Neither, in general. See Figure 3-4 on the following page, for the ground state of hydrogen:

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html

Warning: You often see plots of the "radial probability density" which goes to zero as the distance from the center goes to zero, like this:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html

This is something different from the first link. The quantity plotted in the first link is the probability per unit volume, whereas the second link shows the probability per unit distance from the center (nucleus). They're different because, crudely speaking, (probability per radial distance) = (probability per volume at that distance) * (number of points at that distance). As the distance from the center increases/decreases, so does the number of points at that distance. Think of the area of a sphere, 4πr². There are fewer points with small r than with large r, and only one point with r = 0.

[Added] Another way to think of the difference: the first graph is (loosely speaking) the probability of the electron being located at a single point with the specified distance from the center, whereas the second graph is the probability of the electron being located anywhere on a spherical shell with the specified radius.

Thank you, it was comprehensive.