Nodes of the hydrogen atom eigenstates 17 replies

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Mr. Matt Advanced Member

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#1 15 years ago

Radial nodes occur when the wave function for the electron is zero on a spherical surface of a particular radius (... hence the name radial node). Shown below is a plot of the probability of the 3s wave function. The two radial nodal surfaces are indicated in the figure. 5c1.jpg

Angular nodes occur when the wave function for the electron is zero along along directions specified by a particular angle (...hence the name angular node). Shown below is a plot of the probability of the 2p wave function. The angular nodal surface indicated in the figure is a plane that makes a 90° angle with the z-axis

In the hydrogen atom, 5c3.jpg where C = 2.18 * 10 -18 J. 5c2.jpg

The eigenstates, or stationary states, of the hydrogen atom are described at length in almost every general chemistry text book. If you haven't studied the hydrogen atom yet, you should turn to your text book before proceeding further with this tutorial. Often stationary states or eigenstates are simply referred to as quantum states in text books because they do not delve as deeply into the subject of quantum mechanics as we do here.

Hydrogen atom stationary states are labeled by a set of quantum numbers (n,l,m,ms), and also have the more informal designations 1s, 2s, 2p, 3s, 3p, 3d, .... The number of nodes in a hydrogen atom ground state is n-1, just by accident the same formula as for the particle between two walls. In hydrogen the situation can be more complicated because it is a 3-dimensional system while the particle between two walls is a simple 1-dimensional example. In hydrogen, nodes can be either radial or angular.

The energy of hydrogen atom eigenstates increases with principle quantum number n and the number of nodes according to the formula shown under the figures. Again, more nodes means more waviness and higher energy. Radial nodes mean more energy exists in motion where the electron moves closer and farther from the nucleus. Angular nodes mean the energy is stored in rotation of the electron around the nucleus.

So there.




Biggus Dickus Advanced Member

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#2 15 years ago

Amazing!




Mast3rofPuppets Advanced Member

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#3 15 years ago

Bah, I already knew that.




SpiderGoat

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#4 15 years ago
Mr. Matt Hydrogen atom stationary states are labeled by a set of quantum numbers (n,l,m,ms), and also have the more informal designations 1s, 2s, 2p, 3s, 3p, 3d, .... The number of nodes in a hydrogen atom ground state is n-1, just by accident the same formula as for the particle between two walls.

Yeah, well, we see this stuff when we're 15...




pInK_eLePhAnT

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#5 15 years ago

good to know.




Biggus Dickus Advanced Member

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#6 15 years ago

How a thread in the spam forum can be relevant to another thread?




Mr. Matt Advanced Member

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#7 15 years ago

It wasn't in the Spam forum.




Biggus Dickus Advanced Member

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#8 15 years ago

Haaaaa...Moved?




Mr. Matt Advanced Member

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#9 15 years ago

No. The other thread is where it has always been. This thread was created in the spam forum, however.




Biggus Dickus Advanced Member

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#10 15 years ago

Hmm I wonder...If this thread is relevant to another thread which is not in the spam forum, then why didn't you posted this in it? (if you wanted us to take that seriously, in the spam forum, nothing is really serious, IMHO)




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