The hydrogen atom ground state

📚 The hydrogen atom is the simplest and most abundant of all elements. In this video, we study a range of properties of the ground state of the hydrogen atom. We explore the energy necessary to dissociate the proton and electron in hydrogen, called the ionization energy; the typical size of a hydrogen atom, called the Bohr radius; and the relative contribution of kinetic and potential energies in hydrogen, which we relate to the virial theorem.

0:00 Intro
1:12 Hydrogen atom basics
4:04 Ground state energy: ionization energy
8:50 Ground state wave function: Bohr radius
22:55 Virial theorem
29:20 Wrap-up

⏮️ BACKGROUND

⏭️ WHAT NEXT?

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Director and writer: BM
Producer and designer: MC

[paulbk]

One of those safest places in YouTube where I can press the like button and praise the video first and then relax back to watch the you very much Prof. M team👍👍👍👍

[itsawonderfullife]

Your high quality QM videos are greatly appreciated. Thanks. Anxiously waiting for more in other topics.

[YossiSirote]

Excellent explanation of p(r) vs R(r)! I really appreciated your geometric insight. 😊

[greenstar]

Those videos are beyond excellent, do you mind sharing your future projects on the channel or maybe present a map of the several components of QM, then say what we've covered so far and where we are heading to

[sandippaul]

Ma'am can you please start a full course on Quantum Optics? That will be very helpful. And we missed you two.

[YossiSirote]

At 20:15 you ask: “what is the mean of this?” I thought you meant what is the mean value of the electron distance <r>, which is actually 1.5a_0. But in the captions you said “meaning”. 😂 … Either way - great video.

[quantumeveryone]

Thanks for another very nice video. I have just two comments. The first one is relatively minor. When mentioning the virial theorem, you might also want to include the much more general Kramers-Pasternak relations, which give closed-form solutions for the expectation values for any power of r (positive or negative) in any energy eigenstate. Very powerful, but not very well known.
The second comment is more substantial. When discussing the maximal probability for the electron in the ground state, you need to discuss two different cases. One is looking at the probability to be in a thin spherical shell, while the other is simply the probability to be in an infinitesimal cube. You do properly describe the former, which shows that the location where the maximum occurs is at the Bohr radius for the ground state. You also describe properly why the probability goes to zero at the origin, namely that the volume of the thin shell shrinks to zero as r goes to zero. But, if you instead look at the probability to be in an infinitesimal cube, the probability is maximal at the origin, indicating for s-wave states, one can think of them as being most likely inside the nucleus. This is not a crazy thing to think of, as the phenomenon of electron capture occurs precisely because s-wave electrons have a nonzero probability to be inside the nucleus. The main reason why the electron is not found inside of the nucleus “most of the time, ’ even if it is most probable to (in the cubic volume case), is because the size of the nucleus is so small.

[hugom]

Would it be correct that at higher energy levels the kinetic energy of the electron decreases as potential energy increases?

[StephenGillie]

It's so weird hearing "so-called" in a neutral way, when it was originally an insult. But I guess YouTube has reclaimed it.

[Handelsbilanzdefizit]

Replace electron with anti-proton! Would this work?
Now you studied hydrogen well enough, make suggestions about fusion.
Some of the first quant.-physicists had enormous pressure to deliver something practical (A-Bomb).
Funding, personal career, etc. ... depended on results.
Think, climate doesn't create enough urgence to todays scientists.

[haniamritdas]

We can learn so much from statistics. But these single points on a root mean square distribution normalised over an infinite domain are nothing but statistical necessities. They give us information about the world, but they are not a theory of motion or composition; just generalized quadratics from abstract number theory.

These days the scientists are claiming that our statistical analysis proves that reality is merely a statistical composition, but this is a tautology at best, and a metaphysical foundation at worst.

There are lies, damnable lies, and statistics. Then there's quantum mechanics.