What is the radius of the hydrogen atom? How has this answer changed over time? Quantum mechanics is fun and cool. Tablet math is tedious.
If anyone is trying to solve a homework problem and just googled this, a_0= 0.53e-10 m
Does anybody actually read these things?
The textbook is Principles of Quantum Mechanics by Professor R. Shankar.
Here is a link to his YaleOpenCourse course: https://www.youtube.com/watch?v=KOKnWaLiL8w&list=PLFE3074A4CB751B2B
You can join my Patreon if you like. I post a new, patron-only video each month. https://www.patreon.com/acollierastro
1h video, so I won’t watch it right now. (I do recommend people to do it though - from quick glances she’s rather didactic.)
That said, the radius depends on what you’re looking for, and odds are that her video explains this:
If you’re dealing with an isolated hydrogen atom, and you want to be bloody 100% sure that you got it full (electron and nucleus), then the radius is infinite. Because that’s how wave functions work, even if the nucleus is here there’s a non-zero chance that the electron is in the Moon.
If “infinite” is too much you can’t be picky. You can use a₀ instead (Bohr radius), that is the most probable distance between the electron and the nucleus. Then the radius is 53pm, it’s the distance that she mentions in the video description.
There are other ways to do this if you’re accepting that your atom is not isolated. You could use the covalent radius instead, measuring the distance between two hydrogen nuclei in a H₂ and dividing it by two. You’ll get 25±5pm; smaller than the above because they share the electrons, so it’s like the atoms overlap.
Then there’s the Van der Waals radius; it’s a bit of a silly simplification, where you pretend that the atoms are dense, tightly packed, and non-overlapping spheres at 0°K. Then from the resulting volume you get the radius of each atom, for hydrogen it’s 109pm. (This “let’s pretend” stuff might sound weird, and it is, but it’s still useful to know the volume of the gas more precisely than the equation pV = nRT would allow you to.)
It’s more of a “what I remember about this” than a “TL;DW”, as I didn’t watch the vid. It seems to me that she’s focusing on the maths behind the isolated H atom, that I simply glossed over. Still, glad to be of help!
1h video, so I won’t watch it right now. (I do recommend people to do it though - from quick glances she’s rather didactic.)
That said, the radius depends on what you’re looking for, and odds are that her video explains this:
If you’re dealing with an isolated hydrogen atom, and you want to be bloody 100% sure that you got it full (electron and nucleus), then the radius is infinite. Because that’s how wave functions work, even if the nucleus is here there’s a non-zero chance that the electron is in the Moon.
If “infinite” is too much you can’t be picky. You can use a₀ instead (Bohr radius), that is the most probable distance between the electron and the nucleus. Then the radius is 53pm, it’s the distance that she mentions in the video description.
There are other ways to do this if you’re accepting that your atom is not isolated. You could use the covalent radius instead, measuring the distance between two hydrogen nuclei in a H₂ and dividing it by two. You’ll get 25±5pm; smaller than the above because they share the electrons, so it’s like the atoms overlap.
Then there’s the Van der Waals radius; it’s a bit of a silly simplification, where you pretend that the atoms are dense, tightly packed, and non-overlapping spheres at 0°K. Then from the resulting volume you get the radius of each atom, for hydrogen it’s 109pm. (This “let’s pretend” stuff might sound weird, and it is, but it’s still useful to know the volume of the gas more precisely than the equation pV = nRT would allow you to.)
Thanks for the TL;DW! Will definitely check it out!
It’s more of a “what I remember about this” than a “TL;DW”, as I didn’t watch the vid. It seems to me that she’s focusing on the maths behind the isolated H atom, that I simply glossed over. Still, glad to be of help!