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
I watched it just yesterday and even though the maths gets over my head sometimes (especially here when she demonstrates the analytical solution with the Schrödinger equation thing), she’s really good at explaining these concepts.
The only thing I didn’t quite understand, and maybe I just didn’t pay attention in the video: If electrons aren’t particles but waves, what does it mean for an atom/molecule to have x electrons? Are “two electrons” just a more intense wave than “one electron”? And this electron wave… wouldn’t it constantly change its position due to it being a wave (stuff needs to move to create waves, right?) or is that what physicists are talking about when they say the probability of the electron to be at location y?
An electron is both a particle and a wave. This can be confusing, because an electron can also create waves (called photons, which are both waves and particles too) when it changes energies. Basically if you measure an electron’s position, it will behave like a particle, but when unmeasured, it will exist in a region of space described by a probability equation, like a wave. If you measure the location repeatedly over a time period and super-impose those measurements, it will look like a cloud of electrons taking the shape of the electron’s probable location in space. But when it is not being measured, it doesn’t constantly ‘move’ - it exists everywhere inside that shape at the same time, the same way a sound exists everywhere in a room at once.
Those regions of probability are called orbitals, but they don’t look like planetary orbits – that’s just the name they got from Bohr’s flawed model. Here’s a sample of some of the more elegant shapes an orbital can take. In these pictures, the hazy cloud you might see in the super-imposed example is replaced with a solid shell so the shape is more obvious.
The pictured shapes are all scaled to look roughly the same size, but with more electrons, you get larger and stranger shaped electron clouds, which again, represent the likelyhood of finding an electron there if you measured it.
I watched it just yesterday and even though the maths gets over my head sometimes (especially here when she demonstrates the analytical solution with the Schrödinger equation thing), she’s really good at explaining these concepts.
The only thing I didn’t quite understand, and maybe I just didn’t pay attention in the video: If electrons aren’t particles but waves, what does it mean for an atom/molecule to have x electrons? Are “two electrons” just a more intense wave than “one electron”? And this electron wave… wouldn’t it constantly change its position due to it being a wave (stuff needs to move to create waves, right?) or is that what physicists are talking about when they say the probability of the electron to be at location y?
An electron is both a particle and a wave. This can be confusing, because an electron can also create waves (called photons, which are both waves and particles too) when it changes energies. Basically if you measure an electron’s position, it will behave like a particle, but when unmeasured, it will exist in a region of space described by a probability equation, like a wave. If you measure the location repeatedly over a time period and super-impose those measurements, it will look like a cloud of electrons taking the shape of the electron’s probable location in space. But when it is not being measured, it doesn’t constantly ‘move’ - it exists everywhere inside that shape at the same time, the same way a sound exists everywhere in a room at once.
Those regions of probability are called orbitals, but they don’t look like planetary orbits – that’s just the name they got from Bohr’s flawed model. Here’s a sample of some of the more elegant shapes an orbital can take. In these pictures, the hazy cloud you might see in the super-imposed example is replaced with a solid shell so the shape is more obvious.
The pictured shapes are all scaled to look roughly the same size, but with more electrons, you get larger and stranger shaped electron clouds, which again, represent the likelyhood of finding an electron there if you measured it.