Incoming links: Hydrogen
web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:The breakdown is:
- the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
- the speed of light in vacuum c is 299 792 458 m/s
- the Planck constant h is 6.626 070 15 × J s
- the elementary charge e is 1.602 176 634 × C
- the Boltzmann constant k is 1.380 649 × J/K
- the Avogadro constant NA is 6.022 140 76 × mol
- the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W,
- actually use some physical constant:
the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
Defines the second in terms of caesium-133 experiments. The beauty of this definition is that we only have to count an integer number of discrete events, which is what allows us to make things precise.the speed of light in vacuum c is 299 792 458 m/s
Defines the meter in terms of speed of light experiments. We already had the second from the previous definition.the Planck constant h is 6.626 070 15 × J s
Defines the kilogram in terms of the Planck constant.the elementary charge e is 1.602 176 634 × C
Defines the Coulomb in terms of the electron charge.
- arbitrary definitions based on the above just to match historical values as well as possible:
the Boltzmann constant k is 1.380 649 × J/K
Arbitrarily defines temperature from previously defined energy (J) to match historical values.the Avogadro constant NA is 6.022 140 76 × mol
the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W
Arbitrarily defines the Candela in terms of previous values to match historical records. The most useless unit comes last as you'd expect.
Predicts fine structure.
Bibliography:
How To Solve The Dirac Equation For The Hydrogen Atom | Relativistic Quantum Mechanics by Dietterich Labs (2018)
Source. 2s/2p energy split in the hydrogen emission spectrum, not predicted by the Dirac equation, but explained by quantum electrodynamics, which is one of the first great triumphs of that theory.
Note that for atoms with multiple electrons, 2s/2p shifts are expected: Why does 2s have less energy than 1s if they have the same principal quantum number?. The surprise was observing that on hydrogen which only has one electron.
Initial experiment: Lamb-Retherford experiment.
On the return from the train from the Shelter Island Conference in New York, Hans Bethe managed to do a non-relativistic calculation of the Lamb shift. He then published as The Electromagnetic Shift of Energy Levels by Hans Bethe (1947) which is still paywalled as of 2021, fuck me: journals.aps.org/pr/abstract/10.1103/PhysRev.72.339 by Physical Review.
The Electromagnetic Shift of Energy Levels Freeman Dyson (1948) published on Physical Review is apparently a relativistic analysis of the same: journals.aps.org/pr/abstract/10.1103/PhysRev.73.617 also paywalled as of 2021.
TODO how do the infinities show up, and how did people solve them?
Lamb shift by Dr. Nissar Ahmad (2020)
Source. Whiteboard Lecture about the phenomena, includes description of the experiment. Seems quite good.www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)
Freeman Dyson - The Lamb shift by Web of Stories (1998)
Source. Mentions that he moved to the USA from the United Kingdom specifically because great experiments were being carried at Columbia University, which is where the Lamb-Retherford experiment was done, and that Isidor Isaac Rabi was the head at the time.
He then explains mass renormalization briefly: instead of calculating from scratch, you just compare the raw electron to the bound electron and take the difference. Both of those have infinities in them, but the difference between them cancels out those infinities.
Hans Bethe - The Lamb shift (1996)
Source. Ahh, Hans is so old in that video, it is sad to see. He did live a lot tough. Mentions that the shift is of about 1000 MHz.
The following video: www.youtube.com/watch?v=vZvQg3bkV7s Hans Bethe - Calculating the Lamb shift.
Lamb shift by Vidya-mitra (2018)
Source. Previously known as "Food From Electricity", "NeoCarbonFood" sounds like a more commercializable version of it.
Uses electricity to electrolyse water into hydrogen and oxygen molecules, and then use bacteria that do hydrogen chemosynthesis to convert it into food.
Let's do a sanity check.
Searching for "H" for hydrogen leads to: physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on
From there we can see for example the 1 to 2 lines:
- 1s to 2p: 121.5673644608 nm
- 1s to 2: 121.56701 nm TODO what does that mean?
- 1s to 2s: 121.5673123130200 TODO what does that mean?
We see that the table is sorted from lower from level first and then by upper level second.
So it is good to see that we are in the same 121nm ballpark as mentioned at hydrogen spectral line.
TODO why I can't see 2s to 2p transitions there to get the fine structure?
Ciro Santilli once visited the chemistry department of a world leading university, and the chemists there were obsessed with NMR. They had small benchtop NMR machines. They had larger machines. They had a room full of huge machines. They had them in corridors and on desk tops. Chemists really love that stuff. More precisely, these are used for NMR spectroscopy, which helps identify what a sample is made of.
Basically measures the concentration of certain isotopes in a region of space.
Introduction to NMR by Allery Chemistry
. Source. - only works with an odd number of nucleons
- apply strong magnetic field, this separates the energy of up and down spins. Most spins align with field.
- send radio waves into sample to make nucleons go to upper energy level. We can see that the energy difference is small since we are talking about radio waves, low frequency.
- when nucleon goes back down, it re-emits radio waves, and we detect that. TODO: how do we not get that confused with the input wave, which is presumably at the same frequency? It appears to send pulses, and then wait for the response.
How to Prepare and Run a NMR Sample by University of Bath (2017)
Source. This is a more direct howto, cool to see. Uses a Bruker Corporation 300. They have a robotic arm add-on. Shows spectrum on computer screen at the end. Shame no molecule identification after that!Proton Nuclear Magnetic Resonance by Royal Society Of Chemistry (2008)
Source. This video has the merit of showing real equipment usage, including sample preparation.
Says clearly that NMR is the most important way to identify organic compounds.
- youtu.be/uNM801B9Y84?t=41 lists some of the most common targets, including hydrogen and carbon-13
- youtu.be/uNM801B9Y84?t=124 ethanol example
- youtu.be/uNM801B9Y84?t=251 they use solvents where all protium is replaced by deuterium to not affect results. Genius.
- youtu.be/uNM801B9Y84?t=354 usually they do 16 radio wave pulses
Is the only atom that has a closed form solution, which allows for very good predictions, and gives awesome intuition about the orbitals in general.
It is arguably the most important solution of the Schrodinger equation.
In particular, it predicts:
- the major spectral line of the hydrogen atom by taking the difference between energy levels
The explicit solution can be written in terms of spherical harmonics.
A Better Way To Picture Atoms by minutephysics (2021)
Source. Renderings based on the exact Schrödinger equation solution for the hydrogen atom that depict wave function concentration by concentration of small balls, and angular momentum by how fast the balls rotate at each point. Mentions that the approach is inspired by de Broglie-Bohm theory.Originally done with (neutral) silver atoms in 1921, but even clearer theoretically was the hydrogen reproduction in 1927 by T. E. Phipps and J. B. Taylor.
The hydrogen experiment was apparently harder to do and the result is less visible, TODO why: physics.stackexchange.com/questions/33021/why-silver-atoms-were-used-in-stern-gerlach-experiment