Incoming links: Spectral line
Discovering them was not so easy because they don't form chemical compounds. So they exist only as gases. And Helium disperses off into space.
Argon was the first to be found by density considerations because it is so abundant on Earth's atmosphere (~1%): Argon is abundant on Earth's atmosphere because it comes from the decay of Potassium-40.
Then basically all of the others were discovered by spectral lines. Helium notably was first found on the Sun like that, and only later on Earth! Thus its name. Pretty cool.
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?
On a new, strongly radioactive substance contained in pitchblende Updated 2024-12-15 +Created 2024-08-15
This is the paper where Marie Curie announced the discovery of Radium.
It came out only 6 months after the Polonium paper and ended up in the same tome of the Comptes rendus de l'Académie des Sciences, number 127 which is funny.
French text on Wikisource: fr.wikisource.org/wiki/Œuvres_de_Pierre_Curie/24. It's from a 1908 collection of works, and it has made minor corretions, such as using "radioactive" without dash instead of "radio-active" to update the terminology a bit, which is a crime!
The original can be found inside the original tome PDF: archive.org/details/ComptesRendusAcademieDesSciences0127/page/n5/mode/2up
An English translation by the American Institute of Physics: history.aip.org/exhibits/curie/discover.htm
Basically they extracted a Barium solution, but were unable to separate Barium and Radium. If you look at a periodic table, you will see that Radium is directly below radium which explains it as they have very similar chemical properties.
Two of us have shown that by purely chemical procedures it is possible to extract from pitchblende a strongly radio-active substance. This substance is related to bismuth by its analytical properties. We have expressed the opinion that perhaps the pitchblende contained a new element, for which we have proposed the name of polonium.The investigations which we are following at present are in agreement with the first results we obtained, but in the course of these investigations we have come upon a second, strongly radio-active substance, entirely different from the first in its chemical properties. Specifically, polonium is precipitated from acid solution by hydrogen sulfide; its salts are soluble in acids and water precipitates them from solution; polonium is completely precipitated by ammonia.The new radio-active substance which we have just found has all the chemical appearance of nearly pure barium: it is not precipitated either by hydrogen sulfide or by ammonium sulfide, nor by ammonia; its sulfate is insoluble in water and in acids; its carbonate is insoluble in water; its chloride, very soluble in water, is insoluble in concentrated hydrochloric acid and in alcohol. Finally this substance gives the easily recognized spectrum of barium.We believe nevertheless that this substance, although constituted in its major part by barium, contains in addition a new element which gives it its radio-activity, and which, in addition, is closely related to barium in its chemical properties.
Like with Polonium they once again found a new spectral line, though it was somewhat weak in this case as they didn't manage to purify as much:
M. Demarçay has consented to examine the spectrum of our substance with a kindness which we cannot acknowledge too much. The results of his examinations are given in a special Note at the end of ours. Demarçay has found one line in the spectrum which does not seem due to any known element. This line, hardly visible with the chloride 60 times more active than uranium, has become prominent with the chloride enriched by fractionation to an activity 900 times that of uranium. The intensity of this line increases, then, at the same time as the radio-activity; that, we think, is a very serious reason for attributing it to the radio-active part of our substance.
Name the thing:
The various reasons which we have enumerated lead us to believe that the new radio-active substance contains a new element to which we propose to give the name of radium.
They did not have enough purity to clearly measure the mass difference:but it is cute to see that they called radium as "active barium".
We have measured the atomic weight of our active barium, determining the chlorine in its anhydrous chloride. We have found numbers which differ very little from those obtained in parallel measurements on inactive barium chloride; the numbers for the active barium are always a little larger, but the difference is of the order of magnitude of the experimental errors.
Polonium and radium can be used as a light source without power source, so oops, it looks like we broke the conservation of energy!Later on radium came to be used as a phosphorescent light source for things like watch handles, which led to girls getting cancer in the factories; the Radium Girls.
The new radio-active substance certainly includes a very large portion of barium; in spite of that, the radio-activity is considerable. The radio-activity of radium then must be enormous.Uranium, thorium, polonium, radium, and their compounds make the air a conductor of electricity and act photographically on sensitive plates. In these respects, polonium and radium are considerably more active than uranium and thorium. On photographic plates one obtains good impressions with radium and polonium in a half-minute's exposure; several hours are needed to obtain the same result with uranium and thorium.The rays emitted by the components of polonium and radium make barium platinocyanide fluorescent; their action in this regard is analogous to that of the Röntgen rays, but considerably weaker. To perform the experiment, one lays over the active substance a very thin aluminum foil on which is spread a thin layer of barium platinocyanide; in the darkness the platinocyanide appears faintly luminous above the active substance.In this manner a source of light is obtained, which is very feeble to tell the truth, but which operates without a source of energy. Here is at least an apparent contradiction to Carnot's Principle.Uranium and thorium give no light under these conditions, their action being probably too weak.
Experiments explained:
- via the Schrödinger equation solution for the hydrogen atom it predicts:
- spectral line basic lines, plus Zeeman effect
- Schrödinger equation solution for the helium atom: perturbative solutions give good approximations to the energy levels
- double-slit experiment: I think we have a closed solution for the max and min probabilities on the measurement wall, and they match experiments
Experiments not explained: those that the Dirac equation explains like:
- fine structure
- spontaneous emission coefficients
To get some intuition on the equation on the consequences of the equation, have a look at:
The easiest to understand case of the equation which you must have in mind initially that of the Schrödinger equation for a free one dimensional particle.
Then, with that in mind, the general form of the Schrödinger equation is:where:
Equation 1.
Schrodinger equation
. - is the reduced Planck constant
- is the wave function
- is the time
- is a linear operator called the Hamiltonian. It takes as input a function , and returns another function. This plays a role analogous to the Hamiltonian in classical mechanics: determining it determines what the physical system looks like, and how the system evolves in time, because we can just plug it into the equation and solve it. It basically encodes the total energy and forces of the system.
The argument of could be anything, e.g.:Note however that there is always a single magical time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.
- we could have preferred polar coordinates instead of linear ones if the potential were symmetric around a point
- we could have more than one particle, e.g. solutions of the Schrodinger equation for two electrons, which would have e.g. and for different particles. No matter how many particles there are, we have just a single , we just add more arguments to it.
- we could have even more generalized coordinates. This is much in the spirit of Hamiltonian mechanics or generalized coordinates
The general Schrödinger equation can be broken up into a trivial time-dependent and a time-independent Schrödinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrödinger equation, and the full equation comes out as a result.
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.Split in the spectral line when a magnetic field is applied.
Non-anomalous: number of splits matches predictions of the Schrödinger equation about the number of possible states with a given angular momentum. TODO does it make numerical predictions?
www.pas.rochester.edu/~blackman/ast104/zeeman-split.html contains the hello world that everyone should know: 2p splits into 3 energy levels, so you see 3 spectral lines from 1s to 2p rather than just one.
p splits into 3, d into 5, f into 7 and so on, i.e. one for each possible azimuthal quantum number.
It also mentions that polarization effects become visible from this: each line is polarized in a different way. TODO more details as in an experiment to observe this.
Well explained at: Video "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)".
Experimental physics - IV: 22 - Zeeman effect by Lehrportal Uni Gottingen (2020)
Source. This one is decent. Uses a cadmium lamp and an etalon on an optical table. They see a more or less clear 3-split in a circular interference pattern,
They filter out all but the transition of interest.
- youtu.be/ZmObNFAqkBE?t=165 passes the lines through a polarizer, which shows how orbital angular momentum is carried by photon polarization
- youtu.be/ZmObNFAqkBE?t=370 says they are looking at 1D2 to 1P1 changes.
Zeeman Effect - Control light with magnetic fields by Applied Science (2018)
Source. Does not appear to achieve a crystal clear split unfortunately.