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8

The decay of potassium-40 to argon-40 is either a $\beta^+$ decay in which what is emitted is not an electron but a positron $$ {}^{40}{\rm K} \to {}^{40}{\rm Ar} + e^+ + \nu_e $$ or, more frequently (if we have whole atoms), an electron capture that you mentioned in which no charged leptons are emitted at the end! About 11% of the potassium-10 decays ...


7

For a simple example of atomic hyperfine splitting from the formal literature, a good place to go is Hyperfine splitting in the ground state of hydrogen. David J. Griffiths. Am. J. Phys. 50, 698 (1982). which includes a self-contained derivation. Griffiths gives the splitting, with a full roster of constants (i.e. nothing set to 1) as $$ \Delta E_\...


5

Electron capture Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shell. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission ...


5

Short answer: of the order of a nanosecond for hydrogen for "allowed" transitions, and the emission rate scales roughly as $Z^2$, where $Z$ is the atomic number. For an oxymoronically named "forbidden" transition, these times increase to tens of milliseconds or fractions of a second. So let's elaborate: what sets these times? A point not made enough is ...


5

Hoax. Let's read the caption of the picture: Note "energy lines" extending from atoms' nuclei ...energy lines? Does that sound serious to you? Ok, let's do an internet search (Elmer Nemes microscope). The first result is this page. The inventor of the Nemescope was a brilliant brain surgeon. His name was Elmer P. Nemes and he ran the Nemes ...


2

It's possible to imagine living in a different universe where most nuclei of the element with charge 1 were deuterium, and the lighter protium was the rare outlier. However, we don't live in that universe. Most of the ordinary matter in the universe is hydrogen (75% by mass) and helium (25% by mass) which has been unprocessed since the Big Bang. Deuterium ...


2

the typical spontaneous emission time scale in atomic physics is on the order of 10^−6 s. In contrast, in nuclear physics, many radioactive nucleus have a half-time of 10^6 years or even more. I beg to humbly disagree with your picture of generalization of atomic and nuclear time scale of events and putting up a contrast/relation with the atomic and ...


2

The slow nuclear transitions have a potential barrier so they proceed by tunnelling and the rate is supressed by a factor of $e^{-E/E_0}$, where $E$ is the barrier height and $E_0$ is some characteristic energy. Your golden rule calculation is giving you the rate in the absence of a barrier. Potential barriers are rare in atomic physics, but frequent in ...


2

Please explain by what means electrons extraction can be done. Hot enough plasmas have all the electrons in the plasma leaving the nuclei positive. How person can focus activity on single atom (from precision point of view) to do so? One cannot deal with individual atoms. It is a statistical phenomenon and one can get a beam of ions without any ...


2

In addition to the answer by hsinghal it is worth point out some historical notational quirks. An expression such as $^2P_{3/2}$ is called a Term Symbol. The superscript is the multiplicity of the electron spins, i.e. 2$S$+1 for total spin S. The capital letter, P in this example is the total orbital angular momentum and has letters and values of S=0, P=1, D=...


1

As you know that zeeman splitting is due to the phenomena known as spatial quantization. i.e. if there is a fixed or preferred direction in the space (i.e. symmetry of the space is broken by the electric or magnetic field) then the atom can not assume arbitrary orientation. This orientation depends on the angular momentum of the atomic/spectroscopic state. ...


1

The forces driving these two atoms apart are electrostatic forces of repulsion. Thus the kinetic energy that these atoms receive comes from the electrostatic interaction. This kinetic energy is later transformed into heat in an atomic reactor when two released atoms slow down colliding with the molecules of water. I think in nuclear processes one should ...


1

You are correct. The neutron absorbed by the unstable U235 nucleus makes its decay via fission much more probable. The U235 nucleus then decays into two smaller nuclei and a few neutrons which overall have a higher binding energy per nucleon than the U235 nucleus. This decrease in binding energy manifests itself as kinetic energy of the fission fragments (...


1

The "spin allowed" refers to the fact that the exited electron can decay to the ground-state orbital without changing it spin. The proces is $|\uparrow_{es},\downarrow_{gs}> \to |\uparrow_{gs},\downarrow_{gs}>$ wich is ok. The opposite $|\downarrow_{es},\downarrow_{gs}> \to |\downarrow_{gs},\downarrow_{gs}>$ is prohibited since $|\downarrow_{...


1

The statement of Martin above: Now, can we "see" atoms? This depends, as I already hinted at, what you mean by "see". If you mean "make a picture in visible light", then you can't do that. is actually not quite true. One can take images using visible light that show single atoms. Here is an example: (1) The reason this works is that this is a ...


1

There exists something called Kramers's recursion rule and I think it is what are you looking for. $\frac{k+1}{n^2} \left\langle r^k \right\rangle - \frac{a_0}{Z} \left(2k+1\right)\left\langle r^{k-1} \right\rangle + \frac{k a_0^2}{4Z^2} \left( \left(2l+1\right)^2 - k^2 \right) \left\langle r^{k-2} \right\rangle$ , where $k$ is integer and $a_0$ Bohr ...



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