I´m not sure, but think it is like with bound planets in orbit about the sun in circular orbit |PE|= 2|KE|but as PE is negative the total energy is -KE. (why bound) A planet in elliptical orbit has this same relationship averaged over the full orbit, but when near the sun both PE & KE magnitudes increase so the total energy is unchanged. I´m not sure it makes any sense to speak about how the KE & PE vary over the electron´s orbits,* but if it does, the energy total is conserved but except for hydrogen the nuclear attraction force, if it makes any sense to speak of that, is more complex than simple 1/(r^2) for electons that penetrate thru deeper shells. *With the Bohr wave length POV I stated in post 28, about the orbitals, I tend to think there is little sense in speaking of the elctron´s speed, KE etc. I.e. I think of the orbital more like static clouds of charge with probability density varying in space.
NO. first remember the energy in the emitted photon is almost exactly equal to the energy level difference of the TWO states. (Not exact as the photon carries momentum too so there is a tiny, very tiny, part of the level energy difference left behind in the recoil of the emitting atom.) As there is angular momentum carried away by an emited photon, the quantum number, normally designated by lower case L, ie l, must decrease by 1. (or increas by 1 if the photon is absorbed.) These (and a few others) are called: The radiation "selection rules." I forget the details, but something like there is slight energy difference due to different l quantum numbers and that can produce two nearly the same energy radiation lines for the Double lines. It has been 50 or so years since I knew these details - Perhaps Trippy or exchemist will reply better.
Have consulted Atkins and I think what I told you before is right: there is PE and KE associated with the electron in all orbitals, and in those where l>0 some of the KE is in angular momentum. The non-classical element is that even electrons with zero angular momentum nevertheless possess kinetic energy.
Old quantum theory, which is what you're pushing, was never complete, or self consistent, and was abandoned in 1925 when we developed modern quantum mechanics. There's nothing adhoc about my explanation, its starting point is the probability density function, the probability density fuinction comes out of wave mechanics, have you seen the animated gifs of the drumhead analogs? The probability density fucntions are, as I recall, derived by treating the electron as a three dimensional standing wave, or (alternatively), as I recall, a particle in a three dimensional box (the end result is the same). Essentially, if you put a marble in a storage cube, and shake the storage cube around, you can derive a probability density function that represents the probability of finding the marble at a particular point in the storage cube. Using this probability function, you can preform the same calculation that you perform to calculate the expected value (3.5 for a 6 sided dice). You can do this as a radius from the center of the cube, and you will get a non zero radius - as illustrated by my table. Think of my table as being the same process, except applied to a particle in a 2d box. The answer I gave is a natural consequence of how probability is calculated. I can provide you with a primer in statistics if you want? For example, if you refer back to the table in the image I provided in post #27, if the nucleus is in the middle of that table, then there is only one way that an electron can be at the distance labled 1 in the graphs, that one outcome has a 6.6% chance of occuring, so there is a 6.6% chance of finding the electron at that distance form the nucleus. IN the next shell out, there is only a 3.3% chance of finding the electron in each little cube of space, but, there are eight ways this outcome can be achieved, so the probability of this outcome occuring is 3.3%*8 or 26.4%. Do you see how it works yet? Or do you need me to go into more detail for you? You're welcome. Please Register or Log in to view the hidden image! 3.4 eV is the energy of the n=2 level, 1.89ev is the energy of the transition from n=3 to n=2. My recollection is that if you want to see atoms interfer you need to look at Bose-Einstein condensates.
Not quite. The radial probability is dependent on the probability density. The radial probability is more like the expected value. It's kind of the average location of the electron. It's the realization that if we divide the space occupied by the 1s orbital into a bunch of tiny cubes, those cubes close to the nucleus have a higher probability of having an electron in them, but there's fewer of them and those cubes further out from the nucleus have a lower probability, but there are more of them. If we compare 0.5 Bohr radii to 1 bohr radius, for example. While the probability of finding an electron at 0.5 bohr radii might be twice that of finding it at 1 bohr radius, the surface area of a sphere of 1 bohr radius is 4 times bigger than that of a sphere of 0.5 bohr radii, so there are 4 times as many possible locations for the electron to be at. So the probability of finding an electron at a distance of 1 bohr radius is higher than the probability of finding it at 0.5 bohr radii.
From the link I provided in post 26: So as the electron approaches the tiny volume of space occupied by the nucleus, its potential energy dives down toward minus-infinity, and its kinetic energy (momentum and velocity) shoots up toward positive-infinity. This "battle of the infinities" cannot be won by either side, so a compromise is reached in which theory tells us that the fall in potential energy is just twice the kinetic energy, and the electron dances at an average distance that corresponds to the Bohr radius. as the electron approaches the nucleus, potential energy approaches negative infinity, kinetic energy approaches positive infinity, total energy remains zero.
Each transition releases one photon. The transition has a specific energy, that energy is the energy that is available to the photon. So each transition has one spectral line associated with it. This image: Please Register or Log in to view the hidden image! Shows the spectral lines of the Balmer series that occur in the visible portion of the spectrum, and the transitions they correspond to. There are, of course, things that can complicate this (magentic fields and intrinsic motion, for example), however, they all start from the same point of one spectral line per transition.
This seems to reflect a POV that the electron is a very tiny point. Do don´t really mean that do you?
No Billy, that's not what I literally meant. Can I safely assume you're familiar with Integration? Also keep in mind that: A Proton has a charge radius of 8.57x10[sup]-16[/sup]m. The Bohr radius is 5.29x10[sup]-11[/sup]m. Even gold nuclei only have a radius of 8.54x10[sup]-15[/sup]. So from that perspective, the nucleus only occupies a tiny volume of space.
Perhaps we are looking at this te wrong way. Color could indicate the energy level instead of relying on the calculations of energy to represent color. Workin from reality into science instead of science into reality
