[Physics] list of all atomic electron state transitions and the corresponding radiation emitted

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Here's a quote from Wikipedia:

As an example, the ground state configuration of the sodium atom is 1s22s22p63s, as deduced from the Aufbau principle (see below). The first excited state is obtained by promoting a 3s electron to the 3p orbital, to obtain the 1s22s22p63p configuration, abbreviated as the 3p level. Atoms can move from one configuration to another by absorbing or emitting energy. In a sodium-vapor lamp for example, sodium atoms are excited to the 3p level by an electrical discharge, and return to the ground state by emitting yellow light of wavelength 589 nm.

Usually the excitation of valence electrons (such as 3s for sodium) involves energies corresponding to photons of visible or ultraviolet light. The excitation of core electrons is possible, but requires much higher energies generally corresponding to x-ray photons. This would be the case for example to excite a 2p electron to the 3s level and form the excited 1s22s22p53s2 configuration.

The questions this prompted for me are this:

1) Does each atom have a finite number of possible state transitions, or could any electron in any atom theoretically be excited to some absurdly high orbital, if the photon it absorbed was energetic enough?

2) Does a given transition (e.g. the 3p to 3s sodium transition) always emit a photon of the exact same energy for a given atom (e.g. the 589 nm example above)? Does the same transition in a different atom emit the same photon (i.e. does a 3p to 3s transition always emit a photon of 589 nm)?

Best Answer

  1. There's an infinite number of orbitals, and thus an infinite number of possible state transitions. However, the energy of the orbitals asymptotes to a finite value - for example, a hydrogen atom has energy levels given by the formula $E_n = -\frac{13.6\text{ eV}}{n^2}$ (ignoring some very tiny quantum corrections). If you let $n$ go up to infinity, the energy approaches zero. So a photon with enough energy, namely 13.6 eV, will knock the electron past all those infinite energy levels and out of the atom entirely.

    Furthermore, if you look at some of the numerical values that come out of that formula: -13.6 eV, -3.4 eV, -1.51 eV, -0.85 eV, -0.54 eV, etc., you'll notice that they get closer and closer together as $n$ gets higher. At some point, the difference between one energy level and the next becomes so small that you can't measure it.

  2. All instances of a particular atom are exactly the same, and so a given transition will always have the same energy for a particular kind of atom (including the isotope). This is how we are able to identify elements by their spectral lines. However, different atoms have different energy levels, because of the different nuclear charge and mass, and also because of multiple electron interactions, so the energy will vary from one atom to another, even for the same transition.

To address the question in your title, there is a list of the spectral lines of most elements in the CRC Handbook of Chemistry and Physics. I'm not sure if it lists the corresponding state transitions, though. Unfortunately the CRC website itself is restricted, so you'd need to pay to access it, but the table itself is probably available elsewhere online. It's quite extensive, listing hundreds of spectral lines for each of the elements.

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