Question

What determines the particular energy shell an excited electron relaxes to?

Is it random or some intrinsic property of the material / atom?

For example, Hydrogen will display 4 spectral lines, representing the various drops in energy levels.

Answer 1

the energy shell (orbital) an electron relaxes on is the lowest-energy orbital available. It is not random, and the energy necessary for an electron to "jump" from an energy shell to another is fixed for each shell.

Answer 2

yup, all electrons jump down to their ground state.

Answer 3

There are certain rules that must be followed in an electronic transition. the electron will relax to the lowest possible energy that is allowed. If you know about the quantum description of the atom, then you can say that an electron can only make a transition where \[\Delta s = 0\] and \[\Delta l = +/-1\]

Answer 4

As mentioned by kaisands there are specific selection rules that govern which energy levels electrons in atoms can decay to. Consider the attached diagram for the lithium atom. The left hand scale is the energy of each energy level of bound electrons (with free electrons defined as zero). On the right is the corresponding principle quantum number, \(n\). For each value of \(n\) there is are \((n-1)\) values of \(l\), which is the angular momentum (or azimuthal) quantum number. So if \(n=3\), then \(l=0, 1, 2\). therefore angular momentum of the electrons will split the energy levels. You will see the energy levels corresponding to the different \(l\) numbers as you move to the right in the attached diagram. the selection rules state that transitions between energy levels require that \(n\) increases or decreases in integer values, and that \(l\) must change by \(\pm 1\). Following these rules one can follow the allowed transitions in the diagram, with each transition resulting in one spectral line.

There are other quantum numbers that cause further smaller line splittings (not shown in the diagram), such as the magnetic quantum number \(m_{l}\) which can take integer values over the range \(-l\) to \(+l\). The selection rule then for this is that \(\Delta m_{l}=0, \pm1\).

As a consequences of this, some electrons can find themselves (through atomic collisions etc) in what is known as "metastable states", meaning that they end up in an energy level where there is no allowed transition. They will decay eventually, but this means that their lifetime in that state is longer than in normal states (of the order of a million times longer, or sometimes more) Metastable states are made use of in lasers, to pump a lot of electrons in the collection of atoms up to the same energy level, to achieve what is known as population inversion that is one of the principles behind lasing.

Answer 5

Just to clarify something mentioned above. Electrons won't "always" relax to the ground state. The ground state is certainly favored energetically, but there can be jumps from the d shell to the p shell, or f shell to d shell, or any number of combination.
Look into the Rydberg Formula for the general case of an electron transition. Special cases of the Rydberg Formula are: the Lyman series (transition to ground state), the Balmer series (transition to 2nd excited state), and Paschen series (transition to 3rd excited state). There are more named series, and a theoretically infinite number of series, but these 3 do come up a lot.
In fact, the 4 strong spectral lines to hydrogen (those that you might observe in a laboratory class) are due to the Balmer series. The spectral lines produced by the Lyman series are beyond the visible spectrum, so you won't see those.

Answer 6

To further clarify what has been mentioned above, you can see the Lyman Series, but it reqires observations in the Ultraviolet since the lyman Alpha line first occurs at an intristic wavelength of 1216 angstrom and the series has a limit at the 912 angstrom wavlength.

Also, like everyone else has said there exist specfic rules on what what transitions are allowed and forbidden based on Quantum Mechanics, if you describe an atom as a series of principal quantum levels described by a series of combinations given by nLS, where n is the principal quantum number starting at one for ground level and L is defined as the angular momentum quantum rand S is the total spin. Recalling that L is composed of the sum individual electrons angular momentum quantum numbers\[L=\sum_{n -1}^{\infty} l _{i}\] , where l=n-1, and \[\ S=\sum_{n -1}^{\infty} s_{i} \] where for an electron \[s=\pm \frac{1}{2}\]. So any parituclar level can be desribed by a combination of the aboved terms which means for an electron to decay to a particular level it must under go \[\Delta L=\pm1\] and \[\Delta S=0\] It become particularly important what happens when \[\Delta S\ne 0\] because now you are in the region of Frobidden lines(transitions), which can occur but require that you be in LOW density regiones, since their life time is much longer than the stable(allowed/premitted) transitions. This is what actually occurs with the Hydrogen 21cm line for example.