7 Spectroscopy of N2

Physics 272 Laboratory Experiments Dr. Greg Severn Spring 2016 7 Spectroscopy of N2 wax lyrical about how all chemistry arises from the fundamentals of physics, and how biology arises from the 7.1 Introduction fundamentals of chemistry, and so on, and so forth. But this reductionist point of view is too simple, and it al- Emission spectroscopy of molecular nitrogen is the final most blinds us to the possibility of unexpected emergent spectroscopy experiment of the semester. We examine features arising in systems of increasing complexity, fea- a quantum system which comprises two atoms: the di- tures that make it difficult to untangle physics and chem- atomic molecule. We will consider the “simplest” type istry. Whats more, well find that the distinction between of molecule, the homonuclear diatomic molecule. We will simplicity and complexity becomes blurred too. We will use familiar potential energy curves and quantized en- try to see that the simple study of diatomic molecules ergy levels to understand physical characteristics of the introduces us to a system of almost bewildering complex- diatomic molecule, such as the strength of the chem- ity, and that, even in the midst of that virtual forest of ical bond, the fundamental vibrational frequency, and spectral features, we will meet the very first and simplest the mean distance between the atoms. Each of these quantum system ever solved, that of the simple harmonic characteristics depend on the electronic energy state of oscillator. the molecule. Transitions between electronic states give We will look for the simplicity within complexity. A rise to the spectra exhibited by homonuclear diatomic simple way of thinking about how molecules form is de- molecules, and we will try to connect these directly to picted in figure 2. Two neutral atoms, say two hydrogen the potential energy curves. The spectrum molecular ni- atoms, may attract each other weakly because they each trogen is shown in figure 1. It has a much richer structure electrically polarize the other, and so there is, potentially, than that typical of atoms. a kind of electrostatic dipole-dipole force between the atoms. And since each dipole may reorient in the electric field of the other, the result is an attractive electrostatic potential. Their mutual electrical potential energy drops as the atoms get closer. But this process also suggests that if they get too close there will be electrical repulsion between the positively charged nuclei that raises the potential energy, and so, from a classical point of view, one may expect there to be an equilibrium distance between the atoms at the minimum of the potential energy. This is just a sketch of a classical heuristic argument, not a complete argument, nor a proof. Figure 1: The visible emission spectrum of molecular nitrogen Nature, it turns out, does not act in this way over the distances that matter here. A guiding rule of thumb, not far wrong, is to suspect that quantum physics takes over But first things first. Why are molecules stable? What when the wave functions of the atoms overlap. This is are the allowed excited states? And How does the emis- a kind of quantum heuristics. From a quantum point sion spectrum reveal answers to such questions? We will of view, for molecules to be stable, the electrons must be attempt to understand the answers from a physics point shared somehow by the separate atoms so as to complete a of view. Its clear from the questions that physics and quantum energy shell (and subshell). This is at least one chemistry have overlapping interests. We are tempted to important way in which quantum physics creates what 1 the description of its effects. Because electrons are in- distinguishable, the principle also implies that the wave- function describing the molecular orbital be symmetric with respect to the interchange of particle labels. This is a little bit complicated, but to put it simply, it also means that wherever the electron of the hydrogen atom can be, there also the shared electron can be, and just as often, with its spin upside down! This is not what we wouldve expected on the basis of classical physics. The re- quirements of quantum physics, and the constraints of the Pauli Exclusion Principle play an essential role in forming covalent bonds. The picture shown in figure 2 is meant to address our classical imagination. It relates to the actual reality only poetically. The nuts and bolts of reality Figure 2: A classical cartoon of molecular formation from however are found in the spectra, shown in figure 1. two of the same atoms. The picture of the little spheres At the risk of straining your powers of concentration is wrong in that they must overlap somehow, but artists, just a little too much, I would like to give a kind of quan- feeling the need to show the spring which accounts (classi- tum version of the classical physical picture of what is cally) for the vibration spectrum, tend to draw the atoms going on in connection with the spectrum. We imag- as completely separate. Of course, quantum mechani- ine that in a diatomic molecule, the total internal en- cally, they must overlap very significantly. ergy will have an electronic component and a nuclear component which is further subdivided into vibrational chemists call a chemical bond, in this case, the covalent and rotational energies. I will pass over the very differ- bond. ent times scales of these individual motions which permit For example, Carbon with its 6 nuclear protons pos- this neat separation of energies (and wavefunctions). The sesses an electron configuration (1s22s22p2) that is in electrostatic energy, which well associate with the elec- want (so to speak) of 4 more electrons to complete the 2p trons (by calling them electronic states, even though it subshell, and the second energy shell. Hydrogen atoms, is the electric potential energy of the entire system), de- in want of 1 electron to complete their 1s energy shell, pends now upon the relative distance between the nuclei, four of them, can combine with Carbon by electron shar- and so the electronic energy levels are not “level” levels ing to form the methane molecule (CH4). In the same as in solitary atoms, but instead dip at the equilibrium way, three hydrogen atoms can combine with Nitrogen distance between the nuclei, giving us some feel for the 2 2 3 (1s 2s 2p ) to form ammonia (NH3). The combination actual size of the molecule. I will leave a discussion of of two Hydrogen atoms to complete the first energy shell the spectroscopic term designation for a footnote[2], ex- (H2) would be even simpler. We are interested however in cept to say that the scheme is somewhat analogous to the homonuclear diatomic molecule Nitrogen (N2), which the scheme for atomic energy states, with addition of ex- is curiouser than molecular hydrogen, because, although tra symmetry designations. Within this confining poten- nitrogen needs 3 electrons and has 3 to share, it must com- tial, the nuclei vibrate and rotate. The molecule then bine with itself in a different way than we are describingit is one of natures fundamental harmonic oscillators (note, is a triple bond, but one of the bonds has a different ge- Ive left out the word ”simple” - we will come back to that ometry associated with it than that which characterizes presently). The allowed energy levels within the electro- molecular hydrogens single covalent bond. static potential now are flat, independent of the internu- I want to add two comments about the physics of our clear distance. Transitions between such a level in one problem. The quantum physics of this sharing of elec- electronic state and another level in another electronic trons leads to some surprising nonclassical behavior. It is state account for molecular emission spectra for homonu- known from NMR measurements that the protons (the clear diatomic molecules, as shown in figure 3. Transition Hydrogen nuclei) in long chain hydrocarbon molecules between levels within an electronic state are possible for exist in a nearly magnetic field free environment. This non-homonuclear molecules, and such molecules can ab- means that the magnetic field due to spin of the shared sorb and emit radiation at much longer wavelengths. This electrons cancels out. The first thing to say is that this fact has enormous implications for the problem of global is what we expect from the constraints of the Pauli Ex- warming. Can anyone guess how and why? clusion Principle. The electrons will have opposite spins. The most important potential energy curves, along But to say that the Pauli Exclusion Principle requires the with their electronic energy state descriptors as described two electrons be in opposite spin states does not exhaust above are shown later in figure 6. Have a look. Simple 2 is not the word that comes to mind. However, there is a deep simplicity in the behavior of quantum oscillators which I hope will become apparent as we actually acquire the data and analyze it. In the mean time, look again at the spectrum of molecular nitrogen (figure 1). Isnt it beautiful? It is an important contributor to the aurorae, which crown the earth above and below with a shimmer- ing glow of awesome beauty. The sheets of luminous color in the upper atmosphere follow our tremulous magnetic field lines, most concentrated at the poles. They bless the earth! However, the earth is threatened by global warming, and we can begin to see how molecules play a role (although we will be happy to find that molecular nitrogen is not one of the culprits).

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