If Bohr's funny idea of allowed energy levels for electrons is real, we should be able to see/measure them in other ways besides just with light. Franck and Hertz had done just that, in 1914, not even knowing about Bohr's ideas.
This is like yet another of our "cathode ray" devices. We add the slight negative bias at the end to make sure that really sluggish electrons don't get measured in the ammeter.
The current vs voltage looks like this:
As the Voltage increases towards 4.9 V, more and more current is collected. (Some electrons might bounce off the Hg's, but it must be elastic collisions). Suddenly, at 4.9V, very little current comes through.
Apparently, electrons with 4.9 V are giving up all their energy to Hg, and thus don't have enough energy to make to the cathode and get collected. Such collisions are called inelastic.
If you look at the spectrum of Hg, the brightest lines is at 2537 A. This has E = hc/lambda = (2 Pi) (2000 eV A)/ 2537A = 4.9 eV!
So if this represents the energy difference between some excited level of Hg and the ground state, then electrons which bump into Hg with just this much energy can (will) dump their energy into the Hg, and stop. Indeed Hertz (Gustav, not Heinrich) saw that up to V=4.9, there was no radiation from the tube but if V>4.9, the 2537 A line appeared (this must be coming from those Hg atoms, excited by the collision, which then fall back down into the ground state)
Why is there a second peak? If there is 9.8 V across the tube, electrons will go halfway (gaining 4.9 eV), bump into a Hg, and lose their energy. Then, they do it again, losing all their energy again just at the end. At higher energies still, more levels start to get excited, all completely consistent with the optical spectrum. You can look at Fig 1-12 in F+T to see this.
Yet another impressive agreement with Bohr's idea came from X-ray spectra. (c.f. Beiser 7.9, or F+T 1.10) Recall we've looked at these earlier (Duane-Hunt law), and I noted that they not only have a sharp cutoff at low lambda (max energy), but also sometimes had peaks. A typical experiment: high voltage electrons are accelerated and hit a metal target. Result:
What's going on in the Mo target? Moseley (1913) explored these "x-ray spectra" of elements. Typically they are much simpler than optical spectra, and different elements often look very much alike.
Moseley labeled the two strongest lines
.
Here's the Bohr picture of what's going on, which Moseley figured out.
I'm labeling the shells, or orbits, for electrons. (like n=1,2,3,... in Hydrogen)
If any given shell can only hold a limited number of electrons, then atoms will be built up of many shells filled with electrons.
Now imagine our very energetic electron smashes in and knocks out the innermost (K shell) electron.
Now there's a hole, and a higher up electron can fall in, releasing a photon. These give the "K-lines". Don't forget, the further out you are, the more electrons there are inside your orbit, so the nuclear charge is screened.
Bohr would predict that
,
where Q is the "effective charge". Drawing these pictures in an energy level
diagram like we did for Hydrogen, we'd have
So the K_alpha line (the most energetic) should have
.
Moseley plotted
vs atomic number:
This looks like Q is proportional to (Z-1). This "minus one" makes sense provided there is still one other electron left in the K shell. The elements all sit on the line beautifully, Q marched up one by one as we moved up the periodic table, clinching the idea that nuclei differ by charge, in quantized steps.
[ An interesting side note: Before Moseley, people assigned atomic number just by the order of the periodic table, following increasing mass/mole, which is measurable with chemistry, as we discussed at the start of this syllabus section. Moseley discovered a few mismatches, e.g., Cobalt has mass 58.93, Nickel has mass 58.71, so was originally first in the table. Moseley showed Z(Co)=27, Z(Ni)=28, and chemically the new ordering made tons more sense! Also, Moseley predicted some missing elements (Z=43, 61, 72, 75) which were radioactive and hard to find. ]
Here is the Next lecture
Back to the list of lectures