Radiation at plate of vacuum tube

Question

Say you have a vacuum tube, such as the kind used in old amplifiers, wherein electrons are accelerated from the cathode to the anode through an electric field. Presuming, for the sake of argument, that electrons coming off of the cathode have a zero energy, and the anode, made of a material with a work function of 4eV, is at a potential of +24V relative to the cathode, then wouldn't a photon with an energy of 28eV be emitted upon impact of the electron on the anode? Using E=h*f and c=lambda*f, then wouldn't the wavelength of this emitted photon be ~44.28nm? That's beyond the highest reaches of ultraviolet light and into X-ray territory, so why are vacuum tubes safe? Is there something wrong with my understanding of how all this electron/photon business works?

Second side question if you care to answer it:

I turn off the filament in my vacuum tube and let the cathode get cold, but I keep it plugged into the circuit, with the anode still at +24V relative to cathode, then I shine a light at 635nm on the cathode. Supposing my cathode has a work function of 4eV as well, do electrons hop off of the cathode due to photoelectric effect or not? Without the anode there, I would say no, because h*f-4eV is negative (-2.05eV), meaning the electron doesn't have enough energy to escape the metal plate. With the anode however, there's an electric field pulling the electron as well, so can it make the jump? I calculate it would reach the anode with 25.95eV of energy if it did.

Answer 1

When the electron strikes the anode there are many ways it can dissipate it's 24eV worth of energy. It could eject an electron from some atom in the anode, and that excited atom could emit a photon as it recombines with an electron, however it is vastly more likely that the energy will end up as lattice vibration i.e. heat. The amount of radiation emitted from the anode is very small, but it does happen and is used as the basis of soft x-ray emission spectroscopy.

In any case 24eV would be an exceedingly soft X-ray, if it could be called an X-ray at all. At that energy any radiation would be rapidly absorbed by pretty much everything including the glass of your valve.

Re your second question, in the absence of the anode the photoemission would charge the cathode and increase the work function. So you'd get some photemission as first, but it would stop after a while. With the anode I guess the electrons would indeed arrive with more than 24ev energy.

Answer 2

"..Say you have a vacuum tube, such as the kind used in old amplifiers, .."

So let's say we do. Nobody would build a vacuum tube with a plate made out of a 4 Volt work function metal. The electron colliding with the plate, is absorbed, and its KE simply heats the anode. So the anodes of vacuum tubes are made from alloys that have very low thermionic emission; so secondary electron emission is suppressed.

Also, good luck on finding a vacuum tube (as used in old amplifiers) that would do much of anything, with just 24 Volts on the anode. 100 to 500 Volts might be a more typical range; but maybe as low as 50-60, in some "starvation" amplifiers. 75-225 would cover most of the designs, I'm familiar with.

So the effect you postulate does not happen.

Answer 3

Well it won't let me comment, so a new answer.

Urgie, I couldn't read the Dutch, but I pretty much figured it out.

Actually a quite cunning circuit.

By grounding (to the cathode), the grid, the tube is operating at zero bias, instead of what would normally be perhaps -2 Volts.

So at zero bias, the current would normally be quite high; but that lets them run the tube at the low plate Voltage. The first grid, is on the border of having a grid current, which normally would be bad, but doesn't matter in this case since the only grid to cathode Voltage, would be a work function difference, and any grid current isn't going to hurt anything.

So now the screen grid acts normally to extract electrons from the cathode region, and send them on to the plate through the third "suppressor" grid. Because the current is lower than normal, and the suppressor grid is a long way from the cathode, the gm for the grid three signal input, is dismal, but not zero, so you do get some useful gain.

The tube behaves more like a triode than a pentode, and now the suppressor grid to plate capacitance is much bigger than the grid 1 to plate capacitance, so the Miller effect of the g3-p capacitance is large, so the circuit can't be very fast, but probably ok for a radio.

Yes quite a clever use of the pentode. A lot of pentodes have the suppressor grid grounded to the cathode, so you can't connect to it signalwise. It is mainly to suppress secondary emission from the plate in normal operation.

As a practical matter, the anode is virtually always completely enclosing everything else, so in the event that any EM radiation was emitted from collision with the anode, very little could escape to the outside anyway; so OP's concern is unfounded.