Franck-Hertz (my head) Experiment

[zippy_magee]

My questions are about the classic Franck-Hertz experiment where electrons are given energy by an accelerating voltage. These collide with mercury atoms, raising their internal energy. The electrons are then left with insufficient energy to overcome the retarding voltage of a collector plate and produce a drop in current. These drops occur at regular intervals which demonstrates the discrete nature of the atom.

Parts of the experiment confuse me, my thought process is scattered at the best of times, so I’d appreciate it if you could help set me straight. Thank you for your time.

1. I have read that if the mercury vapour is too rare, more than one energy level transition may be involved. Why is this?
I thought that the accelerating voltage ( and therefore the energy of the electrons ) would control which energy levels were involved, not the density of the vapour.
I can understand that if the vapour is too dense, too many collisions will occur and the current will remain low, but I have a hard time trying to rationalise why a rare vapour would produce such an effect. The current is measured when
(i) no transitions take place and
(ii) when the ground-lowest transition is present.

Ideally we want the drop in current to be due to this ground-lowest energy level transition only. These electrons have been involved in a collision and now don’t have enough energy to overcome the retarding voltage of the collector plate.

What we don’t want to measure is a lack of an electron due to a different energy transition, unless this electron goes on to cause the lowest energy transition too.

If the vapour is very rare, there’s less chance that this second collision will occur and the drop in current may be due to energy transitions we’re not interested in?

2. The electrons pass through 2 grids, the first controls how many electrons there are, but I ask myself, why do we want to do this and how is it done?

My guess would be that we want the number of electrons entering the chamber at any time to be constant. Fair enough, but I would’ve thought this would be dependant on the number leaving the heated filament, so how can we control it?

How would a negatively charged grid affect the number of electrons passing through? I would have thought it would just repel electrons or slow them down, unless it filtered out those below a certain energy? The energy of the electrons depend on the energy with which they leave the filament. Energy from heat supplied by current minus the ionising energy of the filament maybe?

2.b The idea that the accelerating voltage imparts an energy of V [eV] to each electron is used. At what distance from the grid can you say an electron has this energy? That’s kind of a useless question but my point is that even if we assume it’s traveling from rest and calculate the answer, how do we know, the collisions haven’t taken place before the electrons reach this energy?


3. Admittedly, I’m mostly lost when it comes to electronics. This is my rewording of a lab manual, except the bit in inverted commas which is a direct quote. All I have to say when it comes to this is, what are you talking about, you mad yoke?!?

The electrometer uses a current sensing resistor as a feedback element. This is done to reduce the input resistance to RF/A so as to minimise the voltage-burden problem. This problem is that the “voltage-burden developed across the current sensing resistor adversely affects the experiment” by altering the p.d. between the second grid and the collector plate.

Right, from what little “understanding” I do have of electronics, I can grasp minimising input resistance, minimise voltage developed across it. Good man Ohm! That‘s fine with me. A battery is keeping the collector plate negative with respect to the grid so this voltage must be going in the opposite direction because it “adversely affects the experiment”.
After that, I’m lost with what’s happening here. Where does this gain, A, come into play?

 

[eljose79]

Thank you for your questions about the Franck-Hertz experiment. I would be happy to help clarify some of the confusing parts for you.

1. The reason for multiple energy level transitions in a rare mercury vapor is due to the energy levels of the mercury atoms themselves. The accelerating voltage does control the energy of the electrons, but once they collide with the mercury atoms, the atoms absorb some of that energy and move to a higher energy level. If the vapor is too rare, there is a higher chance that the electrons will collide with an already excited atom, causing a second energy level transition. This can result in multiple drops in current at different intervals, making it difficult to isolate the ground-lowest energy level transition.

2. The purpose of the first grid is to control the number of electrons entering the chamber at any given time. This is important because it allows for a more controlled and consistent experiment. The negatively charged grid does not necessarily filter out electrons based on energy, but it does repel some electrons, which can help regulate the number entering the chamber. The energy of the electrons is determined by the accelerating voltage, but the collisions with the mercury atoms can also affect their energy.

2.b. The energy of the electrons is determined by the accelerating voltage, not the distance from the grid. As the electrons travel through the chamber, they may lose some energy due to collisions, but the overall energy is still determined by the accelerating voltage.

3. The electrometer is used to measure the current in the experiment. The current sensing resistor is used to minimize the voltage-burden problem, which is when the voltage developed across the resistor affects the experiment. This is important because it can alter the potential difference between the second grid and the collector plate, which can affect the results. The gain, A, refers to the amplification of the signal from the current sensing resistor to the electrometer.

I hope this helps clarify some of the confusing parts of the experiment for you. Please let me know if you have any further questions. Best of luck with your experiments!

 

[denian]

I am happy to help clarify some of the confusing aspects of the Franck-Hertz experiment for you. Let's address your questions one by one:

1. In the Franck-Hertz experiment, the density of the mercury vapor does play a role in the number of energy level transitions that occur. This is because the electrons must travel a certain distance through the vapor before they have enough energy to collide with the mercury atoms. If the vapor is too rare, the electrons may not have enough collisions to reach the desired energy level. On the other hand, if the vapor is too dense, there may be too many collisions, causing the electrons to lose energy and not reach the desired energy level. So, the density of the vapor is important in controlling the number of energy transitions that occur.

2. The two grids in the experiment serve different purposes. The first grid, called the control grid, helps to regulate the number of electrons entering the chamber. This is important because we want a constant number of electrons to be present in the chamber to ensure consistent results. The negatively charged grid repels electrons, but it also acts as a filter to only allow higher energy electrons to pass through. This helps to ensure that only electrons with enough energy to reach the desired energy level are entering the chamber. The second grid, called the accelerating grid, provides the electrons with the necessary energy to overcome the retarding voltage of the collector plate. As for your question about the distance at which the electrons have the desired energy, it is difficult to determine a specific distance as it depends on various factors such as the density of the vapor and the energy of the electrons as they leave the filament. However, the accelerating grid is designed to give the electrons enough energy to reach the desired energy level before they reach the collector plate.

3. The electrometer is used in the experiment to measure the current between the second grid and the collector plate. The current sensing resistor is used as a feedback element to minimize the input resistance and reduce any voltage burden that may affect the experiment. The gain, A, comes into play as it is a measure of the amplification of the signal from the current sensing resistor. This helps to improve the sensitivity of the measurement and provide more accurate results.

I hope this helps to clarify some of your questions about the Franck-Hertz experiment. It is a complex experiment, but it is an important one in understanding the discrete nature of atoms and their energy levels. Keep asking