Periodic Table and Quantum Numbers

• Adjust the atomic number to see the electrons filling up the energy levels.
• You can also click on an atomic on the periodic table.
• The states with different values of $m$ have the same energy in the absence of a magnetic field, despite being drawn at different height.

Franck–Hertz Experiment

Theory:

• The region where the electrons travel is filled with a gas (e.g. mercury vapor, argon, ...etc., not drawn in the simulation).
• Electrons, being negatively charges, are attracted to high electric potential, similar to the mechanical analogy where a mass tend to roll toward lower elevation. Therefore the electrons accelerate toward the grid because it has a higher potential than the cathode.
• After the grid the electrons have to overcome the anode potential drop (which repels the electrons) to get to the anode to cause a current.
• If the electrons are too slow when they pass the grid, they will not make it to the anode.
• To make a big current, one naively wants to increase the grid voltage to as high a value as possible.
• However, due to the discrete energy levels in the gas (not drawn) filling the instrument, when the electrons are too fast($KE\geq E_{excitation}$ excitation energy of the gas atoms), they will collide inelastically with the gas atoms and lose all kinetic energy, in the process exciting the atoms.
• Analogy: You want to drive to school fast, but if you drive above the speed limit, the police will stop you, causing you to arrive later.
• The excitation energy determines the "speed limit" of the electrons. If the electrons are too fast, they get stopped by the gas atoms.
• The experiment confirmed Neils Bohr's atomic model of discrete energy levels. Electrons only lose energy at particular values, depending on the gas filling the instrument.

Virtual lab:

• Can any electrons reach the anode if $|\Delta V_{anode}|> E_{excitation}$? If not, why not? Here we use $\Delta V_{anode}$ to denote the anode voltage drop. Note that the actual votlage at the anode is $V_{anode} = V_{grid} + \Delta V_{anode}$.
• Increase the grid voltage and observe a repeating pattern over $\Delta V_{grid} = E_{excitation}$. You can also see the pattern in the $I$ vs $V$ graph.

Simplications made in the simulation:

• Electrons always produced at rest and at regular time interval.
• Electrons only moves along the $x$-direction.
• Elastic collisions not included.
• Inelastic collisions always occur immediately when $KE_{electron}>E_{excitation}$.
• Filament that produces the electrons behind the cathode not shown.
• Time slows down to the $ns=10^{-9}s$ scale so you could see the fast moving electrons.
• When these are taken into account the $I$ vs $V$ curve will be smoothened out to produce the curve in an actual experiment. However, the main idea behind the experiment is captured by this simulation.