Q026 · Collisions / energy / current

Franck–Hertz Excitation

Accelerate electrons through a gas and count those that reach the collector. Inspect a collision, scan the voltage, and measure the spacing between current dips.

Recorded particles $\text{—}$

Collected fraction $\text{—}$

01 / FOLLOW THE ENERGY

One collision can stop an electron reaching the collector.

Scan and save. Remove the gas and repeat. Then shift the contact voltage: does the whole pattern move, or does its spacing change?

Cutaway tube · cathode → accelerating grid → retarding gap → collector · microscopic collision markers are enlarged

Accelerating voltage

U/\mathrm V

11

Each scan voltage gets 200 independent electrons.

TRY A CONTRAST

Gas collision strength

L/\lambda

40

Retarding voltage

U_r/\mathrm V

1.5

Source energy scale

k_BT_s/\mathrm{eV}

0.12

Preparation & sampling

Contact offset

U_c/\mathrm V

1

Voltage scan spacing

\Delta U/\mathrm V

0.25

Sampling seed

s_0

7261

The probe only selects an exposure or voltage. Other changes start a fresh sample; save first. Nothing runs by itself.

A one-dimensional forward-flight model with a single 4.9 eV excitation channel and a declared constant collision hazard above threshold. Counts are simulated. No elastic deflection, grid interception, ionization, space charge or calibrated mercury cross sections.

02 / WHAT DID THE PARTICLES DO?

A current curve made from counted electrons.

$U/\mathrm V$ · Blue: active sample. Amber: last other saved sample. Drag to select the probe.

Show zero-flight-length limit

AT THE SELECTED PROBE

\text{—}

\text{—}

Recorded fraction equals normalized collector-current magnitude for a fixed injected flux. Whiskers are pointwise 95% Wilson intervals.

03 / MEASURE THE SPACING

Mark two observed valleys.

Click a recorded scan point in the chart below. Choose neighboring valleys yourself; the cursors do not consult the excitation energy.

A B

\text{—}

Only cursors on recorded scan voltages produce a spacing. This manual difference has grid and valley-selection uncertainty; it is not an automatic excitation-energy fit.

MODEL INSPECTION · DISTINCT FROM THE READOUT

The electron regains energy after a collision.

$x/L,\quad K/\mathrm{eV}$ · Last simulated flight at this voltage. Drops are actual collision events from its saved record; this diagnostic is not measured by the collector.

\text{—}

04 / KEEP THE EVIDENCE

Save before changing the experiment.

Eight frozen samples. Restoring preserves the original settings and records. Acquiring again starts a new run. CSV also contains simulated collision or recoil diagnostics.

Model, units & primary sources

K_g=K_0+e\max(0,U-U_c)-N\varepsilon,\quad\varepsilon=4.9\,\mathrm{eV}

The 1D accelerating region has uniform field; x runs from cathode to grid. Emission energies follow an exponential flux distribution. Excitation has a constant hazard per unit forward distance above threshold; each event removes one energy quantum. The collector accepts energies above the retarding barrier. Below the contact offset we clamp the accelerating field to zero; we do not model reversed extraction. The ideal reference assumes vanishing excitation flight length, not the finite-hazard data model. Neither curve is calibrated mercury data. Gas density is controlled by optical depth, independently of the source energy scale.

MIT Junior Lab · Franck–Hertz · Leybold · Hg tube geometry

Start with the essentials

Focus question: More voltage. Less current. Why?
One-sentence intuition: The collector tests the remaining kinetic energy, not the total energy the electron received.

Core mathematical model

Energy ledger

K_g=K_0+e\max(0,U-U_c)-N\varepsilon

Uniform acceleration adds energy, and every excitation subtracts the same quantum. There are no inelastic losses below threshold.

Collection condition

K_g>eU_r,\qquad I/I_0=N_{\rm collected}/N_{\rm injected}

Current magnitude is normalized to a fixed injected flux. Increasing the retarding barrier can only reject more electrons at fixed preparation.

Ideal valley spacing

e\Delta U\simeq\varepsilon=4.9\,\mathrm{eV}

The short-excitation-flight limit motivates the spacing estimate. Finite collision paths, source energy spread and a voltage grid move the observed minima.

Common difficulties

What was actually recorded?

Typical misconceptionThe collector measured every collision along the way.

Better mental modelThe collector gives a yes/no result. Collision locations and energies are explicitly exposed model diagnostics.

Scope of the model

Typical misconceptionA successful simulation calibrates a physical instrument.

Better mental modelA one-dimensional forward-flight model with a single 4.9 eV excitation channel and a declared constant collision hazard above threshold. Counts are simulated. No elastic deflection, grid interception, ionization, space charge or calibrated mercury cross sections.

Run the experiment

01
Make a prediction
Before scanning, predict whether raising voltage always increases collected current.
What to observe: The data panel begins empty. Record a sample before interpreting it.
02
Record a contrast
Scan voltage, save, then repeat without gas. Inspect one electron at a valley and another after the current recovers.
What to observe: An electron can lose energy to excitation and then regain energy before the grid.
03
Try to break the explanation
Increase contact offset. Mark neighboring observed valleys before and after the shift. Then broaden the source.
What to observe: Absolute onset is not the same observable as spacing. Broad or poorly sampled valleys need careful selection.