1889

Paschen’s law

• Applying a voltage to electrodes
• at opposite ends of a gas-filled tube
• didn’t always make the tube glow.
• Scientists intending to generate
• an electric arc across a small gap sometimes got
• an arc following a long irregular path.
• Friedrich Paschen tested when the arc begins
• with different gas pressures
• and different distances between the electrodes
• showed that the breakthrough voltage
• is related to the pressure times the distance
• showed there’s an optimal distance and pressure
• for the minimum voltage for each kind of gas.

Breakthrough voltage

• Townsend discharge doesn’t just happen.
• Each gas has its own ionization energy,
• the energy needed to dislodge one of its electrons.
• An electron must accelerate
• far enough without hitting anything
• to reach the ionization energy for a gas.
• If there isn’t enough space to accelerate
• or there are too many or two few atoms that it can hit
• then increasing the voltage might work.

Optimal optimum, minimal minimum

• The lowest point of the Paschen curve
• shows the minimum voltage, which we find
• by setting the derivative of its equation to zero
• and solving for X. In real life, the trick
• is to determine the equation. Paschen
• discovered Paschen’s law empirically;
• that is, by experiment, which often requires
• that you simplify and eliminate noise. In Paschen’s
• case, we ignore the effect of outside light,
• and assume that one impact makes one ionization,
• that atoms recapturing electrons are not factors,
• and that electron production by the cathode
• is not affected by temperature or humidity.