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Difficulty: HardConduction of Electricity Through Gases and Cathode Rays

In the study of electrical discharge through gases and cathode ray behavior, specific physical setups and pressure conditions produce distinct observable phenomena. Match each experimental condition or observation on the left with its corresponding underlying physical mechanism or property on the right.

  • Extension of the Crookes dark space to fill the entire discharge tube at approximately 0.01 mmHg0.01\text{ mmHg}Cessation of gas ionization within the gas volume, resulting in direct electron bombardment and fluorescence of the glass tube wall
  • Casting of a sharp shadow when an opaque metal Maltese cross is placed in the path of the raysRectilinear propagation of energetic cathode rays emitted normally from the cathode surface
  • Deflection of the beam into a circular arc when passing through a uniform magnetic field directed perpendicularly to its motionCentripetal magnetic force (F=qvBF = qvB) acting on moving negative charges, causing curved trajectories
  • Breakdown of gas column into luminous striations separated by dark spaces at intermediate pressures (~1 mmHg1\text{ mmHg})Alternate excitation, ionization, and recombination cycles of gas ions as electrons gain kinetic energy across potential gradients

Answer

1. Extension of the Crookes dark space matches with cessation of gas ionization causing direct glass fluorescence. 2. Maltese cross shadow matches with rectilinear propagation of cathode rays. 3. Magnetic field deflection into circular arc matches with centripetal magnetic Lorentz force (F=qvBF = qvB). 4. Luminous striations match with periodic excitation, ionization, and recombination of gas molecules.
Each matching pair directly connects an observable discharge tube phenomenon with its fundamental physical principle: extreme evacuation (0.01 mmHg0.01\text{ mmHg}) allows unimpeded electron stream travel to fluoresce glass; obstacle shadows confirm rectilinear propagation; transverse magnetic fields induce circular motion via evBevB; and periodic energy exchange of electrons with gas molecules yields striations.

Step-by-Step Solution

1
Analyze the pressure condition at 0.01 mmHg0.01\text{ mmHg}
At very low pressure (0.01 mmHg0.01\text{ mmHg}), gas collisions drop significantly, allowing cathode rays to reach the tube walls directly, extending the Crookes dark space throughout the tube and exciting glass fluorescence.
Mean free path increases beyond tube dimensions when gas density drops.
2
Analyze ray propagation using obstacle shadow formation
The sharp shadow cast by a Maltese cross demonstrates that cathode rays propagate in straight lines normal to the cathode.
Diffraction is negligible and ray trajectories do not bend around macroscopic obstacles.
3
Evaluate magnetic field interaction with cathode rays
The Lorentz force F=q(v⃗×B⃗)F = q(\vec{v} \times \vec{B}) acts as a centripetal force (evB=mv2revB = \frac{mv^2}{r}), bending the negatively charged particle trajectory into a circle.
Moving electric charges experience magnetic forces perpendicular to velocity.
4
Identify the mechanism behind positive column striations
Striations represent repeating regions of inelastic electron collisions with gas atoms resulting in excitation and emission of light, followed by dark zones where electrons re-accelerate.
Quantized energy transfer during gas excitation creates spatial periodicity in luminescence.

Key Concept

Physical mechanisms of gaseous conduction across pressure stages and properties of cathode rays
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Topics

Conduction of Electricity Through Gases and Cathode Rays

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