Overview
This lecture covers J.J. Thomson's cathode ray tube experiment, explaining how it led to the discovery of the electron and allowed calculation of the electron's charge-to-mass ratio.
Cathode Ray Tube Experiment Setup
- The cathode ray tube is an evacuated chamber with extremely low pressure (~0.01 Pa) to prevent electron collisions with gas particles.
- A cathode (negative electrode) and anode (positive electrode) are placed inside the tube.
- Heating the cathode and applying high voltage creates an electron beam moving from cathode to anode.
- The tube's glass is coated with zinc sulfide, which glows green when struck by electrons.
- Early televisions used cathode ray tubes to display images via electron beams.
Key Observations and Discoveries
- The electron beam appears to originate from the cathode, hence the name "cathode ray."
- The cathode ray is deflected by both magnets and electric fields, showing it is made of charged, moving particles.
- The beam deflects toward the positive plate, indicating the particles are negatively charged (electrons).
- Changing the materials of the cathode and anode does not affect the formation of the cathode ray, suggesting all atoms contain electrons.
Determining Charge-to-Mass Ratio (( q/m ))
- The beam's deflection in magnetic and electric fields allows calculation of ( q/m ) for electrons.
- Magnetic force (( F_B )) on a moving charge: ( F_B = B q v ), where ( B ) is magnetic field strength, ( q ) is charge, ( v ) is velocity.
- Centripetal force for circular motion: ( F_C = \frac{m v^2}{r} ), where ( m ) is mass, ( r ) is radius.
- Setting ( B q v = \frac{m v^2}{r} ) leads to ( \frac{q}{m} = \frac{v}{B r} ).
- Electric force (( F_E = q E )) can be balanced with magnetic force to eliminate velocity: ( E = B v ), so ( v = \frac{E}{B} ).
- Full formula: ( \frac{q}{m} = \frac{E}{B^2 r} ).
Results and Constants
- Thomson found the electron's charge-to-mass ratio is ( -1.76 \times 10^8 ) C/g.
- Actual values: electron charge ( = -1.602 \times 10^{-19} ) C, mass ( = 9.11 \times 10^{-28} ) g.
Key Terms & Definitions
- Cathode ray tube — Evacuated chamber to study electron beams.
- Electron — Negatively charged subatomic particle.
- Anode — Positively charged electrode.
- Cathode — Negatively charged electrode.
- Charge-to-mass ratio (( q/m )) — The quotient of a particle's electric charge and its mass.
- Magnetic force (( F_B )) — Force on a moving charged particle in a magnetic field.
- Electric force (( F_E )) — Force on a charged particle in an electric field.
Action Items / Next Steps
- Review the setup and interpretation of the cathode ray tube experiment.
- Practice using the formulas to calculate ( q/m ) for electrons.
- Understand the role of electric and magnetic forces in determining electron properties.