Case Study
Passage with linked questions
Case Set 1
Case AnalysisPassage
In 1897, J.J. Thomson performed a series of experiments using a cathode ray discharge tube. He applied electric and magnetic fields perpendicular to each other and to the path of the cathode rays. When only an electric field was applied, electrons hit point A on the screen. When only a magnetic field was applied, they hit point C. By carefully balancing both fields, electrons returned to point B — the undeflected position. Thomson measured the deflections precisely and determined the charge-to-mass ratio of the cathode ray particles. He found this ratio to be 1.758820 × 10^11 C kg^-1, regardless of the electrode material or the gas inside the tube. This universality of the e/me value was a landmark discovery, proving that these particles are fundamental constituents of all matter.
Question 1: What conclusion did Thomson draw from the fact that the e/me ratio was the same regardless of the electrode material or the gas used?
- The e/me ratio being constant regardless of electrode material or gas type proved that cathode ray particles are not specific to any material — they are universal constituents of all atoms.
- This led to the conclusion that electrons are basic building blocks present in every type of matter, making the electron the first identified sub-atomic particle.
- The universality of the e/me value meant that atoms of all elements contain the same type of negatively charged particle (electron), overturning Dalton's concept of the indivisible, structureless atom.
Question 2: Explain why Thomson had to apply both electric and magnetic fields simultaneously in his experiment, and what he determined by balancing them.
- When only an electric field was applied, electrons were deflected toward the positive plate (hitting point A), showing their negative charge; when only a magnetic field was applied, they were deflected in the opposite sense (hitting point C).
- By carefully adjusting both field strengths until the electron beam was undeflected (hitting point B — the original position), the electric and magnetic forces exactly cancelled each other.
- At this balanced condition, Thomson could use the known field strengths to calculate the velocity of the electrons and subsequently determine the e/me ratio with high precision; this method eliminated velocity-dependent errors from using a single field alone.
Question 3: After Thomson determined e/me = 1.758820 × 10^11 C kg^-1, Millikan later measured the charge on the electron as 1.602176 × 10^-19 C. Using these values, calculate the mass of the electron and explain the significance of combining these two experimental results.
- Mass of electron = e/(e/me) = (1.602176 × 10^-19 C)/(1.758820 × 10^11 C kg^-1) = 9.1094 × 10^-31 kg; this is the accepted mass of the electron.
- Neither experiment alone could give the mass: Thomson measured only the ratio e/me (two unknowns), while Millikan independently measured the absolute charge e; combining both results allowed isolation of the mass.
- The calculated mass (9.109 × 10^-31 kg) is approximately 1/1836 of the proton mass, confirming that the electron is an extremely light particle; this tiny mass is why electrons are deflected easily in electric and magnetic fields while heavier particles like alpha particles are not.