(455) Charge to mass ratio [IB Physics SL/HL]

Charge to Mass Ratio Experiment

• J.J. Thompson (1897):

  • Measured the charge to mass ratio (Q/M) of the electron.

  • Preceded Millikan's work on determining the elementary charge.

Experiment Overview

• Cathode Ray Tube:

  • Used to accelerate electrons across a potential difference (PD).

  • Electrons enter a magnetic field that curves their path.

Steps of the Experiment

1. Acceleration of Electrons:

   • Kinetic energy of electrons: ( KE = \frac{1}{2} mv^2 )

   • After acceleration through a potential difference: ( KE = eV )

   • Setting ( \frac{1}{2} mv^2 = eV ) leads to:

     • ( v^2 = \frac{2eV}{m} )

   • Final equation for speed: ( v = \sqrt{\frac{2eV}{m}} )

2. Motion in Magnetic Field:

   • Electrons experience a magnetic force when entering the field: ( F_M = qvB )

   • Centripetal force required for circular motion: ( F_C = \frac{mv^2}{R} )

   • For circular motion, set ( F_C = F_M ):

     • ( eVB = \frac{mv^2}{R} )

3. Calculating Charge to Mass Ratio:

   • Rearrange to find: ( \frac{e}{M} = \frac{V}{BR} )

   • Substitute: ( e/M = \frac{2V}{B^2R^2} )

   • This shows the charge to mass ratio depends on known quantities of potential difference, magnetic field strength, and radius of curvature.

Importance of the Experiment

• Determining Electron Mass:

  • Once charge was known (from Millikan), this allowed for the calculation of electron mass.

• Generic Application:

  • Charge to mass ratio can apply to unknown charged particles (replace e with Q).

• Mass Spectrometry:

  • Fundamental concept in distinguishing particles based on their charge to mass ratio.

  • Useful for crime scene analysis or identifying unknown charges.

Recap

• Key Formula: ( \frac{e}{M} = \frac{2V}{B^2R^2} )

• Electron behavior in magnetic fields allows researchers to determine properties of unidentified charged particles.