Question

In his experiments on "cathode rays" during which he discovered the electron, J.J. Thomson showed that the same beam deflections resulted with tubes having cathodes made of different materials and containing various gases before evacuation.

Do calculations to show that the charge-to-mass ratio Thomson obtained was huge compared with that of any macroscopic object or of any ionized atom or molecule. How can one make sense of this comparison?

Answer 1

considering the J.J.Thompson cathode ray experiment,

the magnetic force and electric force is F_B= - e v B

F_e = e E

- e v B + e E = 0

v = E / B

in x- direction the position of the particle is

x ( t ) = v t

= E t / B

in y- direction

y ( t ) = 1/2 a t²

= e E t² / 2 m

L = E T / B

T = L B / E

the distance is

d = ( e E / 2 m ) ( L B / E )²

e / m = 2 d E / L² B²  

so the charge-to-mass ratio Thomson obtained was huge compared with

that of any macroscopic object or of any ionized atom or molecule is e / m = 2 d E / L² B²  

here no matter of gas and should be used evacuated chamber.