Quick questions on Cathode rays and Thomson's e/m: HSC Physics Module 8

A cathode ray tube is a sealed glass tube containing two electrodes and a low-pressure gas. A high voltage applied between the cathode (negative electrode) and anode (positive electrode) produces a stream of "cathode rays" travelling from cathode to anode. The rays make the residual gas glow and produce fluorescence on a screen at the far end of the tube.

Several observations pointed to particles:

State Thomson's measured value for the charge-to-mass ratio of the electron and what it implied about cathode rays. [2 marks]

An electron is accelerated from rest through $V = 5000 \text{ V}$. Calculate its final speed (non-relativistic). [3 marks]

Thomson used crossed electric and magnetic fields to measure the speed of cathode rays. (a) Show that when the beam is undeflected, $v = E/B$. (b) When only $B$ remains, derive the equation for $e/m$ in terms of $v$, $r$ and $B$.