Before the advent of solid-state electronics, vacuum tubes were widely used in r

Question

Before the advent of solid-state electronics, vacuum tubes were widely used in radios and other devices. A simple type of vacuum tube known as a diode consists essentially of two electrodes within a highly evacuated enclosure. One electrode, the cathode, is maintained at a high temperature and emits electrons from its surface. A potential difference of a few hundred volts is maintained between the cathode and the other electrode, known as the anode, with the anode at the higher potential. (Figure 1)

Suppose a diode consists of a cylindrical cathode with a radius of 6.200

Explanation / Answer

You have systematically removed all units from the quantities you specify. This makes the question essentially meaningless. However, it is not necessary to know the dimensions of the anode and cathode in order to answer the question, so you are lucky ! However, it is necessary to assume that the voltage is measured in volts.

The final KE of the electron is the product q*V where q is the electronic charge 1.6*10^-19C and V is the potential difference through which it moves. This is 350v (I assume).

You can equate the energy qV to the usual expression for KE (0.5mv^2) to calculate speed (v). m is the mass of the electron (9.1*10^-31kg)

0.5mv^2 = qV

v = sqrt (2qV/m) = 11.1*10^6m/s

This is a sufficiently small fraction of the speed of light for relativistic effects to be ignored.

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