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) Part A Suppose a diode consists of a cylindrical cathode with a radius of 6.200×102 cm , mounted coaxially within a cylindrical anode with a radius of 0.5580 cm . The potential difference between the anode and cathode is 290 V . An electron leaves the surface of the cathode with zero initial speed (vinitial=0). Find its speed vfinal when it strikes the anode.

Explanation / Answer

We know that,

U = e V = 1.6 x 10^-19 x 290 = 4.64 x 10^-17 J

The energy provided by this potential converts to the kinetic energy of electron.

KE = U

1/2 mv^2 = U

v = sqrt (2 U/m)

v = sqrt [ 2 x 4.64 x 10^-17/(9.1 x 10^-31) ] = 1.009 x 10^7 m/s

Hence, v = 1.009 x 10^7 m/s

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