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 6.200×102 cm , mounted coaxially within a cylindrical anode with a radius of 0.5580 cm . The potential difference between the anode and cathode is 340 V . An electron leaves the surface of the cathode with zero initial speed (vinitial=0). Find its speed vfinal when it strikes the anode.

Express your answer numerically in meters per second.

Explanation / Answer

Gain in KE = q deltaV

deltaV = 340 Volt

q = 1.602 x 10^19 C

hence m v^2 / 2 = q deltaV

(9.109 x 10^-31 ) ( v^2 ) / 2 = ( 1.6 x 10^-19) ( 340)

v = 1.093 x 10^7 m/s

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