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. Suppose a diode consists of a cylindrical cathode with radius 0.062 cm, mounted coaxially within a cylindrical anode 0.574 cm in radius. The potential of the anode is 150 V higher than that of the cathode. An electron leaves the surface of the cathode with zero initial speed. Find its speed when it strikes the anode. m/s

Explanation / Answer

Conserving energy

Ui = UEi = Uf = k + UEf

K = UEi -  UEf = - delta UE = q (Vi - Vf) = 1/2 m v2

v = sqrt [2 q (Vi - Vf) / m]

= sqrt [(2 * -1.6 * 10-19 * (0 - 155) / (9.11 * 10-31)]

= 7.38 * 106 m/s

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