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 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 320 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

Initial speed of the electron is vinitial = 0 Final speed of the electron is vfinal Mass of the electron is m = 9.11*10^-31 kg Potential difference between anode and cathode is V = 320 V Then work done in moving the electron from anode to cathode is equal to change in kinetic energy of the electron. Then W = (1/2)m (vfinal^2 - vinitial^2) Here W = q V Here q = 1.6 * 10^-19 C Then (1.6 * 10^-19 C)(320V)= (1/2)(9.11 * 10^-31 kg)(vfinal^2) Then v = 1.06 * 10^7 m/s

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