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 245 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

here by using the formula

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

delta U = 1.6 * 10^-19 * 245 = 392 * 10^-19 J

then by using the formula

v = sqrt( 2 * e * V / me)

v = sqrt( 2 * 392* 10^-19 / 9.1 * 10^-31 )

v = 9.28 * 10^6 m/s

the final speed when it strikes the anode is 9.28 *10^6 m/s

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