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)

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 0.1cm , mounted coaxially within a cylindrical anode with a radius of 0.317cm . The potential difference between the anode and cathode is 305V . 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.   vfinal = 1.04 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 0.1cm , mounted coaxially within a cylindrical anode with a radius of 0.317cm . The potential difference between the anode and cathode is 305V . An electron leaves the surface of the cathode with zero initial speed (vinitial=0). Find its speed vfinal when it strikes the anode. Note that the size of the diode makes no difference, as long as the potential difference between the two electrodes is a known constant. Also, note that the potential at the surface of the anode and cathode are not known separately, but the potential difference is enough for these calculations. In general, the potential at a particular point is not physically important. Only potential differences are important, just as only the change in potential energy is important to mechanics problems. What is the electric field at a point midway between the anode and cathode?

Explanation / Answer

Potential energy of electrone at anode, Ua = -e*Va (Va is anode potential)

Potential energy of electrone at cathode, Uc = -e*Vc (Vc is cathode potential)

Decrease in potential when the electron moves from anode to cathode = Ua - Uc

= e(Vc - Va)

This is equal to KE gained.

m*v*v/2 = e(Va - Vc)

v = sqrt(2e(Va - Vc)/m)

When the potential difference is constant, v will always be constant. (irrespective of the distance between anode and cathode.)

v = 1.035*10^7 m/s

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