1. Parallel conducting plates create nearly uniform fields that are used to acce

Question

1. Parallel conducting plates create nearly uniform fields that are used to accelerate and direct beams of electrons. Typically we would free the electrons from a surface by heating it up.  One way is to run a current a current through a wire with resistance.  The power dissipated in the wire causes it to increase its temperature to the point that it can radiate that power away, mostly carried off as light.  The hot electrons escape the potential barrier at the surface and are "free" to use.

Consider a source of electrons that is small, like a tiny hot filament. The electrons are freed from the surface but the positive charge they leave behind holds them in a cloud near the filament. Now we add another plate at voltage V some distance d away. We put a little hole in that plate to enable the electrons to zip on through. The experiment looks something like this.

While they seem antiquated, the concept is still useful. It is the basis of modern X-ray tubes, and until only a few years ago all television and computer screens used this technology. Of course now we have low voltage flat panels with arrays of light emitting diodes, but before then the cathode ray tube or "CRT" was the way it was done. The beam of electrons was focused and steered to excite a phosphor and we viewed the light emitted by the phosphor to see the images and text. Steering was done by parallel electric plates as we see here, or by using magnetic fields.

Suppose electrons are accelerated by a potential difference of 10,000 V using a cathode ray tube as described

a.) If the potential accelerating the electrons is 10,000 volts (we say 10 kilovolts (KV) ), how much kinetic energy in joules does one electron have as it leaves the "gun" on its way to the screen?

b.) How fast is that electron going, as a fraction of the speed of light?

c.) How long would it take to go 25 cm from the gun to the screen? Give you answer in microseconds, where one microsecond is 10^6 second.

d.) Without doing the math, discuss how the flat plates that steer the beam would affect the place it lands on the screen. How does the mass of the electron enter into the outcome?

Explanation / Answer

A) Potential difference is dV = 10000 V

charge of one electron is q = 1.6*10^-19 C

so required kinetic energy is KE = q*dV = 1.6*10^-19*10*10^3 = 1.6*10^-15 J = 10*10^3 eV

B) KE = 1.6*10^-15 J

0.5*m*v^2 = 1.6*10^-15

0.5*9.11*10^-31*v^2 = 1.6*10^-15

v = 5.93*10^7 m/sec

as as fraction of speed of light (5.83*10^7)/(3*10^8) = 0.194*speed of light C = 0.194*c

C) time taken is t = d/v = 0.25/(5.83*10^7) = 0.00428*10^-6 sec= 0.000428 usec

D) these high kinetic energy electron are capable of entering into the outcome

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.