The first televisions used cathode-ray tubes, or CRTs, to form a picture. Even t

Question

The first televisions used cathode-ray tubes, or CRTs, to form a picture. Even today, when plasma screens, liquid-crystal displays (LCD), and digital light processing (DLP) systems are increasingly popular, the CRT is still a reliable and inexpensive choice for TVs and computer monitors.
The basic idea behind a CRT is fairly simple: use a beam of electrons to "paint" a picture on a fluorescent screen. This is illustrated in the figure.(Figure 1) First, a heated coil at the negative terminal of the tube (the cathode) produces electrons which are accelerated toward the positive terminal (the anode) to form a beam of electrons-the so-called "cathode ray." A series of horizontal and vertical deflecting plates then direct the beam to any desired spot on a fluorescent screen to produce a glowing dot that can be seen. Moving the glowing dot rapidly around the screen, and varying its intensity with the control grid, allows one to produce a glowing image of any desired object. The first televised image-a dollar sign-was transmitted by Philo T. Farnsworth in 1927, and television inventors have been seeing dollar signs ever since.
The interior of a CRT must be a very good vacuum, typically 10?7 of an atmosphere or less, to ensure electrons aren't scattered by air molecules on their way to the screen. Electrons in a television set are accelerated through a potential difference of 25.0 kV, which is sufficient to give them speeds comparable to the speed of light. As a result, relativity must be used to accurately determine their behavior. Thus, even in something as commonplace as a TV set, Einstein's theory of relativity proves itself to be of great practical value.

Find the speed of the electron accelerated through a voltage of 25.0 kV, using a correct relativistic calculation. Express your answer as a fraction times the speed of light.

The first televisions used cathode-ray tubes, or CRTs, to form a picture. Even today, when plasma screens, liquid-crystal displays (LCD), and digital light processing (DLP) systems are increasingly popular, the CRT is still a reliable and inexpensive choice for TVs and computer monitors. The basic idea behind a CRT is fairly simple: use a beam of electrons to ''paint'' a picture on a fluorescent screen. This is illustrated in the figure.(Figure 1) First, a heated coil at the negative terminal of the tube (the cathode) produces electrons which are accelerated toward the positive terminal (the anode) to form a beam of electrons-the so-called ''cathode ray.'' A series of horizontal and vertical deflecting plates then direct the beam to any desired spot on a fluorescent screen to produce a glowing dot that can be seen. Moving the glowing dot rapidly around the screen, and varying its intensity with the control grid, allows one to produce a glowing image of any desired object. The first televised image-a dollar sign-was transmitted by Philo T. Farnsworth in 1927, and television inventors have been seeing dollar signs ever since. The interior of a CRT must be a very good vacuum, typically 10?7 of an atmosphere or less, to ensure electrons aren't scattered by air molecules on their way to the screen. Electrons in a television set are accelerated through a potential difference of 25.0 kV, which is sufficient to give them speeds comparable to the speed of light. As a result, relativity must be used to accurately determine their behavior. Thus, even in something as commonplace as a TV set, Einstein's theory of relativity proves itself to be of great practical value. Find the speed of the electron accelerated through a voltage of 25.0 kV, using a correct relativistic calculation. Express your answer as a fraction times the speed of light.

Explanation / Answer

Electron is accelerated through 25 kV so it will have 25keV energy.

and K.E. = (gamma - 1) mc^2

25 x 10^3 x 1.6 x 10^-19 = (gamma - 1) x 9.109x 10^-31 x (3 x 10^8)^2

gamma -1 = 0.04879

gamma = 1.04879

gamma = 1 / sqrt(1 - (v/c)^2) = 1.04879

sqrt(1 - (v/c)^2) = 0.953478

1 - (v/c)^2 = 0.90912

v/c = 0.3015

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