A cathode-ray tube (CRT) is an evacuated glass tube. Electrons are produced at one end, usually by the heating of a metal. After being focused electromagnetically into a beam, they are accelerated through a potential difference, called the accelerating potential. The electrons then strike a coated screen, where they transfer their energy to the coating through collisions, causing it to glow. CRTs are found in oscilloscopes and computer monitors, as well as in earlier versions of television screens. If the accelerating potential is 95.0 V, how fast will the electrons be moving when they hit the screen?

Question

Physics

Moreno

11 February, 04:43

A cathode-ray tube (CRT) is an evacuated glass tube. Electrons are produced at one end, usually by the heating of a metal. After being focused electromagnetically into a beam, they are accelerated through a potential difference, called the accelerating potential. The electrons then strike a coated screen, where they transfer their energy to the coating through collisions, causing it to glow. CRTs are found in oscilloscopes and computer monitors, as well as in earlier versions of television screens. If the accelerating potential is 95.0 V, how fast will the electrons be moving when they hit the screen?

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Chaz Huerta · Answer 1

Answer: v = 5.79 * 10^10m/s.

Explanation: By using the work-energy theorem, we know that the work done on the electron by the potential difference equals the kinetic energy of the electrons.

Mathematically, we have that

qV = 1/2mv²

q = magnitude of an electronic charge = 1.609*10^-16c

V = potential difference = 95v

m = mass of an electronic charge = 9.11 * 10^-31kg.

v = velocity of electron.

Let us substitute the parameters, we have that

1.609*10^-16 * 95 = (9.11*10^-31 * v²) / 2

1.609*10^-16 * 95 * 2 = 9.11*10^-31 * v²

305.71 * 10^-16 = 9.11 * 10^-31 * v²

v² = 305.71 * 10^-16 / 9.11 * 10^-31

v² = 3.355 * 10^21.

v = √3.355 * 10^21

v = 5.79 * 10^10 m/s