TV Cathode Ray Tube Consider a potential

In summary, the given conversation discusses the calculation of the kinetic energy and wavelength of electrons in an old TV cathode ray tube, as well as the wavelength of photons emitted from the screen. The equations used include E = hf, f = c/\lambda, and \lambda = h/p. The calculations result in a kinetic energy of 2.4 x 10-15 J, a wavelength of 9.97 x 10-12 m for the electrons, and a frequency of 3.62 x 1018 Hz for the photons. It is noted that the wavelength of the photons is not within the visible spectrum due to the possibility of x-rays being emitted from the CRT screen.
  • #1
Tufts
5
0

Homework Statement


In an old TV cathode ray tube, electrons are accelerated by a potential of 15 kV between the gun and screen. Find:

a) Kinetic energy of the electrons when they reach the screen
b) Its respective wavelength
c) Wavelength of the photons with maximum energy that are emitted from the screen.

Homework Equations



E = hf (Energy of a photon with frequency f)
f = c/[tex]\lambda[/tex] ([tex]\lambda[/tex] is the wavelength of respective photons)

[tex]\lambda[/tex] = h/p (wavelength of electron depending on p, its momentum)

The Attempt at a Solution


a) E = e*V = 15000 eV = 15000 * 1.6 x 10-19 = 2.4 x 10-15 J

b) [tex]\lambda[/tex] = h/p
But p = mv (where m = 9.1 x 10-31 kg)
We also know that 1/2 * mv2 = E
So, v = (2/m * E)1/2 => v = (2/(9.1 x 10-31)*2.4 x 10-15)1/2 = 0.73 x 108 m/s (not close enough to c, so we can use our electromagnetism approximation)

Therefore, [tex]\lambda[/tex] = h/p = 6.626 * 10-34 / (9.1 x 10-31 * 0.73 x 108) = 9.97 x 10-12 m

c) Let us suppose that there is 100% efficient exchange of energy between electron and photon. E = hf => f = E/h => f = (15000 * 1.6 x 10-19)/(6.626 x 10-34) = 3.62 x 1018 Hz

But [tex]\lambda[/tex] = c/f => [tex]\lambda[/tex] = 8.28 x 10-11 m



To me, I am using the formulas correctly... but the wavelength of light on part C is not in the visual spectrem. Since we are talking about a TV here... that certainly does not make sense! What am I doing wrong?? Thanks before hand for all the help.

Tufts..
 
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  • #2
Tufts said:
But [tex]\lambda[/tex] = c/f => [tex]\lambda[/tex] = 8.28 x 10-11 m



To me, I am using the formulas correctly... but the wavelength of light on part C is not in the visual spectrem. Since we are talking about a TV here... that certainly does not make sense! What am I doing wrong??
Nothing. CRT screens can and do emit a small amount of xrays. Phosphorescence is a complicated phenomenon by which energy of the electrons stimulates the target molecules to produce visible light.

AM
 
  • #3
Thanks alot, makes sense... I do remember the professor talking about x-rays emitted from CRT screens.

Tufts..
 

Related to TV Cathode Ray Tube Consider a potential

1. What is a TV Cathode Ray Tube (CRT)?

A TV CRT is a vacuum tube used in older television sets to display images by converting electrical signals into visible light.

2. How does a CRT work?

Inside a CRT, there is a cathode, which emits electrons, and an anode, which accelerates the electrons towards a phosphor-coated screen. When the electrons hit the screen, they cause the phosphors to emit light, creating the image on the TV screen.

3. Why was the CRT replaced by other display technologies?

The CRT was replaced because it was bulky, heavy, and consumed a lot of power. Additionally, newer technologies such as LCD and LED provide better image quality and are more energy-efficient.

4. What is the potential difference used in a CRT?

The potential difference, or voltage, used in a CRT is typically between 25,000 and 40,000 volts. This is necessary to accelerate the electrons towards the screen with enough energy to create a visible image.

5. Are there any safety concerns with CRTs?

Yes, there are safety concerns with CRTs due to the high voltage used. It is important to handle CRTs carefully and avoid touching any internal components. Additionally, CRTs can emit small amounts of X-rays, although modern CRTs have safety features to minimize this risk.

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