TV Cathode Ray Tube Consider a potential

[Tufts]

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/\lambda (\lambda is the wavelength of respective photons)

\lambda = 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) \lambda = 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, \lambda = 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 \lambda = c/f => \lambda = 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..

 

[Andrew Mason]

But \lambda = c/f => \lambda = 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

 

[Tufts]

Thanks a lot, makes sense... I do remember the professor talking about x-rays emitted from CRT screens.

Tufts..