In a television picture tube, electrons are accelerated from rest through a pote

Question

In a television picture tube, electrons are accelerated from rest through a potential difference of 12,000 volts and move toward the screen of the tube When the elections strike the screen, x-ray photons are emitted Treat the elections nonrelativistically and determine: the speed of an election just before it strikes the screen the number of electrons arriving at the screen per second if the flow of electrons in the tube is 0 01 coulomb per second A x-ray of maximum energy is produced when an electron striking the screen gives up all of its kinetic energy For such x-rays, determine: the frequency the wavelength the photon momentum

Explanation / Answer

Initial velocity u = 0

Potential difference V = 12000 V

(a). Speed of an electron   v = [ 2Vq / m]

Where q = charge = 1.6 * 10 ^ -19 C

            m= mass = 9.11* 10 ^ -31 kg

plug the values we get v = 64.92* 10 ^ 6 m / s

(b). Charge Q = 0.01 C

So, No.of electrons N = Q / e

Where e = charge of electron = 1.6 * 10 ^ -19 C

Plug the values we get N = 6.25* 10^16

(c). Kinetic energy of electron K = ( 1/ 2) mv ^ 2

                                                    = 1.919* 10 ^ -15 J

We know K = hf

From this frequency f = K / h

Where h = planck’s constant = 6.625 * 10 ^ -34 Js

Plug the values we get f = 2.8977*10^18 Hz

(d). wavelength = c / f

Where c= 3 * 10 ^ 8 m / s

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