Question

The pre-2000’s-style television sets were based on cathode ray tube (CRT) technology. A CRT is a vacuum tube that operates by heating an internal metal filament (the cathode) to a high temperature so that electrons are ejected from its surface. These electrons are then accelerated through a large voltage towards the positively charged anode before striking a phosphor-coated screen to produce visible light. Assume that the electrons start from rest and are accelerated across a voltage difference of 1000~V1000 V. Calculate the speed of the electron when it strikes the phosphor-coated screen.

Answer 1

Given data:

Potential difference through which electrons get accelerated= 1000 V

We know that kinetic energy gained by a charged particle when it is accelerated through the potential difference of V volts is given by:

Where q is magnitude of the charge of the particle ( 1.6 x 10^-19 C (magnitude only) in this case)

m is the mass of the particle ( Mass of electron = 9.1 x 10^-31 kg)

v is the speed of the particle

The above expression can be derived by applying law of conservation of energy i.e. :

Kinetic energy gained by charged particle = Potential energy lost by the charged particle

Rearranging above expression to get velocity :

Substituting values we get:

Which is the required answer

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