Question

An electron in a TV picture tube is accelerated through a potential difference of 10 kV before it hits the screen. What is the kinetic energy of the electron in electron volts?(1 eV = 1.6 ? 10 -19 J)

Answer 1

The kinetic energy of an electron accelerated through a 10 kV potential difference is 10,000 eV, with 1 eV being the energy given to a charge accelerated through 1 V.

Step-by-step explanation:

The kinetic energy of an electron accelerated through a potential difference is directly related to the voltage it is accelerated through. If an electron is accelerated through a potential difference of 10 kV (10,000 V), then it will be given an energy of 10,000 eV since 1 eV is defined as the energy given to a fundamental charge accelerated through 1 V. Therefore, the kinetic energy of the electron in your case is 10,000 eV.

In this scenario, the potential difference represents the energy gained by the electron as it moves through the electric field. The kinetic energy is given by the product of the elementary charge and the potential difference. This is based on the fundamental relationship in electrostatics that the work done (and therefore the energy gained) by a charged particle moving through an electric field is equal to the product of the charge and the potential difference.

Answer 2

10,000 eV

Step-by-step explanation:

According to the law of conservation of energy, the kinetic energy gained by the electron is equal to its change in electric potential energy:

`K=\Delta U=q \Delta V`

where:

K is the kinetic energy of the electron

`q=1 e` is the magnitude of the charge of the electron

`\Delta V` is the potential difference through which the electron has been accelerated

For this electron in the TV, we have

`\Delta V=10 kV=10000 V`

Therefore, the kinetic energy of the electron in electronvolts is

`K=(1 e)(10000 V)=10000 eV`