An electron in a TV is accelerated toward the screen across a potential difference of 52.8 kV. How much kinetic energy does the electron gain while accelerating?

How would you solve this?

52.8 * 10^3 * electron charge

Voltage is electric field E times distance

Force is E q

Force times distance = work = energy gain = E q * distance = V q

That is why they call voltage "potential" :)

To solve this problem, we need to use the relationship between electrical potential energy and kinetic energy.

The electrical potential energy is given by the formula:

PE = qV

where PE is the electrical potential energy, q is the charge of the particle (in this case, the charge of an electron, which is -1.6 x 10^-19 C), and V is the potential difference across which the charge is accelerated.

In this case, we are given a potential difference of 52.8 kV, which can be converted to volts by multiplying it by 1000 (1 kV = 1000 V). So, V = 52.8 kV x 1000 = 52,800 volts.

Substituting the values into the formula, we get:

PE = (-1.6 x 10^-19 C) x 52,800 V = -8.448 x 10^-15 J

Now, the kinetic energy gained by the electron is equal to the negative of the electrical potential energy, because the potential energy decreases as the electron gains kinetic energy. So, the kinetic energy gained is:

K.E. = -PE = -(-8.448 x 10^-15 J) = 8.448 x 10^-15 J

Hence, the electron gains 8.448 x 10^-15 J of kinetic energy while accelerating across a potential difference of 52.8 kV.