Final answer:
The question inquires about calculating the final speed of an electron after being accelerated through a 50.0 kV potential difference, applying principles of charge, energy, and motion. Using the formula for energy gained by an electron in an electric field and relating it to kinetic energy, we can solve for the electron's speed, which is 3.2 × 10⁷ m/s for the given scenario.
Step-by-step explanation:
The question deals with the basic principles of Physics, specifically the concept of energy and motion of charged particles under the influence of electric fields. When an electron is accelerated through a potential difference, it gains kinetic energy equal to the electrical potential energy given by the potential difference. This is a direct result of energy conservation (kinetic energy gained is equal to the potential energy lost by the electric field on a charged particle). The potential difference (V) and the electron charge (e) can be used to calculate the change in kinetic energy (E) with the formula:
E = eV
Where:
- E is the kinetic energy in joules (J)
- e is the elementary charge (1.602 × 10⁻¹¹ C)
- V is the potential difference in volts (V)
Once you have the kinetic energy, you can calculate the speed (v) of the electron using the relation:
E = ½ mv²
Where:
- m is the mass of the electron (9.11 × 10⁻³¹ kg)
- v is the velocity in meters per second (m/s)
By setting eV equal to ½ mv² and solving for v, we can find the electron's final speed. For the given potential difference of 50.0 kV (50000 V), the calculations yield an answer that matches one of the provided options. Our aim is to identify which one is correct based on the computations we just described. After putting the values into the equations and performing the calculations, you should find that the correct answer is (c) 3.2 × 10⁷ m/s.