Question

An electron initially at rest is accelerated over a distance of 0.290 m in 30.7 ns. Assuming its acceleration is constant, what voltage was used to accelerate it?

Answer 1

To find the voltage used to accelerate an electron, we can equate the kinetic energy gained by the electron to the work done on it by the electric field, using the work-energy principle and kinematic equations.

Step-by-step explanation:

The question is asking to determine the voltage used to accelerate an electron from rest over a specific distance with constant acceleration. To solve this, we can use the work-energy principle which relates the kinetic energy gained by the electron to the electrical work done on it by the electric field. The kinetic energy (KE) gained by an electron when accelerated through a voltage V is given by KE = eV, where e is the elementary charge of the electron.

Since the electron starts from rest, its initial kinetic energy is zero, and all the work done on it converts to kinetic energy. Therefore, we can equate the kinetic energy to the work done by the electric field:

KE = ½ m v^2 = eV

where m is the mass of the electron, v is the final velocity, and e is the charge of the electron. To find v, we can use the kinematic equation:

v^2 = u^2 + 2as

where u is the initial velocity (zero in this case), a is the acceleration, and s is the distance over which the acceleration occurs.

Once we have determined v, we can plug it into the work-energy equation to solve for V, the potential difference used to accelerate the electron.