Calculate the speed achieved by an electron accelerated in a vacuum through a p.d of 2000 V. (5 marks)

Sure, here's how you can calculate the speed of an electron accelerated in a vacuum through a potential difference (p.d) of 2000 V:

Step 1: Understand the basic principle An electron accelerated through a potential difference will gain kinetic energy. The kinetic energy (KE) gained by the electron is equal to the work done on it, which is the charge of the electron (e) times the potential difference (V). So, KE = eV.

Step 2: Write down the known values The charge of an electron (e) is 1.6 x 10^-19 C (coulombs) and the potential difference (V) is 2000 V.

Step 3: Calculate the kinetic energy Substitute the known values into the equation: KE = eV = (1.6 x 10^-19 C) x (2000 V) = 3.2 x 10^-16 J (joules).

Step 4: Use the kinetic energy to find the speed The kinetic energy of an object is also given by the equation KE = 1/2 mv^2, where m is the mass and v is the speed. The mass of an electron (m) is 9.11 x 10^-31 kg.

Step 5: Solve for speed Rearrange the equation to solve for speed: v = sqrt((2KE)/m). Substitute the known values: v = sqrt((2 x 3.2 x 10^-16 J) / (9.11 x 10^-31 kg)) = 2.64 x 10^7 m/s.

So, the speed achieved by an electron accelerated in a vacuum through a p.d of 2000 V is approximately 2.64 x 10^7 m/s.