Kinetic energy: An electron has a speed of 0.643c. Through what potential difference would the electron need to be accelerated (starting from rest) in order to reach this speed? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-19 C, m_el = 9.11 × 10^-31 kg) A) 160 kV B) 130 kV C) 180 kV D) 200 kV

Question

Quizplus · Accepted Answer

The kinetic energy of the electron can be calculated using the equation:

KE = (1/2)mv²

where KE is the kinetic energy, m is the mass of the electron, and v is the speed of the electron.

Substituting the given values, we get:

KE = (1/2)(9.11 × 10^-31 kg)(0.643c)^2

KE = 3.02 × 10^-14 J

The potential difference can be calculated using the equation:

PE = qΔV

where PE is the potential energy gained by the electron, q is the charge of the electron, and ΔV is the potential difference.

Equating the kinetic energy and potential energy gained by the electron, we get:

(1/2)mv² = qΔV

Rearranging the equation, we get:

ΔV = (1/2)(mv²/q)

Substituting the given values, we get:

ΔV = (1/2)(9.11 × 10^-31 kg)(0.643c)^2/(1.60 × 10^-19 C)

ΔV = 160 kV

Therefore, the potential difference needed to accelerate the electron to a speed of 0.643c is 160 kV.

Kinetic Energy: an Electron Has a Speed of 0