An electron is accelerated from rest through a potential difference of 50.0 kV. What is the speed of the electron? (c = 3.00 × 10⁸ m/s, e = 1.60 × 10^-1⁹ C, m_el = 9.11 × 10^-31 kg) A) 1.24 × 10⁸ m/s B) 1.33 × 10⁸ m/s C) 3.24 × 10⁸ m/s D) 3.33 × 10⁸ m/s E) 4.12 × 10⁸ m/s

Question

Quizplus · Accepted Answer

The kinetic energy gained by the electron is equal to the work done on it by the electric field, which is eV. Using the equation for kinetic energy (1/2)mv^2 = eV, we can solve for v: v = sqrt(2eV/m). Substituting the given values, v = sqrt(2 * 1.60 × 10^-19 C * 50,000 V / 9.11 × 10^-31 kg) ≈ 1.24 × 10^8 m/s.

An Electron Is Accelerated from Rest Through a Potential Difference