In an electron gun, electrons are accelerated through a region with an electric field of magnitude 1.5 × 10⁴ N/C for a distance of 2.5 cm. If the electrons start from rest, how fast are they moving after traversing the gun? A) 1.1 × 10⁴ m/s B) 1.1 × 10⁷ m/s C) 2.3 × 10⁴ m/s D) 2.3 × 10⁷ m/s E) 2.6 × 10¹⁵ m/s

Question

Quizplus · Accepted Answer

The speed of the electrons can be calculated using the work-energy principle. The work done on the electrons by the electric field is equal to the change in kinetic energy. Using the formula $ v = \sqrt{2 \cdot e \cdot E \cdot d / m_e} $, where $ e $ is the charge of an electron, $ E $ is the electric field, $ d $ is the distance, and $ m_e $ is the mass of an electron, the speed is approximately $ 1.1 \times 10^7 $ m/s.

In an Electron Gun, Electrons Are Accelerated Through a Region