What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV? A) 1.1 × 10⁶ m/s B) 9.8 × 10⁵ m/s C) 8.8 × 10⁵ m/s D) 1.2 × 10⁶ m/s E) 6.2 × 10⁵ m/s

Question

Quizplus · Accepted Answer

The kinetic energy gained by the proton is equal to the electrical energy provided by the potential difference, which can be calculated using the formula $KE = qV$, where $q$ is the charge of the proton (approximately $1.6 \times 10^{-19}$ C) and $V$ is the potential difference (4.0 kV or $4.0 \times 10^3$ V). The kinetic energy is also given by $KE = \frac{1}{2}mv^2$, where $m$ is the mass of the proton ($1.67 \times 10^{-27}$ kg) and $v$ is the velocity. Equating the two expressions for kinetic energy and solving for $v$ gives the speed of the proton. The correct answer is the one that matches this calculation, which is $8.8 \times 10^{6}$ m/s.

What Is the Speed of a Proton That Has Been