Question

Linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of -2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?

Short answer

$N=9\times {10}^{13}electrons$are travelled down the accelerator during the$2.0$h run.

Step-by-step solution

Content Introduction

Q is the charge and for an object, its charge equals the number of carrier N times the charge of the carrier which is $-e$for electrons and $+e$for protons.

The equation so formed is $Q=Ne$where $e=-1.6\times {10}^{-19}C$

Content Explanation

The rate of accumulation of charge is $\frac{Q}{t}=-2nC/s$.

We are given, $t=2hor7200s$

$$\begin{gathered} Q=(-2nC/s)t \\ Q=(-2nC/s)\left(7200s\right) \\ Q=-14400nC \end{gathered}$$

Now put the value in the equation

$$\begin{gathered} N=\frac{Q}{e} \\ N=\frac{-14400\times {10}^{-9}C}{-1.6\times {10}^{-19}C} \\ N=9\times {10}^{13}electrons \end{gathered}$$