Question

A proton beam in an accelerator carries a current of 134 µa. if the beam is incident on a target, how many protons strike the target in a period of 16.0 s?

Answer 1

The intensity of current is defined as the quantity of charge Q that passes through a certain point in a time
`\Delta t`:

`I= (Q)/(\Delta t)`

In our problem, the current is

`I=134 \mu A= 134 \cdot 10^(-6)A` while the time interval is 16.0 s, so we can use the previous equation to find the total charge that strikes the target in this time:

`Q=I \Delta t=(134 \cdot 10^(-6)A)(16.0 s)=2.1 \cdot 10^(-3)C`

We know that each proton carries a charge of
`q=1.6 \cdot 10^(-19)C`, so we can find the number of protons that strike the target by dividing the total charge by the charge of a single proton:

`N= (Q)/(q)= (2.1 \cdot 10^(-3) C)/(1.6 \cdot 10^(-19)C)=1.3 \cdot 10^(16)`