In a certain particle accelerator,a current of 800 $\mu$A is carried by a 6.00-MeV proton beam that has a radius of 1.50 mm.The mass of a proton is 1.67 $\times$ 10^-27 kg.If the beam hits a target,how many protons hit the target in 5 s? A)2.50 $\times$ 10¹⁶ B)6.78 $\times$ 10¹⁶ C)5.68 $\times$ 10¹⁶ D)1.37 $\times$ 10¹⁶ E)3.71 $\times$ 10¹⁶

Question

Quizplus · Accepted Answer

First, we need to calculate the total charge of one proton using the current and the time:
q = It = 800 μA × 5 s = 4 mC
Next, we need to calculate the number of protons in the beam using the energy and the mass of a proton:
E = mv2/2
m = 2E/v2 = 2 × 6.00 MeV × 1.602 × 10-13 J/MeV / (3.00 × 108 m/s)2 = 3.35 × 10-19 kg
n = q/e = 4 × 10-3 C / (1.60 × 10-19 C/proton) = 2.50 × 1016
Therefore, the number of protons hitting the target in 5 seconds is 2.50 × 1016. The closest answer choice is A.

In a Certain Particle Accelerator,a Current of 800 μ\muμ A Is Carried by a 6

In a Certain Particle Accelerator,a Current of 800 $\mu$ A Is Carried by a 6