In an ion accelerator, \(3.0 \times 10^{13}\) helium-4 nuclei (charge \(+2 e\) ) per second strike a target. What is the beam current?

Short Answer

Expert verified
Answer: The beam current is \(9.6 \times 10^{-6} \text{A}\).

Step by step solution

01

Understand the given information and the problem

We are given: - Number of helium-4 nuclei striking the target per second: \(N = 3.0 \times 10^{13}\) nuclei/second - Charge of each helium-4 nucleus: \(q = +2e\) Our task is to find the beam current.
02

Use the formula for current

The formula for current (I) is given as follows, $$ I = n \cdot q $$ where "n" is the rate at which charges are flowing (number of helium-4 nuclei striking the target per second) and "q" is the charge of each helium-4 nucleus. In our case, we have: \(n = 3.0 \times 10^{13}\) nuclei/second \(q = +2e = +2 (1.6 \times 10^{-19} \text{C})\)
03

Calculate the current

Now, we will plug in the values of n and q into the formula to calculate the current: $$ I = n \cdot q = (3.0 \times 10^{13}) \times (+2 \times 1.6 \times 10^{-19}) $$ Solve for I: $$ I = 3.0 \times 10^{13} \times 3.2 \times 10^{-19} $$ Multiply the numbers: $$ I = 9.6 \times 10^{-6} $$ Therefore, the beam current is \(9.6 \times 10^{-6} \text{A}\).

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