10,000 alpha particles per minute passing through a straight tube of radius r. what is the resulting electric current?

Answer

To solve the problem of finding the resulting electric current from 10,000 alpha particles passing through a straight tube per minute, we can follow these steps:

### Step 1: Understand the charge of an alpha particle
An alpha particle consists of 2 protons and 2 neutrons. Since neutrons do not carry charge, the charge of an alpha particle is equivalent to the charge of 2 protons. The charge of one proton is approximately \( +1.6 \times 10^{-19} \) coulombs. Therefore, the charge of one alpha particle is:
\[ Q_{\text{alpha}} = 2 \times (1.6 \times 10^{-19}) = 3.2 \times 10^{-19} \text{ coulombs} \]

### Step 2: Calculate the total charge per minute
Given that there are 10,000 alpha particles passing through the tube per minute, the total charge (\(Q\)) contributed by these alpha particles in one minute is:
\[ Q = \text{Number of particles} \times \text{Charge per particle} = 10,000 \times (3.2 \times 10^{-19}) \]
\[ Q = 32,000 \times 10^{-19} = 3.2 \times 10^{-15} \text{ coulombs} \]

### Step 3: Convert time from minutes to seconds
Since current is defined as charge per unit time in seconds, we need to convert the time from minutes to seconds. There are 60 seconds in a minute:
\[ t = 1 \text{ minute} = 60 \text{ seconds} \]

### Step 4: Calculate the electric current
The electric current (\(I\)) can be calculated using the formula:
\[ I = \frac{Q}{t} \]
Substituting the values we have:
\[ I = \frac{3.2 \times 10^{-15}}{60} \]
\[ I = 0.0533 \times 10^{-15} \text{ amperes} = 5.33 \times 10^{-17} \text{ amperes} \]

### Final Result
Thus, the resulting electric current is approximately:
\[ I \approx 5.33 \times 10^{-17} \text{ A} \]

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