Solution:

Let’s solve the problem step by step:

1. Key Concepts

• Alpha particles ($\alpha$) have a charge of $q_\alpha = 2e$, where $e = 1.6 \times 10^{-19} \, \text{C}$ is the elementary charge.
• Electric current $I$ is the rate of flow of charge: $$I = \frac{\text{Total charge passing}}{\text{Time}}$$

2. Total Charge Passing per Minute

We are given:

• $N = 10,000 \, \alpha$-particles per minute,
• Each $\alpha$-particle carries a charge $q_\alpha = 2e = 2 \times 1.6 \times 10^{-19} = 3.2 \times 10^{-19} \, \text{C}$.

The total charge passing in 1 minute is:

$$Q = N \cdot q_\alpha = 10,000 \cdot 3.2 \times 10^{-19} = 3.2 \times 10^{-15} \, \text{C}.$$

3. Current

Convert the time from minutes to seconds:

$$t = 60 \, \text{seconds}.$$

The current is:

$$I = \frac{Q}{t} = \frac{3.2 \times 10^{-15}}{60} = 0.533 \times 10^{-16} \, \text{A}.$$

Rounding off, the current is approximately:

$$\boxed{0.5 \times 10^{-16} \, \text{A}}.$$