An `alpha` particle is placed in an electric field at a point having electric potential 5V. Find its potential energy ?

Answer

To find the potential energy of an alpha particle placed in an electric field at a point with an electric potential of 5V, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charge of the Alpha Particle**:
An alpha particle consists of 2 protons and 2 neutrons. The charge of a proton is approximately \(1.6 \times 10^{-19}\) coulombs. Therefore, the total charge \(q\) of the alpha particle is:
\[ q = 2 \times (1.6 \times 10^{-19}) = 3.2 \times 10^{-19} \text{ coulombs} \]

2. **Use the Formula for Potential Energy**:
The potential energy \(U\) of a charge \(q\) in an electric potential \(V\) is given by the formula:
\[ U = q \times V \]

3. **Substitute the Known Values**:
We know the electric potential \(V = 5 \text{ volts}\) and the charge \(q = 3.2 \times 10^{-19} \text{ coulombs}\). Substituting these values into the formula gives:
\[ U = (3.2 \times 10^{-19}) \times (5) \]

4. **Calculate the Potential Energy**:
Performing the multiplication:
\[ U = 16 \times 10^{-19} \text{ joules} \]

5. **Express in Standard Form**:
We can express \(16 \times 10^{-19}\) joules in standard scientific notation:
\[ U = 1.6 \times 10^{-18} \text{ joules} \]

### Final Answer:
The potential energy of the alpha particle is \(1.6 \times 10^{-18} \text{ joules}\).

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