An aluminium nail has an excess charge of `+3.2 muC`. How many electrons must be added to the nail to make it electrically neutral ?

Options

A. `2.0 xx 10^(13)`
B. `3.2 xx 10^(16)`
C. `2.0 xx 10^(19)`
D. `3.2 xx 10^(6)`

Answer

To solve the problem of how many electrons must be added to an aluminum nail with an excess charge of +3.2 µC to make it electrically neutral, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Charge of the Nail**:
The aluminum nail has an excess charge of +3.2 µC (microcoulombs). This means it has a positive charge that needs to be neutralized.

2. **Convert Microcoulombs to Coulombs**:
Since 1 µC = \(10^{-6}\) C, we convert +3.2 µC to coulombs:
\[ +3.2 \, \mu C = 3.2 \times 10^{-6} \, C \]

3. **Charge of One Electron**:
The charge of one electron is approximately \(-1.6 \times 10^{-19}\) C. Since electrons have a negative charge, adding electrons will neutralize the positive charge of the nail.

4. **Calculate the Number of Electrons Needed**:
To find out how many electrons are needed to neutralize the charge of +3.2 µC, we can use the formula:
\[ \text{Number of electrons} = \frac{\text{Total positive charge}}{\text{Charge of one electron}} \]
Substituting the values we have:
\[ \text{Number of electrons} = \frac{3.2 \times 10^{-6} \, C}{1.6 \times 10^{-19} \, C} \]

5. **Perform the Calculation**:
\[ \text{Number of electrons} = \frac{3.2}{1.6} \times \frac{10^{-6}}{10^{-19}} = 2 \times 10^{13} \]

6. **Conclusion**:
Therefore, the number of electrons that must be added to the aluminum nail to make it electrically neutral is:
\[ 2 \times 10^{13} \text{ electrons} \]

### Final Answer:
To make the aluminum nail electrically neutral, **2 × 10^13 electrons** must be added.