Is a charge of `(5.8xx10^(-18))C` possible?

Options

A. yes
B. No
C. May be
D. Cannot be determined

Explanation

To determine if a charge of \(5.8 \times 10^{-18} \, C\) is possible, we can use the relationship between charge, the number of electrons, and the elementary charge. The elementary charge \(E\) is approximately \(1.6 \times 10^{-19} \, C\).

### Step-by-Step Solution:

1. **Understand the relationship**: The total charge \(Q\) can be expressed as:
\[ Q = N \cdot E \]
where \(N\) is the number of electrons and \(E\) is the charge of a single electron.

2. **Rearrange the formula**: To find the number of electrons \(N\), we can rearrange the formula:
\[ N = \frac{Q}{E} \]

3. **Substitute the values**: Substitute the given charge \(Q = 5.8 \times 10^{-18} \, C\) and the elementary charge \(E = 1.6 \times 10^{-19} \, C\):
\[ N = \frac{5.8 \times 10^{-18}}{1.6 \times 10^{-19}} \]

4. **Calculate \(N\)**: Perform the division:
\[ N = \frac{5.8}{1.6} \times \frac{10^{-18}}{10^{-19}} = 3.625 \times 10^{1} = 36.25 \]

5. **Interpret the result**: The calculated value of \(N\) is \(36.25\). Since \(N\) must be a whole number (as you cannot have a fraction of an electron), this indicates that the charge \(5.8 \times 10^{-18} \, C\) is not possible.

### Conclusion:
The charge of \(5.8 \times 10^{-18} \, C\) is not possible because the number of electrons \(N\) calculated from this charge is not an integer.

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