The electronic charge is `1.6xx10^(-19)` coulomb. If a body carries a negative charge of `9.6xx10^(-10)` coulombs, what is the number of excess electrons on the body?

Options

A. `6xx10^(9)`
B. `1//6xx10^(-29)`
C. `6xx10^(29)`
D. `6xx10^(29)`

Explanation

To find the number of excess electrons on a body carrying a negative charge of \(9.6 \times 10^{-10}\) coulombs, we can follow these steps:

### Step 1: Understand the relationship between charge and number of electrons
The charge \(q\) on a body is related to the number of excess electrons \(n\) by the equation:
\[ q = n \cdot e \]
where \(e\) is the charge of a single electron, which is approximately \(1.6 \times 10^{-19}\) coulombs.

### Step 2: Rearrange the equation to solve for \(n\)
We can rearrange the equation to find the number of excess electrons:
\[ n = \frac{q}{e} \]

### Step 3: Substitute the known values
We know:
- \(q = -9.6 \times 10^{-10}\) coulombs (we can ignore the negative sign as we are interested in the magnitude)
- \(e = 1.6 \times 10^{-19}\) coulombs

Substituting these values into the equation gives:
\[ n = \frac{9.6 \times 10^{-10}}{1.6 \times 10^{-19}} \]

### Step 4: Perform the division
To simplify the calculation:
\[ n = \frac{9.6}{1.6} \times \frac{10^{-10}}{10^{-19}} \]

Calculating \( \frac{9.6}{1.6} \):
\[ \frac{9.6}{1.6} = 6 \]

Now, for the powers of ten:
\[ \frac{10^{-10}}{10^{-19}} = 10^{-10 + 19} = 10^{9} \]

Combining these results:
\[ n = 6 \times 10^{9} \]

### Step 5: Conclusion
The number of excess electrons on the body is:
\[ n = 6 \times 10^{9} \]